title: When a neutral star with a magnetic field collapses to form a black hole, what happens to the magnetic field?

text: By the no-hair theorem, black holes are only characterized by mass, charge and angular momentum. If the star is neutral, the black hole will have only mass and angular momentum - and therefore it cannot have a magnetic dipole field. Where did it go? * * * These three questions are similar but I think the answers will be different for each one: > What happens to an embedded magnetic field when a black hole is formed from > rotating charged dust? It seems to me a rotating charged black hole must > have a dipole magnetic field. But the strength of the dipole field seems > like an extra parameter that black holes are forbidden by the no-hair > theorem. > > If a magnetic monopole falls into a schwarzchild black hole, what happens to > the magnetic field? Here there would be only radial magnetic field lines > leaving from the event horizon to infinity. So if magnetic charge is counted > as charge this should be no problem. But if the black hole were rotating > wouldn't that produce an electric dipole field? > > When a neutral star with a magnetic field collapses to form a black hole, > what happens to the magnetic field? Here there is no charge so how can there > be a magnetic field associated with a black hole? That would definitely > violate the no-hair theorem.


title: Rotating hoop in Relativity

text: What does a rotating hoop, with each point moving at a velocity close to the speed of light, appear like with respect from a stationary observers perspective. For example how does the shape of the hoop change? (Note, I'm not intending to ask about optical effects, but rather what physically happens, analogous to length contraction of a moving train.)


title: If a magnetic monopole falls into a schwarzchild black hole, what happens to the magnetic field?

text: By the no-hair theorem, black holes can only have mass, charge and angular momentum. Does "charge" include "magnetic charge" (such as from a magnetic monopole)? Can black holes have magnetic charge in addition to electric charge? [By the way, I believe theory says magnetic monopoles have to exist, the reason why we haven't discovered any is because inflation diluted them to such an extent that there are none or only a few in our Hubble volume.] * * * These three questions are similar but I think the answers will be different for each one: > What happens to an embedded magnetic field when a black hole is formed from > rotating charged dust? It seems to me a rotating charged black hole must > have a dipole magnetic field. But the strength of the dipole field seems > like an extra parameter that black holes are forbidden by the no-hair > theorem. > > If a magnetic monopole falls into a schwarzchild black hole, what happens to > the magnetic field? Here there would be only radial magnetic field lines > leaving from the event horizon to infinity. So if magnetic charge is counted > as charge this should be no problem. But if the black hole were rotating > wouldn't that produce an electric dipole field? > > When a neutral star with a magnetic field collapses to form a black hole, > what happens to the magnetic field? Here there is no charge so how can there > be a magnetic field associated with a black hole? That would definitely > violate the no-hair theorem.


title: Classical approach to Schwarzschild radius

text: The Schwarzschild radius from general relativity is given to be $r = \frac{2GM}{c^2}$. One can obtain the same answer using classical calculations. That is, the escape velocity of a particle is given by $v = \sqrt\frac{2GM}{r}$, which can be arranged to give $r = \frac{2GM}{v^2}$, which can be interpreted as the maximum radius for which a particle travelling at velocity $v$ cannot escape. By treating light as simply a particle travelling at velocity $c$ and substituting in the above equation, one arrives at the Schwarzschild radius. Is it just a coincidence that the classical approach gives the same result as the general relativity result, or is there some merit to the classical approach?


title: Differences the nonlinerarties

text: I want to comparison between oscillons based on non-linearities. Can someone elaborate it with the reason behind it : > When the sinusoidal vibrations are of the correct amplitude and frequency > and the layer of sufficient thickness, a localized wave, referred to as an > oscillon. > > Astonishingly, oscillons of opposite phase will attract over short distances > and form 'bonded' pairs. Oscillons of like phase repel. Oscillons have been > observed forming 'molecule' like structures and long chains. In comparison, > solitons do not form bound states. Reference: Wiki


title: How do I rearrange dE/dt to find an electron's 'half-life' due to synchrotron radiation?

text: I know that $-\frac{\mathrm{d}E}{\mathrm{d}t} \propto E^2$ for an electron losing energy to synchrotron radiation, but I can't find how to arrange this to give the time it would take for the electron to lose half of its original energy. How would I go about working that out?


title: Hydrogen 2P Probability Density Question

text: I'd like to calculate the probability density for Hydrogen in the $|2,1,1\rangle$ and $|2,1,-1\rangle$ states. There is an $\exp(\pm i\phi)$ term attached to the wave function for these states. It seems to me that $|\Psi|^2$ in this case would be the same for $|2,1,1\rangle$ and $|2,1,-1\rangle$ since $|\exp(i\phi)| = 1$ with the same being true for $|\exp(-i\phi)|$. Where am I going wrong here? Also, since I'm working in spherical coordinates the PD should be $r^2|\Psi|^2$, right (this will result in those classic energy orbital diagram functions)?


title: Effective mass of a black hole?

text: Suppose a black hole forms from a given mass of particles such as the core of a star going supernova. The black hole formed will have an effective mass due to the curvature of space time induced. Such a mass is presumably the inferred mass deduced from the effect of the black hole on the motion of nearby bodies. How does this effective mass compare with the original mass of particles all of which ended up "in the black hole"? Is the effective mass less greater or the same as the formation mass?


title: How do they draw collision pictures in Atlas?

text: Is the picture below a simulation? How to they draw these pictures? The picture is from here. ![enter image description here](http://i.stack.imgur.com/HUz5T.png)


title: I want to charge 48V 108Ah battery from 48V 80Watt solar panel. Can anyone write that how much time will take this battery to fully charge?

text: > **Possible Duplicate:**   >  Charging 12V 150Ah battery I want to charge 48V 108Ah battery from 48V 80 Watt solar panel. Can anyone write that how much time will take this battery to fully charge?


title: Exertion from swinging on a playground swing

text: I've read about how by tilting one's body one changes one's center of mass while swinging on a playground swing, and thereby increases the energy of the swing. But I would like to get a better sense of why one can get into a swing of ~1.5 meters above the ground on the back and front peaks of the swing (elevating an adult body weight that height each time), and do that repeatedly for, say, 10 minutes, and yet not at all feel fatigued--whereas if you were trying to jump up from the ground to that height you would be fatigued after just a few jumps. I get the sense that the answer is related to the idea that you are "loading" the swing gradually with potential energy on each swing, and that each iteration of that requires only a little effort, but I'm still sort of surprised at how much sustained energy you can generate with so little feeling of exertion (it feels like one can keep swinging high with little effort for an hour, easily), and I thought there might be some subtleties to this that I don't understand.


title: Molecular formula of a compund

text: I have no idea on how to get information out of this one. > A compound contains only hydrogen and nitrogen. Nitrogen makes up for 87.4% > of the mass. A sample of this have a density of 0.977 g/L at 740 torr and > 100 C. What is the molecular formula of the compound? The best I could think of was to put it in $PV=nRT$, so $n=PV/RT$. But since there is no defined volume I can't put in anything for $V$.


title: Why is the observed signal the convolution of the true signal with the instrumental function?

text: Imagine we are observing a star. The light coming from a star enters an optical instrument that will give us some observed data, such as the spectrum of light say. What we observe is not the true signal coming from the star but the signal after it has been affected by the optical instrument (because the instrument is not perfect, no instrument is) The true signal, call it T(x) is related to the instrument function, call it I(x), and the observed signal, call it O(y) through the following relation $O(y)=\int T(x) I(y-x) dx$ This is nothing but the definition of a convolution of 2 functions. My question is, why those 3 functions are related in that particular way, I mean can we prove that the relation between them must be the convolution relation?


title: Phase shifting using the Hilbert transform

text: I am still struggling to understand how the phase shift of a complex signal works. Today I stumbled over the Hilbert transform and heared that it is possible to phase modulate a signal $f(t)$ calculating its conjugate using this transformation and then combining the input signal and the conjugate trace, modified by a specified phase angle. Unfortunately I have no clue how this works. Can somebody help me?


title: Can acceleration be achieved without reaction mass?

text: In a previous question, I asked whether a flashlight can accelerate me. The answer is yes. This has led me to wonder, this is inferior to all other known propulsion methods in all aspects except one: Shooting light (photons) accelerates the shooter without ejecting any mass. This means we can space travel forever, assuming we have enough electricity. **Are there any other ways to accelerate without losing mass?** Note that there are lots of way to do it with external forces like laser propulsion, but I am only interested in doing it without those. e.g. consider a spacecraft swimming in the void trying to accelerate.


title: Why do excitonic absorptions have small bandwidth?

text: Below is an image of the optical density (proportional to the absorption coefficient) of KBr crystal at low temperature. Indicated at 6.6 ev and 7.7 eV are the absorption by excitons. As you can see, it has a small width. Can you explain why? ![enter image description here](http://i.stack.imgur.com/NQgRN.jpg) Source:Theory of Excitons, Robert S Knox, 1954


title: How should I understand the Hilbert space of field theory on non-commutative spaces?

text: I have a naive question about quantum field theory on non-commutative spaces. I apologize if my question is somewhat vague. Also, I have a weak mathematical background, and I apologize if my question is mathematically unsound. To start with, let us consider a real scalar field theory defined on a spatial lattice (the time direction is continuous). Each spatial lattice point $x$ is assigned a pair of conjugate operators $\phi(x)$ and $\pi(x)$, and a Hilbert space $\mathcal{H}_x$ on which $\phi(x)$ and $\pi(x)$ act. The Hilbert space for the entire theory can be thought of as the tensor product $\otimes_x\mathcal{H}_x$. I have been reading the pedagogical review by Richard Szabo about quantum field theory on non-commutative space. It seems to me that the way to define a field theory on non-commutative space is simply replacing every product by a star product in the Euclidean action. Similar to a conventional field theory, we integrate over all possible configurations in the path integral. In some sense, a quantum field theory on a non-commutative space is simply a non-local field theory on a conventional space. My question is, is it possible to find a Hamiltonian for quantum field theory on non-commutative space? I expect it is not going to be easy as the time direction is also non-local. If this is indeed possible, how should I think of the Hilbert space of such a theory? Thank you, Isidore


title: How must you spin the ball to make it alternate between 2 positions?

text: ![enter image description here](http://i.stack.imgur.com/y6JZ2.jpg) Assume any parameters you may need. Thanks in advance.


title: What is the limit of vanishing density?

text: I've been asked to examine the limit of vanishing density for the virial equation of state derivation of $\left(\frac{\partial U}{\partial V}\right)_T$ and quite frankly, I have no idea what this is and a Google search doesn't seem to net anything extremely helpful. Assuming density can be isolated in my derivation above, am I just taking the limit as $\rho \rightarrow 0$ ?


title: why does the CMB change so slowly

text: If anisotropies of the CMB originated from "quantum fluctuations of matter in a very tiny space that expanded to the size of the observable universe we see today" (quote from Wikipedia) would they represent a cross section through some feature that is roughly spherical and if such a feature could be considered to be one light year across ( I appreciate that is a tricky statement) it should change dramatically in appearance over a year.


title: How does an optic-mechanical laser read and send binary bytes to a CPU?

text: Thid greatly concerns physics, since a more refined version of my title will be rehearsed below: How is the physical structure of the mechanical eye use a laser to read binary bits held on an optical track that is basically smaller than one nano meter in size? how does the laser do this?


title: Life time of a wave

text: Let us consider, we have guessed a potential for a wave like non linear, which is propagating through space. We guess a Lagrangian for the wave $$L= \int r^{d-1} dr \left[\frac{1}{2}\dot \phi^2 -\frac{1}{2} \left(\frac{\partial \phi}{ \partial r}\right)^2- V \right]$$ The lagtrangian is due to Minkowski- space time dimensions. IF we know the total energy from the wave equation of the lagrangian then how can we get the decay rate of the wave?


title: Can a black hole bounce?

text: Is there a limit to the amount of matter that a black hole can accrete per second and if so could a certain sized black hole bounce off a dense enough surface?


title: What is the spatial mode of light or the spatial mode of a massive particle?

text: I'm extremely confused by what physicists mean by the spatial mode of light. I am also equally if not more confused by what the spatial mode of a massive particle is. Can anyone help me out by providing an explanation? (I'm also a visual learner, so diagrams will help) Spatial mode of light makes no sense to me because I don't understand what its referring to! I'm thinking that the spatial mode of a massive particle is like the eigenstate of an atom. At every energy level, there is a corresponding eigen state and this is the atom's spatial distribution. I'm guessing that taking a particle in general also has eigen states, and to distinguish them from atoms, they call them spatial modes? I'm reading this paper: > Heaney, Libby. Teleportation of a quantum state of a spatial mode with a > single massive particle. Proceedings of the 5th Conference on Theory of > Quantum Computation, Communication and Cryptography. _Lect. Notes Comput. > Sc._ **6519** pp. 175-186 (2011). doi:10.1007/978-3-642-18073-6_15, > arXiv:1011.3743 [quant-ph].


title: Connecting 4-velocity to equation for adding velocities

text: Is there a way to connect 4-velocity to equations for adding speeds? I know 4-velocity $U^\mu$ is derived like this: * * * \begin{equation} \begin{split} P^\mu &= m U^\mu \Longrightarrow U^\mu = P^\mu \frac{1}{m} = \begin{bmatrix} p_x\\\ p_y\\\ p_z\\\ \frac{W}{c} \end{bmatrix} \frac{1}{m} = \begin{bmatrix} \frac{mv_x \gamma(v)}{m}\\\ \frac{mv_y \gamma(v)}{m}\\\ \frac{mv_z \gamma(v)}{m}\\\ \frac{mc^2 \gamma(v)}{c m}\\\ \end{bmatrix} = \begin{bmatrix} v_x \gamma(v)\\\ v_y \gamma(v)\\\ v_z \gamma(v)\\\ c \gamma(v)\\\ \end{bmatrix} \end{split} \end{equation} Or like this: \begin{equation} \begin{split} U^\mu = \frac{d X^\mu}{d \tau} = \frac{d}{dt}X^\mu \gamma(v)= \frac{d}{dt} \begin{bmatrix} d x\\\ d y\\\ d z \\\ c d t \end{bmatrix} \gamma(v) = \begin{bmatrix} v_x\gamma(v)\\\ v_y\gamma(v)\\\ v_z\gamma(v)\\\ c \gamma(v) \end{bmatrix} \end{split} \end{equation} * * * And i know how to derive Lorentz transformations for velocities $\perp$ to relative velocity $u$ (which is in direction of $x$, $x'$ axis) and $\parallel$ to $u$. It goes like this: * * * **a.) $\parallel$ to $u$:** \begin{equation} \begin{split} v_y' &= \frac{dy'}{dt'}=\frac{d y}{\gamma \left(d t - d x \frac{u}{c^2} \right)} = \\\ &= \frac{\frac{dy}{dt}}{\gamma \left(\frac{dt}{dt} - \frac{dx}{dt} \frac{u}{c^2} \right)}\\\ &\boxed{v_y' = \frac{v_y}{\gamma \left(1 - v_x \frac{u}{c^2} \right)}} \end{split} \end{equation} **b.) $\perp$ to $u$:** \begin{equation} \begin{split} v_x' &= \frac{dx'}{dt'}=\frac{\gamma (d x - u d t)}{\gamma \left(d t - d x \frac{u}{c^2} \right)} = \\\ &= \frac{d x - u d t}{d t - d x \frac{u}{c^2}} = \frac{\frac{d x}{d t} - u \frac{d t}{d t}}{\frac{d t}{d t} - \frac{d x}{d t} \frac{u}{c^2}}\\\ &\boxed{v_x' = \frac{v_x - u}{1- v_x \frac{u}{c^2}}} \end{split} \end{equation} * * * **QUESTION:** Where is the connection among 4-velocity and equations derived under **a.)** and **b.)**? How can i show the connection?


title: Why is the diffraction pattern for an annular aperture the difference of the two Bessel functions?

text: Inspired by this question, the pattern for the annular intensity is given by the square of the difference of the two Bessel functions. I would have thought the sum was more appropriate, could someone explain why not?


title: Questions about the speed of light and the extent of the universe

text: What is the reason that speed of light is the maximum speed in the universe? Why there is no speed swifter than light? Or is it just we haven't found yet? A similar question is like this: why the light speed in vacuum has to be 299,792,458 m/s? Why couldn't it be faster? Who or what is controlling this speed in vacuum? Who is stopping it from being faster? Another question confusing me is this, if light from a far away Galaxy travels to us and we see the stars tonight, couldn't it be fully possible that at this time, they actually are already dead? Which means by modern scientific methods, there is absolutely no way to know what is really happening out there, all we know is just what was there, right? So our knowledge is going to be forever limited unless we have something that can travel much faster than light?


title: Do we reside in any particular dimension(s)?

text: In other words does it make sense to say that we live or exist in dimension _x_? Or do dimensions not apply to ~~reality~~ the universe its self?


title: Infinitesimal transformations and Poisson bracket for Dirac spinors

text: I apologize for the cumbersome calculations. Let's have $\Psi$, $i\Psi^{\dagger}$, which are canonical coordinate and impulse in space of solutions of Dirac equation. It can be showed that they have infinitesimal transformations $$ \delta \Psi = \frac{1}{2}\omega^{\mu \nu}\eta_{\mu \nu}\Psi , \quad i\delta \Psi^{\dagger} = -\frac{i\omega^{\mu \nu}}{2}\Psi^{+}\gamma^{0}\eta_{\mu \nu}\gamma^{0}, \quad \eta_{\mu \nu} = -\frac{1}{4}(\gamma_{\mu}\gamma_{\nu} - \gamma_{\nu}\gamma_{\mu}), \qquad (.1) $$ and $\omega^{\mu \nu}$ are local coordinates of the Lorentz group in bispinor representation. I wanted to use Poisson's (i.e., introducing Poisson's bracket with all convenient consequences) formalism for Dirac equation. So after introducing Poisson's brackets $$ [A, B]_{P} = \frac{\partial A}{\partial \Psi}\frac{\partial B}{i\partial \Psi^{\dagger}} - \frac{\partial A}{i\partial \Psi^{\dagger}}\frac{\partial B}{\partial \Psi} $$ I also decided to introduce generating function for canonical transformations (I have problem with them; see the question). For function $F(\Psi , i\Psi^{+}{'})$ the canonical equations are following: $$ \Psi {'} = \frac{\partial F}{i\partial \Psi^{\dagger}{'}}, \quad i \Psi^{\dagger} = \frac{\partial F}{\partial \Psi}. $$ So for infinitesimal transformations $$ F = \Psi i\Psi^{\dagger}{'} + G(\Psi , i\Psi^{\dagger}{'}), $$ where $G$ is called generator, I got $$ \Psi{'} = \Psi + \frac{\partial G}{i\partial \Psi^{\dagger}{'}} \approx \Psi + \frac{\partial G}{i\partial \Psi^{\dagger}}, \quad i\Psi^{+} = i\Psi^{\dagger}{'} +\frac{\partial G}{\partial \Psi} \Rightarrow $$ $$ \delta \Psi = \frac{\partial G}{i\partial \Psi^{+}}, \quad i\delta \Psi^{\dagger} = -\frac{\partial G}{\partial \Psi} \Rightarrow $$ $$ \delta \Psi = [\Psi , G]_{P}, \quad i\delta \Psi^{\dagger} = [i\Psi^{\dagger}, G]_{P}. \qquad (.2) $$ As result I can get the generator for $(.1)$ by using $(.2)$. For $\delta \Psi$, $$ \frac{\partial G}{i\partial \Psi^{\dagger}} = \frac{1}{2}\omega^{\mu \nu}\eta_{\mu \nu}\Psi, \qquad (.3) $$ for $i\delta \Psi^{\dagger}$, $$ \frac{\partial G}{\partial \Psi} = -\frac{i\omega^{\mu \nu}}{2}\Psi^{\dagger}\gamma^{0}\eta_{\mu \nu}\gamma^{0}. \qquad (.4) $$ Then I expected that the density of the generators of the Lorentz group in bispinor case, which has the expression $$ i\omega\Psi^{\dagger}\eta_{\mu \nu}\Psi , $$ can be naturally interpreted as the generator of infinitesimal transformations. So by substituning it into $(.2)$ I got $$ \delta \Psi = \frac{1}{2}\omega^{\mu \nu}\eta_{\mu \nu}\Psi , \quad i\delta\Psi^{\dagger} \neq -\frac{i\omega^{\mu \nu}}{2}\Psi^{\dagger}\gamma^{0}\eta_{\mu \nu}\gamma^{0} , $$ which contradicts with $(.3), (.4)$. Also, it seems that system $(.3), (.4)$ doesn't have solution. Where is the mistake? **An addition.** My attempt to solve $(.3), (.4)$. From $(.3)$ I can get $$ G = \frac{i\omega^{\mu \nu}}{2}\Psi^{\dagger}\eta_{\mu \nu}\Psi + G_{1}(\Psi) $$ and by substituting it in $(.4)$ it follows that $$ -\frac{i\omega^{\mu \nu}}{2}\Psi^{\dagger}\eta_{\mu \nu} - \partial_{\Psi}G_{1} = -\frac{i\omega^{\mu \nu}}{2}\Psi^{\dagger}\gamma_{0}\eta_{\mu \nu}\gamma_{0}. $$ It is possible to transform the right part of this expression by using commutator $$ [\gamma_{0}, \eta_{\mu \nu}] = \frac{1}{2}\left( g_{0 \nu}\gamma_{\mu} - g_{0\mu}\gamma_{\nu}\right): $$ $$ -\frac{i\omega^{\mu \nu}}{2}\Psi^{\dagger}\eta_{\mu \nu} - \partial_{\Psi}G_{1} = -\frac{i\omega^{\mu \nu}}{2}\Psi^{\dagger}\eta_{\mu \nu} - i\omega^{\mu 0}\gamma_{\mu}, $$ so $$ \partial_{\Psi}G_{1}(\Psi) = i\omega^{\mu 0}\Psi^{\dagger}\gamma_{\mu}, $$ which leads to the problems.


title: do lenses with curved focal planes exist

text: I know about spherical, aspherical, cylindrical lenses, but are there lenses that could have a curved focal plane? for example, the retina of the eye is curved, and still we see sharp images of distant objects. In a recent problem I studied, I wanted to have a lens that would transform a flat object (a book cover, for example) into a curved image. That is, each point of my book cover would be imaged correctly (i.e. the image would be sharp enough) by my lens - only, on a curved screen, like a spherical screen for example. Would there be a specific form of lens that could do exactly this, the same way that aspheric lenses do "perfect" images of distant objects on flat screens, better than any spherical lens? I am asking this because, in my application, the screen will need to be _strongly_ curved, and I still want the best possible stigmatism in these conditions, without reducing the aperture too much...


title: $\mathcal{N}=4$ SUSY in $d=3$ versus $\mathcal{N}=2$ in $d=4$

text: Which is the field content of the hypermultiplet and the vector multiplet in $\mathcal{N}=4 \ d=3$ Supersymmmetry? Is it correct to state that $\mathcal{N}=4$ in $d=3$ has $8$ supercharges, (since there are $4$ minimum dimension spinors, and the lowest dimensional representation of $SO(1,2)$ has real dimension 2), is completely equivalent to $\mathcal{N}=2$ in $d=4$ (where I have $2$ Weyl spinors of $SO(1,3)$ each of real dimension $4$), which also has $8$ supercharges, and therefore the multiplets in those two cases are completely identical?


title: Rigged Hilbert space and QM

text: Are there any comprehensive texts that discuss QM using the notion of rigged Hilbert spaces? It would be nice if there were a text that went through the standard QM examples using this structure.


title: Relation between electric charge and gauge parameter of the moduli space of monopoles

text: I am studying about the moduli space of a 2 monopole system from Harvey's notes, and Manton's paper. In both of these, (Harvey section 6.2), after constructing the Lagrangian for a two dyons system, the author replaces the electric charge $e$ with $\dot{\chi}$. $$e \to \dot{\chi}$$ to obtain the the equation of motion is geodesic form, from which the Taub-NUT metric can be seen. Why is this identification made? Why does the rate of change of the gauge parameter, give the electric charge?


title: Bound States in a Double Delta Function Potential

text: Let $V(x) = −u \delta(x) - v \delta(x − a)$ where $u, v > 0$ correspond to a potential with two $\delta$ wells. Let $v > u$. If $a$ is very large, there is certainly a bound state: the particle sits in the $\delta$-well. As $a$ decreases to a certain critical value, the bound state disappears. I need help finding that value. My idea was: Before the bound state disappears, its energy approaches $0$. I'm trying to assume that the energy $E$ is a very small negative number, solve the Schrodinger equation, and find the suitable value of $a$, but I'm having trouble doing this. Would someone be able to help me with this problem?


title: How and under what principle are measurements made at quantum level?

text: There's a lot of news about amazing quantum phenomena, but even without the expert knowledge I would still like to know how it is done and think about the possibility of errors in measurements. How, in other words using what physical method can quantum level measurements be made? (Basic enough so most people can understand.) And using what scientific principals is this method based on?


title: Tidal force when planets and smaller objects collide

text: There are lots of animations on the Web of planet collisions. In most, the planets maintain their (almost perfectly) spherical shape and their surface features right up to the point of impact. In some, the surface of one or both planets begins breaking up shortly before impact. This is due to **tidal force**, the differential between the near and far side of the object being acted upon by gravity. According to Wikipedia, > the Roche limit is the distance from a planet at which tidal effects would > cause an object to disintegrate because the differential force of gravity > from the planet overcomes the attraction of the parts of the object for one > another. In this **National Geographic video**, not only does the larger planet's crust begin to break apart seconds before impact, it even appears to bulge outward (taking on an **ovoid** shape?) to meet its collision partner a fraction of a second before impact. (Shouldn't it be the smaller object that breaks apart first, as in Wikipedia's visualization of a body crossing the **Roche limit**?) The Roche limit applies only to > the distance within which a celestial body, held together only by its own > gravity, will disintegrate due to a second celestial body's tidal forces > exceeding the first body's gravitational self-attraction although > [s]ome real satellites, both natural and artificial, can orbit within their > Roche limits because they are held together by forces other than > gravitation. Jupiter's moon Metis and Saturn's moon Pan are examples of such > satellites, which hold together because of their tensile strength (that is, > they are solid and not easily pulled apart). In extreme cases, objects > resting on the surface of such a satellite could actually be lifted away by > tidal forces. A weaker satellite, such as a comet, could be broken up when > it passes within its Roche limit. Then again, > [i]t is also worth considering that the Roche limit is not the only factor > that causes comets to break apart. Splitting by thermal stress, internal gas > pressure and rotational splitting are a more likely way for a comet to split > under stress. We saw this happening in the spectacular pictures of comet Shoemaker-Levy disintegrating as it plunged into Jupiter. And now for the really stupid part of my question. **Why does the fracturing due to tidal effects apply only to celestial bodies and not to every macroscopic object?** What I'm asking is, if I hold a raw egg in each hand and move them towards each other, why does the mutual gravitational attraction and the front-back differential not make one or both eggshells fracture? Doubtless the answer to my question is already contained in the Wikipedia articles if only I read them right. Does it have to do with the fact that surface area does not grow at the same rate as volume increases? Is the ratio of tensile force to gravitational self-attraction much greater for small objects than for planet-sized ones? Or is my error even more elementary?


title: A James Clerk Maxwell Disproof

text: One of my favorite physicists to learn about was James Clerk Maxwell, for the fact that he unified the study of E&M in physics and he would often disprove theories that did not work as a Mathematician. I remember my physics professor mentioning a disproof Maxwell had done with what was then the current knowledge of how currents flowed or were held through capacitors... This is probably way off from what he actually did disprove since it has been over 5 years since I had been to this particular lecture but could anyone tell me or demonstrate the exact disproof by counterexample that Maxwell had done with capacitance?


title: What happens to ice cream when you stir it?

text: I hope this is the appropriate forum for my question. I also considered posting it in the chemistry forum. When I eat ice cream I often stir it into a texture similar to that of soft serve. During the process, the bowl in which the ice cream is kept, tends to become quite cold. Temperature measurements indicate that temperature of the ice cream increase in the stirring process, so it seems to be the case that the bowl gets cold as a result of heating the ice cream. I am however not quite sure about why the ice cream is heated. Could it simply be that stirring the ice cream constantly brings parts of lower temperature to the surface thus speeding up the heat transfer that would otherwise occur anyway? Thanks in advance!


Why must quantum logic gates be linear operators? I mean, is it just a consequence of quantum mechanics postulates?


title: Acceleration: A ball sliding down the inside of a semicircular bowl

text: Edit: To clarify, this is a homework question. But I couldn't care less about getting the answer to this specific question as it's not even assigned yet. It looks interesting and I want to understand the concepts behind it. Not understanding these things bothers me :p Here is the given question: The face of block **M** in the figure below is shaped like a semicircular bowl of radius **R**. A mass **m** is placed at the top-left corner of the bowl and then let go. Find the acceleration of block **M** relative to the surface it is sitting on when **m** is a distance of **0.8R** from the bottom of the bowl. There is no friction between **M** and **m** , or between **M** and the surface on which it sits. There is a diagram provided: ![Image](https://i.imgur.com/zDuzjzH.png) I define $cos(\theta) = \sqrt{1-0.2^2}$ , as if the ball is **0.8R** from the bottom it is **0.2R** from the top, then using the Pythagorean Identity to solve for $cos(\theta)$. It states the answer is $a_{block}=\frac{-mgcos(\theta)}{M}$ My answer was that $a_{block}=\frac{-mgsin(\theta)cos(\theta)}{M}$ I split the $F_g$ vector into its parallel and perpendicular components such that $F_{g\perp}=m_1gsin(\theta)$ The parallel component is irrelevant for this question. $F_N=F_{g\perp}=m_1gsin(\theta)$ Then finding the horizontal component of $F_N$ is simple. Drawing a triangle it is apparent that: $F_{Nx}=F_Ncos(\theta)$ $F_{Nx}=m_1gsin(\theta)cos(\theta)$ Since $a=\frac{F}{m}$, I get my equation: $a_{block}=\frac{m_1gsin(\theta)cos(\theta)}{M}$. Could anyone enlighten me on what my mistake is? I think I'm running into a similar issue in another problem involving a block sliding down a wedge that is free to move as well (literally this exact problem, but instead of a semicircular surface it's simply a wedge). Thanks in advance!


title: Simplest Hamiltonian for 2d wave equation with periodic boundary conditions

text: I want to use the 2d wave equation ($\frac{\partial^2u}{\partial t^2}=\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}$) with periodic boundary conditions as a simple toy model of a quantum mechanical system. A formulation in the form $i\hbar\\!\frac{\partial}{\partial t}\left|\psi\right\rangle=H\left|\psi\right\rangle$ with a suitable Hamiltonian $H$ in a suitable Hilbert space would be nice. For this I could use Dirac's trick of turning the second order in time Klein- Gordon-equation into the first order in time Dirac-equation. This will turn my second order equation in one real component into a first order equation in 4 complex components. I guess I won't get away with less than 2 complex components, but 4 components seem a bit excessive. Is there is a simple Hamiltonian that gets away with 2 complex components?


title: Are circularly defined {velocity, distance, and time} a problem in physics?

text: In order to measure velocity, one needs a calibrated measuring stick and clock. But in order to calibrate a measuring stick you need a calibrated clock and velocity. And in order to calibrate a clock you need a calibrated measuring stick and velocity. Thus velocity, distance, and time are all defined in terms of each other. Is this circularity a problem that needs to be addressed by a fundamental theory of the universe? And is it addressed by any theories on the market?


title: what is it called: box potential with one infinite wall

text: The finite square well and the infinite square well problem are well known, however is there a reason that there is almost no reference to the one sided infinite square well? > Consider a particle with mass $m$ moving in the one dimensional potential > $V(x)= \infty$ for $x<0$ , $V(x) = -V_{0}$ for $0\le x \le L$; $V(x) = 0$ > for $x>L$   >  i) Can you scale this problem so that all units drop out ?   >  ii) Can you find the boundstate eigenenergies and associated wavefunctions > as a function of the parameter $\lambda$?   >  iii) Can you find the free eigenstates which are characterized by the > eigenenergies $E\ge 0$? I searched Griffiths Quantum Mechanics, but it didn't have any clue to how to solve this. **Can anybody tell me the proper formal name, so I can look it up, or tell me a reason why none such does exist?**


title: What does an $n$-body system with constant $T$ and $U$ look like?

text: Can someone give an example of a system where the kinetic $T$ and potential $U$ energy are constant (but not zero)? Here's what I have in mind: Say you have $n-1$ satellites of negligible mass sharing the same eccentric elliptical orbit around a star (the $n^{th}$ body), and say that these satellites are always positioned and have velocity such that $\nabla U=0$ at all times in the orbit. (As usual in such a case, $U\sim -\sum^n_i \frac{1}{r_i}$ where $r_i$ is the distance of the $i^{th}$ satellite from the star.) This would mean that $U$ remains constant throughout the orbit, but that (given the eccentricity of the orbit) the $r_i$'s of each of the satellites are always changing. Since total energy is conserved, the very fact that $U$ is constant means that $T$ must also be constant even though all of the velocities of the individual satellites are always changing. So this hypothetical system would be one in which $T$ and $U$ are constant, right?


title: Friction between air and a tube

text: I would like to know how I could estimate the friction caused by air flowing at a speed of 1000 km/h in a tube. The tube could be made out of any material, which makes it possible to calculate, preferably plastics, steel or Teflon. Edit: The tube has a form of the Large Hadron Collider in Cern just with a circumference of 10000 km instead of 27 km.


title: How do you super impose two or more signals to occupy a fix area of space with the resultant summed wave?

text: Is it possible to super-impose two or more signals all sent from different directions as a standing wave with the resulting summed wave occupying a fix area of space that is also a complex area? Do you understand my question? It is not obvious probably what i am trying to say-feel free to ask for more of an explanation. These signals could be electro magnetic waves or micro waves designed to pass thru solid objects under normal circumstances but then excite the solid only when at a certain frequency - this excite frequency would come about when two or more signals interact within the solid.


title: Do we know how matter moves matter?

text: I was surprised when reading an apologetics book recently that attempted a rebuttal of the claim that "An immaterial mind cannot interact with the physical order." Here was the response: > How could a spiritual entity interact with the physical order? How could a > god, an immaterial mind, affect or move matter? If mind cannot interact with > matter, then a supernatural entity cannot create a natural or physical > world. > > Admittedly, we have no idea how mind can move matter. But how big a problem > is this? **It could be monumental if it were not for one thing: in the end, > we have no idea how _matter_ moves matter.** Despite what is sometimes said, > we do not actually experience physical causality in any deep way. We see > _that_ matter moves matter in some sense, but we do not see _why_ or _how_ > it happens. We see someone throw a pencil across the room: we can see the > hand grasp the pencil, we can see the arm move back, and we cna see the > pencil leave the hand and fly across the room. We do not, however, see the > causation. Hume was right on this point: all we have are laws _associating_ > causes with effects. Is this an accurate statement? I'm hoping that this is more of a physics question than a philosophical one. Perhaps the answer is as simple as to whether we understand how matter moves matter. Though, I'll grant that I can't tell if they are using "moves" in the billiard ball striking sense or in the sense of some philosophical first cause sense. All of their examples use a human choosing to do something rather than just discussing whether we know how a moving billiard ball moves one it strikes.


title: Braiding statistics of anyons from a Non-Abelian Chern-Simon theory

text: Given a 2+1D Abelian K matrix Chern-Simon theory (with multiplet of internal gauge field $a_I$) partition function: $$ Z=\exp\left[i\int\big( \frac{1}{4\pi} K_{IJ} a_I \wedge d a_J + a \wedge * j(\ell_m)+ a \wedge * j(\ell_n)\big)\right] $$ with anyons (Wilson lines) of $j(\ell_m)$ and $j(\ell_n)$. One can integrate out internal gauge field $a$ to get a Hopf term, which we interpret as the braiding statistics angle, i.e. the phase gained of the full wave function of the system when we do the full braiding between two anyons: $$ \exp\left[i\theta_{ab}\right]\equiv\exp\left[i 2 \pi\ell_{a,I}^{} K^{-1}_{IJ} \ell_{b,J}^{}\right] $$ see also this paper and this paper. I would like to know **the way(s)** to obtain **braiding statistics of anyons from a Non-Abelian Chern-Simon theory**? (generically, it should be a matrix.) How to obtain this braiding matrix from Non-Abelian Chern-Simon theory?


title: Getting back out of an Alcubierre warp bubble

text: Does the theory on paper provide a way for hypothetical travelers to get back out of the bubble that has gotten them close to their distant destination by compressing all the space in front of them and expanding the space behind it? I was picturing space as a sheet of rubber and my warp bubble as the space of rubber under my finger as I press my finger down and drag the 'space' under my finger to where it's near a distant part of the sheet. But despite the fact that I'm now closer to the distant location as measured if you can 'jump over' the compressed rubber, unless there really is a way to 'jump over,' you still have the same amount of rubber between you and the destination.


title: What does "tagging" mean in experimental high energy physics?

text: Could someone explain in details the meaning of the terminology "tagging" in experimental high energy physics and how is it used in the analysis?


title: In dimensional analysis, why the dimensionless constant is usually of order 1?

text: Usually in all discussions and arguments of scaling or solving problems using dimensional analysis, the dimensionless constant is indeterminate but it is usually assumed that it is of order 1.   1. What does "of order 1" mean? 0.1-10?   2. Is there any way, qualitative or quantitative, to see why the dimensionless constant is of order 1?   3. Are there exceptions to that? I mean cases where the dimensionless constant is very far from 1? Could you give some examples? Can such exceptions be figured out from dimensional analysis alone?


title: Do hot objects moving at relativistic speeds slow down as they emit radiation?

text: In an astrophysics class I learned about the Poynting-Robertson effect, by which grains of dust orbiting a star slow down and eventually fall into the star. Every source that I have been able to find on this subject explains it by saying that in the star's reference frame the dust mote emits more light in the direction it is moving due to relativistic beaming. In the dust mote's reference frame it emits radiation isotropically, but due to relativistic aberration it absorbs slightly more radiation on the front than the back. I understand this explanation, but it seems a bit unsatisfying. ![](http://i.stack.imgur.com/Y6teK.png) What about a hot object that is not orbiting a star? If I heated up a cannon ball and launched it out into deep space at a significant fraction of the speed of light, wouldn't it slow down over time due to relativistic beaming? **How does this look in the ball's frame of reference if it isn't absorbing radiation from a star?** If there were nothing else but myself and the cannonball in space and I launch the cannonball directly away from myself, what would this look like? In the ball's frame, I would appear to accelerate away as I absorb radiation emitted by the ball, but otherwise it emits isotropically. The ball and I appear to be accelerating away from each other in this frame. In my frame, I would expect to see redshifted blackbody radiation from the cannonball. If it is slowing down, the radiation should become bluer over time. I am also absorbing the momentum of that radiation so maybe it would just stay the same color. If I measured its temperature before launching it, I can infer that it must be emitting blueshifted blackbody radiation on the other side, slowing it down. It is not clear to me whether the cannonball is slowing down or accelerating away in this frame. I must be missing something here, can anyone help me out?


title: How do radio telescopes work?

text: If I search online for how radio telescopes work, the found articles talk about how RF is on the spectrum, etc, how the parabolic collector is the aperture which contributes to the sensitivity and reflects the signals into the detector at the focal point. Then they skip to the signal processing circuitry the leads to a rendered image. They also mention that the furthest nodes in a telescope array determine the virtual aperture of the array. There are a few parts I don't understand: How does the detector work? From my reading, it is merely an RF antenna. I can't think how you'd get but one pixel per "moment" of detection. That the telescope is positioned and begins listening, and as the earth turns one scan-line of image is captured. For high resolution 2D image this would take thousands of passes. This seems impractical as the earth is orbiting and time marches on, otherwise. Perhaps multiple telescopes each take a scan line and interlace the results ... but especially at such high resolutions, I can't see how you'd engineer the huge machines with such precision. Please explain this to me. Do I have the 1D scan-line-antenna idea wrong? Is it more like a 2D CCD sensor in a digital camera with the antenna just behind the focus of the dish? If so, I assume the sensor would have to be a 2D array of nanometer scale antennas? This may be clear in the explanation, but in layman's terns, how are do telescope arrays work together to create the virtual aperture? What is lost, if any between the virtual and a theoretical "real" aperture of equal size? (I consider this a physics question because understanding the answer to this real-world application will help correct whatever theoretical misconceptions I have about RF, antennas, and radio telescopes) Thanks!


title: What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?

text: I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean? More specifically,   * why is it that dot product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB \cos{\theta}$   * why is it that cross product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB \sin{\theta}$ To me, both these formulae seem to be arbitrarily defined (Although, I know that it definitely wouldn't be the case). If Cross product could be defined arbitrarily, why can't we define division of vectors? What's wrong with that? Why can't vectors be devided?


title: Delayed Phase Transition at Condensation of a Gas?

text: It is known that super heated liquids do exist, eg. when purified water is carefully heated above its boiling point. However I've never heard of subcooled gas having a temperature below its saturation temperature. Why is that?


Does the rotational speed of a planet consistently become faster and faster given that there are no conflicting events?


title: Is this process possible for L=0? $e^+e^- \to 2\eta_c$

text: For the following $$e^+ e^- \to \eta_c \eta_c$$ I think it violates parity conservation so it can't happen, but is there any other reason as to why it can't take place? Or is it actually possible?


title: How to calculate the moment of inertia of a solid cube

text: How do I calculate the `moment of inertia of a uniform solid cube about an axis passing through its center of mass?` I also wanted to know if the moment of inertia of a body is independent of its shape. Also, recently I read somewhere that the moment of inertia of a uniform solid cube is `minimum about an axis` passing through its `COM` because the mass is more concentrated at its center. Does the statement make any sense?


> In thermodynamics, the Helmholtz free energy is deemed as a thermodynamic > potential which calculates the “useful” work retrievable from a closed > thermodynamic system at a constant temperature and volume. For such a > system, the negative of the difference in the Helmholtz energy is equal to > the maximum amount of work extractable from a thermodynamic process in which > both temperature and volume are kept constant. In these conditions, it is > minimized and held constant at equilibrium. (citation) My questions are   1. How can one say that if we subtract "TS" from "U" then what we get is free energy? Why do we have to subtract "TS"? What if we subtract pV instead of "TS".   2. If the system is in constant temperature and Volume , then how it is possible to do work?   3. Is it the statement true for Ideal gas also. If it is true then a thermodynamic system(with ideal gas) at a constant temperature and volume is also at constant pressure. so it is at equilibrium. Does that mean for a ideal gas system free energy is always minimum?


title: Representations of Lie algebras in physics

text: Why is an invariant vector subspace sometimes called a representation? For example in Lie algebras, say su(3), the subspace characterized by the highest weight (1,0) is an irreducible representation of dimension 3 of su(3). However, a representation of a Lie algebra is a Lie algebra homomorphism from the algebra to a subspace of the so called general linear algebra of some vector space. Or in other words, the representation is a map that assigns elements of the algebra to elements of the set of linear endomorphisms of some vector space. In the previous example, the subspace (1,0) is a subspace in which the action of the endomorphisms maps its elements into themselves. So by the definition, the irreducible representation should be the mapping that associates the endomorphisms to the elements of the algebra and not the space in which they act.


title: Dependence of Friction on Area

text: Is friction really independent of area? The friction force, $f_s = \mu_s N$. The equation says that friction only depends on the normal force, which is $ N = W = mg$, and nature of sliding surface, due to $\mu_S$. Now, less inflated tires experiences more friction compared to well inflated tire. Can someone give clear explanation, why friction does not depend on area, as the textbooks says?


title: Friction force and contact area

text: It's usually stated that the friction force is independent of the area of contact (Amontons' Second Law). I've always thought that this shouldn't be true, because the atraction between molecules would be higher and there would be more peaks. I've read that this is important for rubber surfaces. Is it important for nonelastic materials, like wood? Are there any quantitave studies of this phenomenon?


title: Question about proper time in general relativity

text: I think I may have some fundamental misunderstanding about what $dt, dx$ are in general relativity. As I understand it, in special relativity, $ds^2=dt^2-dx^2$, we call this the length because it is a quantity that is invariant under Lorentz boosts. If a ball is moving in space and I want to calculate the $ds$ for the ball to travel from point A to point B, then $d\tau=ds$ (where $\tau$ is proper time) because according to the ball, $dx=0$, since point A and point B are at the same place in its own frame. Assuming this is correct, this is all fine with me. Now fast forward to general relativity. $ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}$...so if a ball is travelling in spacetime under whatever metric, then to me it would seem like, in the ball's frame, we should set $dx^i=0$, and then we get $ds^2=g_{00}d\tau^2$...however, from what I am told and from what I have read, $ds^2=d\tau^2$. When I look at the Schwarzschild metric, for example, $g_{00}$ doesn't appear to be 1 in a travelling ball's frame. What have I misunderstood about the interval $ds$?. Is it that $ds$ only purely has to do with geometry of spacetime, and doesn't quite represent the distance between events?


title: Impact of covering glass on lens performance

text: I've seen microscope lenses optimized for 0.17mm covering glass. I don't see what needs to be optimized here? As glass does not touch the lens (as in case of oil/water immersion) - it should just affect focal distance without introducing any aberrations. Is that correct, or covering glass will cause aberrations imbalance, and will require recalculating the lens? (I can probably only think of very slight chromatic aberration, but it's not important in my case) Same for water immersion: If we cover sample with 1mm of water, but water does not touch the lens, will it cause any additional aberrations and require recalculating the lens? Same for diffraction-limited laser focusing optics: I've seen some of them are optimized for laser output windows - what is the nature of this optimization?


title: De-excitation and vibrational frequency

text: By utilising energetic beams of particles it is possible to set atomic nuclei into vibration. For a certain nucleus the subsequent de-excitation results in the emission of photons of energy $1$ $MeV$. Use this information to make an estimate of the vibrational frequency of the nucleus, stating any assumptions that you make. Using $E=hf$ I can calculate the frequency of the energetic beams. However I don't get the vibrational frequency bit...


title: How are X-rays focused? Specifically in XRD. Well do they even focus X-rays in XRD?

text: I read in a government website that reflecting an x-ray from a parabolic mirror followed by a reflection from a hyperbolic mirror results in focusing the x-ray, but this was for astronomical purposes. I was wondering if in x-ray diffraction this same method is employed, or what method is employed.


title: What potential energy functions are mostly used in Schrodinger equation?

text: In the time-independent Schrodinger equation $$\left(-\frac{\hbar^2}{2m}\Delta+V(\mathbf{r})\right)\psi(\mathbf{r})=E\psi(\mathbf{r})$$ What functions $V(\mathbf{r})$ are mostly used in research (e.g. Constant potential, Inverse Power-Law Potentials, Finite square well and Infinite square well)? And who can give a brief history of different potential functions studied in Schrodinger equation? And can anyone explain to me what is 'Hartree Potential'?


title: Finding the electric field on a point (x,y,z) using Coulomb's Law

text: Using Gauss' Law, the answer is $$\frac{Q}{4 \pi \epsilon R^2}.$$ However if I were to do the integration using Coulomb's Law, I get $$ \int_0^{2\pi} \int_{0}^{\pi}\int_r^a \frac{\rho \sin\theta dR d\phi d\theta}{4 \pi \epsilon |a - r_0|^\frac{3}{2}} .$$ where $a$ is the radius of the point outside the sphere with a charged surface, and $r_0$ is the radius of the sphere. Which is the incorrect integral because it does not compute to the solution received using Gauss' Law. How do I correct this?


title: Interesting properties exhibited by particles at negative temperature

text: I recently read an article which claims that "engine can do more work at negative temperature". The article seemed to have used a lot of jargon and hence a tough read for an amateur physics enthusiast. Particles seem to behave strangely at "negative" temperatures and this new phenomenon seems promising. **What are interesting properties exhibited by particles at negative temperature in simple language?**


What is the difference between scale-free network and small-world network? I can't understand from the definitions around the web if they are both the same name for one thing. Do both follow a power-law distribution of the nodes degree? In particular is it true that scale-free networks are a subset of small-world networks?


title: What forms are theoretically predicted for orbitals or quarks in hadrons and of hadrons in tritium?

text: We all know very illustrative spatial representations of predicted electron orbitals in atoms which are essentially spatial plots of the solutions of wave equations. In all atoms the electrons occupy the positions around the nucleus, sometimes, spatially symmetric. But I wonder which form could take orbitals of three particles of nearly- similar mass, such as quarks in a hadron or hadrons in tritium nucleus? Seems there is no place in the center for one of them...


title: SU(2) yang-mills EOM

text: I'm just playing around tonight trying to better myself, but I'm having trouble with some indices on my yang-mills lagrangian. I have a gauge group $SU(2)$ and a field strength tensor $$ F_{ab}^{i}=\partial_{a}A^{i}_{b}-\partial_{b}A^{i}_{a}+\epsilon^{i}_{\,\,jk}A^{j}_{a}A^{k}_{b}$$ and a lagrangian $$\mathcal{L}=-\frac{1}{4}F_{ab}^{i}F_{i}^{ab}$$ I have at the end of the exercise that the correct EOM are $$\partial^{a}F_{ab}^{i}+\epsilon^{ij}_{\;\;\;k}A^{a}_{j}F^{k}_{ab}=0$$ I am getting the first term on the left, but the second term I am getting something slightly different, instead, when I hit the lagrangian with $\partial \mathcal{L}/\partial A_{a}^{i}$ I get a term $\epsilon^{i}_{\,\,jk} A_{b}^{k}F_{i}^{ab}$ which leaves a free $j$ index. Now I know summed indices don't matter and can change letters freely, but order and contraction does matter, now I'm not sure how to make it come out with matching indices. When I do $\partial_a \partial \mathcal{L}/\partial (\partial_{a}A_{b}^{i})$ I come out with the typical $\partial_a F^{ab}_{i}$ but my free index there is $i$, not $j$, and I can't get them to match for the life of me. Please help, Thanks.


title: Objects falling on Slopes

text: An object falls on a slope and then rebounces....and it is known it hits the slope again...how do I calculate it's second point of contact with the slope....how can a projectory equation be used in this case?


title: How much energy was consumed when we turn on/off light?

text: My parents told me to turn off the light when I am not using it. But I remember my physics teacher told me that the action of turning on/off a light can cause huge energy. I am wondering how much is that? Someone said the energy caused by this action are enough to keep the light on for 15 minutes. If we require a configuration here, let's assume we use a T8 light tube, with 220V voltage from the house and 30W of the tube.


title: If particles are excitations what are their fields?

text: After reading these :   1. http://www.symmetrymagazine.org/article/july-2013/real-talk-everything-is-made-of-fields   2. http://www.physicsforums.com/showthread.php?t=682522 It was clear to me that all particles are merely excitation in fields. But it caused a few questions   1. If electron is excitation in electron field, then how does it produce it's own field?    2. For whatever reason electron even after being an excitation produces an electric field, but why doesn't photon (or other such particles if there are) create any such field?   3. All these particles have mass and exert gravity how can they produce gravitational fields? The major question that partly summarises all three of them has to be " when particles are excitation in some field how do fields arise from them? "


title: Evaluate singularity in numerical iterative physical optics integral

text: My goal is to implement a code to numerically compute the radar cross section (RCS) of an open-ended PEC cavity by the approach of "iterative physical optics" [1]. The idea is to iteratively compute the current distribution on the PEC surface (to account for multiple scattering), from which the far field can finally be derived. In the approach, the cavity surface $S_c$ is discretized by flat (triangular or rectangular) facets (with a side length of 0.5 to 0.33 times the wavelength), and a constant current density $J(\vec{r}_c)$ is assumed per facet. The location of a cavity facet is given by $\vec{r}_c$. Now the central part of the IPO algorithm is the repeated evaluation of an integral of the form $$ \vec{J}_N(\vec{r}_c) = \ldots + 2\hat{n} \times -\\!\\!\\!\\!\\!\\!\int_{S_c} \vec{J}_{N-1}(\vec{r}_c') \times \nabla G_0(\vec{r}_c - \vec{r}_c') dS_c' $$ where $$ \nabla G_0(\vec{R}) = \hat{R} \left(jk + \frac{1}{R} \right) \frac{e^{-jkR}}{4\pi R} $$ is the gradient of the free space Green's function with $R = |\vec{R}|$ and $\hat{R} = \vec{R}/R$. My question is: **How can the principal value integral be implemented? How can the singularity in the integral (for $R = 0$) be handled?** Note that for the IPO approach, the integral is replaced by a sum over the cavity facets (assuming a constant current density per facet). The problem of computing the diagonal elements of the resulting matrix must come up repeatedly in similar algorithms. How is this typically handled? I have found approaches which replace the surface integral by a line integral along the triangle edges [2]. This would require to determine the fields at the mesh vertices also (and not only at the facet centroids), which apparently wasn't done by the original authors. What am I missing? Apparently the self- patch integral can also be solved analytically, but I would expect a much less efficient code. I am confused... Thanks for any pointers! * * * [1] Obelleiro-Basteiro, F., Rodriguez, J. L., & Burkholder, R. J. (1995). An Iterative Physical Optics Approach for Analyzing the Electromagnetic Scattering by Large Open-Ended Cavities. IEEE Transactions on Antennas and Propagation, 43(4), 356–361. [2] Graglia, R. D. (1993). On the numerical integration of the linear shape functions times the 3-D Green’s function or its gradient on a plane triangle. IEEE Transactions on Antennas and Propagation, 41(10), 1448–1455.


title: Smoothed particle hydrodynamics in cosmological N-body simulations

text: What is the role of smoothed particle hydrodynamics (SPH) in cosmological N-body simulations like the Millenium Run (performed with Gadget-2)?


title: What is the motivation for introducing "ontological state" in 't Hooft's deterministic quantum mechanics

text: I tried to read Prof. 't Hooft's new paper The Cellular Automaton Interpretation of Quantum Mechanics A View on the Quantum Nature of our Universe, Compulsory or Impossible? and encountered difficulty about the motivation for introducing ontological states and cogwheel models. Suppose quantum mechanics is deterministic, the probabilistic nature in the Born's rule must be an artifact. Namely the Born's rule somehow likes throwing a classical dice. The probability comes from our incomplete knowledge and limited computational power. In another paper, How a wave function can collapse without violating Schroedinger's equation, and how to understand Born's rule, it is stated that > According to our ontological theory of quantum mechanics, the probabilities > generated by Born’s rule, are to be interpreted exactly in the same terms. > If we do not know the initial state with inﬁnite accuracy then we won’t be > able to predict the ﬁnal state any better than that. I am fine with all that. However, in the "The Cellular Automaton Interpretation of Quantum Mechanics", if I understood correctly, Prof. 't Hooft constructed a series cogwheel models to show these deterministic models exhibit Schrodinger equation. My question is, what is the motivation for introducing ontological states and cogwheel model? Would the Schrodinger equation itself to be sufficient, since it is already deterministic anyway? If one wants to get rid of Bell's inequality, Schrodinger equation seems to be sufficient (Related post, Why was quantum mechanics regarded as a non-deterministic theory? ). And even tried to derive Born's rule? If one feels the Schrodinger equation is insufficient, _i.e._ there is something behind it, why the object behind Schrodinger equation is so essential? I think I missed some important aspect in his paper... (Presumably I did not read it carefully enough)


title: Making elementary guess regarding current in AC circuits

text: I was just studying the comparisons, between A.C, and D.C, and the effects they can produce in electrical circuits (viz, Joule-heating, Peltier-effect and Seebeck-effect in thermocouples, Electrolysis, Magnetic effect). I found from what is written in my textbook, that all of these effects could be produced by a purely D.C circuit, but a purely A.C circuit can produce only Joule-heating, and none of the others. So, I made some elementary guess, which, if correct, I think I could use to save time, in competitive-exams, based on multiple-choice questions: _Guess:_   * _Effects, that are directly, or inversely proportional to odd-powers of current through a circuit, are not exhibited in a purely AC circuit, for a complete cycle, and hence, forever._   * _Effects, that are directly, or inversely proportional to even-powers of current through a circuit, are not exhibited in a purely AC circuit, for a complete cycle, and hence, forever._ But I just found out, that in purely capacitive, and inductive AC circuits, no power is dissipated through the respective element, for a complete cycle, and thus, forever,and as well in A.C circuits containing all 3 elements in series- resistor, inductor, and capacitor, power-loss in circuit is zero for a complete cycle, if the current and voltage-drop throgh combination, differ by a phase angle of 90 degrees. The current through these circuits is called **wattless current**. Does the last paragraph oppose my guess?


title: Could dark matter be expanded atoms, and dark energy expanded radiation?

text: After watching Lawrence Krauss' lecture 'life, universe, and nothing', an interesting idea lighted up in my mind. Is it possible that dark matter is just spread out matter waves and dark energy extremely long wavelength light? matter -> expansion -> dark matter (delocalized matter waves/huge atoms) visible and xray radiation -> expansion -> invisible light with wavelength greater than the diameter of universe (perhaps the source of energy of the empty space?!!!!) so dark matter today may be what we will become in the future. and we are what dark matter was in the past. eternal expansion just spreads out everything but new stuff is created all the time. anyone living in such a universe at any point of time will see the universe almost as we see it today, expanding with a beginning.


title: Why do whips crack?

text: Whips have been discussed in a previous question last year. I wish to ask a further question on the subject. (I can not comment or reply to the previous question since I am a new member here and my score is too low.) The explanation why a whip cracks, given by the top rated answer to the aforementioned question, is similar to the one given in the Wikipedia article on whipcracking: The answer says that the momentum (wave) moving down the whip is concentrated to a gradually smaller part of the whip (at the end, the whiptail), thereby making the speed of the moving part higher to conserve momentum. m*v is constant, m (mass of the moving part of the whip) decreases and therefore v increases. This is how the high (supersonic) speed of the whip end is produced, according to this answer. The explanation given in the answer is, at least to me, similar to comparing the whip to the sliding hammer we use to remove the break pads (or ball bearings) in our cars. You set a weight in motion by pulling on it and and when it comes to a sudden stop at the end something happens. What happens in the sliding hammer is that the other end experiences a yank. But using the hammer, there is no "energy concentration" with e.g. supersonic speed like in the whip, involved. (To me the break pads would just be like the handle of the whip. The sliding weight of the sliding hammer would be like the wave travelling down the whip.) What I do not understand in this explanation is thus the following: In a whip, the momentum is moving down the whip, away from the person holding it. To neutralize this momentum (when the wave of the whip reaches the end) you would just need to pull on the whip's handle in the opposite direction. (force f during T (the period for the wavelength) f*t=momentum m*v). Nothing more would be needed to neutralize the momentum. I can not see how this answer explains the extremely high (supersonic) speed of the whip tail.


title: Frequency shift without affecting signal length

text: Non-physicist here. From what I've learned in university and what common sense says, a shift in frequency of a signal results in a change in its length in time. For example, if a sinusoid signal of frequency $f$ and length $t$ is transferred to frequency domain, it's $f$ divided by $2$, then converted back to time domain, the length of the signal would be $2t$. Correct me if I'm wrong! But this is quite intuitive. If you make a signal slower, it would take more time to finish and vice versa. This is a reason why I've been told it's impossible to change frequency of a streaming signal and output it with the same speed. For example, it would be impossible to take a man's speech and change it to sound like a woman without making it faster. Now I've had various observations:   * In Coursera, you can increase the speed of course lectures and the sound is also of course sped up. However, there is no rise in the pitch of the voice of the speaker. In fact, the speaker sounds very similar to the normal speed. How is it possible to change in speed of the signal didn't affect its frequency?   * My amplifier has a dial for shifting the pitch. So, while playing, you can here the output with a different pitch. Again, how is this possible? If the amplifier is rising the pitch, shouldn't its output be faster than its input? (i.e. a contradiction!) I'm suspecting some trick though, as the output sounds rather "artificial". It seems that it is somewhat possible to change the frequency of a signal without affecting its length. One (theoretical) way I can think of would be to understand the current "notes" playing (i.e. the different frequencies making the signal) in very small intervals, change the note and replay them for the duration of that interval. My question is, first if my understanding is at all correct. Either way, is there a mathematical way for changing the pitch of a signal without affecting its length in time? If not, how can they be doing it in practice?


title: Can somebody explain the graphical integration method in a better way?

text: After hours of research all what I can find is this: http://www.public.iastate.edu/~fanous/ce332/virtualwork/homepage.html can somebody explain this method in a better way. > If the moment diagram due the applied loads or the moment diagram due to the > virtual load is not continuous, one MUST divide the integration into > segments, each of which is continuous over the integration length.see this > example: The example is somehow hard to understand, Does anybody has a simpler example. I'v been trying to do this method in the conjugate beam method and then trying it with the virtual work method but the results are different. See this example: ![enter image description here](http://i.stack.imgur.com/ot0jD.png) Now assume that $w=50$ and $L=8$. According to the conjugate beam method, the deflection at the center will be -2666.66 but using the virtual concept it is: $\frac{2}{3} \times 400(8)(1.25) = 2666.66$ which is positive, why is this? Also even if I use this method to another load it still give me a different result.


title: In scattering, how does a particle 'know' which direction it is being illuminated from?

text: In scattering experiments, for example light scattering, the scattering strength from different sized particles is depicted as below. ![Scattering examples](http://i.stack.imgur.com/uoXQb.gif) What I can't understand is: how does a particle know which direction the light is coming from and therefore which direction to bias the scattering (as in the case of large particles)? For instance, if we are just thinking about the electron oscillations, don't they just occur perpendicular to the light source? So in my example below, I have a particle being illuminated from the left, and one from the right. If we were to look at JUST the electron oscillations inside particle, wouldn't they be doing the exact same thing? So how does the scattered wave seem to 'know' where 0 degrees is in relation to the incoming beam? For clarification I am not talking about the angular dependent interference due to Rayleigh or Mie scattering. I hope this makes sense. ![Enter image description here](http://i.stack.imgur.com/NNggh.png)


title: How to calculate electric force between two tubes?

text: Let's say the electric field due to a charged tube is $E$,length of the charged tube is $l$, radius is $r$ and the surface charge density is $\lambda$. I know that to calculate the electric force between two charged rods we use $\vec F=\lambda \times dl \times \vec E$ where $\lambda$ is linear charge density of the secon rod, $dl$ is an infinitesmal portion of the second rod and $\vec E$ is electric field due to the first rod. However, I don't know how to derive this equation to find the equation for calculating the electric force first tube exerts to the second tube. I am guessing it should be like that: $\vec F=\lambda \times \vec E \times d\theta dl$ where $\lambda$ is surface charge density of the second tube, $d\theta$ is the infinitesmal angle and $dl$ is the infinitesmal length of the second tube. I don't know whether it is correct or wrong.


title: Describing a circular current loop as delta functions

text: It would be really nice to see how Jackson got eqn 5.33 on his example problem for finding the vector potential of a circular current loop $$ J_{\phi}=I\sin\theta'\delta(\cos\theta')\frac{\delta(r'-a)}{a} $$ for describing this geometry: ![enter image description here](http://i.stack.imgur.com/myeLT.jpg) I've found a few 'explanations' googling, but I'm still confused on the origin of the $\sin\theta$ My best guess $$ \int \vec{J}\cdot\hat{n} \; d^3x=\int \vec{I}\cdot d\vec{l} \\\ \nabla_\phi \left ( \int \vec{J}\cdot\hat{n} \; d^3x=\int \vec{I}\cdot d\vec{l} \right) \\\ \frac{1}{\sin\theta} \frac{\partial}{\partial\phi} \int \vec{J}\cdot\hat{n} \; r^2 dr d\cos\theta d\phi = \frac{1}{\sin\theta} \frac{\partial}{\partial\phi} \int I a d\phi \\\ \frac{1}{\sin\theta} \int J_\phi r^2 dr d\cos\theta = \frac{1}{\sin\theta} I a \\\ \frac{1}{\sin\theta} \int A \delta(\cos\theta) \delta(r-a) r^2 dr d\cos\theta =\frac{1}{\sin\theta} I a \\\ Aa^2=Ia \\\ A=\frac{I}{a}\\\ \therefore J_\phi = I \delta(\cos\theta) \frac{\delta(r-a)}{a} $$ I know the $\sin\theta$ doesn't really matter.. because $$ \int \sin^2\theta \delta(\theta-\pi/2)d\theta=1 $$ but I'd still like to know where it comes from. **EDIT**   The explanation that "it doesn't matter, so lets include it" bothers me. There must be some place in the derivation he picks it up. What possible reason would there be for adding it in at the end? The change of variables [ref] doesn't work because $$ \delta(\cos\theta)=\frac{\delta(\theta-\pi/2)}{\sin\frac{\pi}{2}} $$ so you still end up with $$ \int \sin^2\theta \delta(\theta-\pi/2)d\theta $$ I also don't think that it comes out of the Jacobian. Because he later goes on to integrate over the solid angle $$ \int J r^2 d\Omega dr = \int J r^2 \sin\theta d\theta d\phi $$ which would, again, give something of the form $\sin^2\theta$ **EDIT**   Jackson's next step (Eqn. 5.35) $$ A_\phi(r,\theta)=\frac{\mu_0I}{4\pi a}\int r'^2dr'd\Omega' \frac{\sin\theta'\cos\phi'\delta(\cos \theta')\delta(r'-a)}{\left | \mathbf{x}-\mathbf{x'} \right |} \\\ \; \\\ \text{with } d\Omega' = d\cos\theta' d\phi = \sin\theta' d\theta' d\phi $$ I would agree that a $\sin \theta$ belongs in the formula if he only integrated over $d\theta$ not $\sin\theta d\theta$


title: Dependence of sign on operators in wave equation?

text: In the time-dependent Schrödinger equation, our teacher told us about energy and momentum operators. He just defined them, the equation was of the form $A\exp(i(kx-\omega t))$, if we take the equation of the form $A\exp(i(kx+\omega t))$ will those operators change? If so, how do we determine the operators for a wave?


title: Formation of atoms

text: If a Proton goes toward an Electron with a trajectory that forms a circular motion, these particles will form an atom ?


title: Work in circular motions

text: Suppose that a satellite circles around a planet that exerts $2000N$ of gravitational force on the satellite. I understand the fact that since the circular motion and the centripetal force are always perpendicular to each other, the work done by gravity is 0. However, the satellite is being moved from one point to another, so Intuitively I am thinking "there must be some work done to move the satellite from point A to point B". But besides the gravitational force, there is no force acting on the satellite. Can some one explain me the gap with my logic and intuition ?


title: How do objects outside a spacecraft fall "around" the earth?

text: Now I get what `microgravity` is, how spacecrafts (even moon) fall around the earth to keep up themselves in their orbits and other related concepts after reading this. The spacecrafts at certain heights will have to travel at as much as `17,500 miles per hour` to stay in their orbits. If they want to orbit at any lower altitudes, they may have to travel faster and at higher altitudes, they can afford to travel slower. When on `EVA's`, the astronauts will have to have their `jetpacks`/`MMUs`/`thrusters` on to stay afloat, closer to the spacecraft and do what they wanted to do. While all these things are understandable, objects outside of the spacecraft floating around is not so much. Shouldn't the objects, right after they are out of the spacecraft, decelerate and so enter the earth's atmosphere within seconds (knowing `micro-gravity` is still enough gravity to pull objects towards earth)? Obviously some of these observations are based on the movie: `Gravity`. The dead bodies floating around, one of the astronauts (Sandra) with no thrusters on drifts off of the spacecraft due to momentum - I can't seem to get my head around these things. Do these objects travel at enough speed to fall around the earth, _despite_ being out of the spacecraft which travels at a constant speed? Even though it's the `vacuum`, why does the `momentum` have so much effect? Surely `gravitional` force should be strong enough to pull objects towards earth almost as easily at those altitudes despite apparent lack of air resistance?


title: Protect drone from lightning

text: I am designing a dirigible, robotic drone. It is basically a polyurethane airship, approx 3.6 m length and 2.1 m diameter. I am worried about lightnings: as far as I know, a Faraday Cage should be able to protect its interior from external electrostatic fields. Now my question is: a lightning is much more likely to strike on a conductive material mid-air rather than on its surroundings, right? Now, even if the Faraday Cage could protect it from the electrostatic field, there should be a huge amount of energy released in the Faraday Cage due to the Joule effect of the lightning streaming through it, enough energy to melt the structure. So I was wondering: is there any other strategy to protect the drone? On example, could it be possible to cover it with some dielectric (is there anything stronger than air?) so that lightning would rather strike somewhere else?


title: Silicon/silicon dioxide interface

text: Suppose we have an interface of silicon/silicondioxide. If we shine light on the top surface electron-hole pairs are generated in silicon. since there is always a field directing from surface to bulk in silicon (taking n type silicon), electron moves to the bulk and hole moves to the interface states. Is there any change of holes being reached in silicon dioxide surface?


title: Physics of the Internet?

text: Is there a way to describe the Internet in terms of a physics theory, like how the atom is described by quantum mechanic? If there is, how is it described by this theory.


title: Application of Heisenberg's uncertainty principle

text: I've the following application of Heisenberg's uncertainty principle. If a beam of particles in localised in the $x$-direction by a long slit, what is the uncertainty in position? Firstly, I believe that uncertainty is equivalent to the standard deviation in this case, as I have seen the equation is written $\sigma_x \sigma_p \ge \frac{h}{4 \pi}$ and $\Delta x \Delta p \ge \frac{h}{4 \pi}$ (why is this swap allowable? Surely the uncertainty is the range of possible values it can take, whereas the SD is simply the _average_ deviation from the mean?). Now, the question: What is $\sigma_x$? Is it the width of the slit (because that is the range of (classically) allowed values of $x$*), or half-width of the slit (as the middle of the slit is assumed to be the average position, and the standard deviation measures the deviation from the average)? *I have a problem with those possible answers if one of them _is_ correct: particles really have a nonzero probability of existing in classically forbidden regions (i.e. inside the metal or wood that surrounds the slit), so why do we base the values of a quantum mechanical number ($\sigma_x$) on a value (the slit width, which is the classically allowed region) that is classical? Additionally, does the particle have a nonzero probability of existing everywhere? If so, and uncertainty takes the meaning I thought it did in the first paragraph, isn't the uncertainty infinite? I hope that badly written popularisations haven't misguided me too much.


title: Does the shielding around a solenoid actuator affect the force on the plunger?

text: I'm looking to minimize the weight of some solenoid actuators I want to build, so I'm trying to better understand the effects of the shielding / frame commonly found on solenoid actuators. My understanding is the force exerted on the plunger is essentially only dependent on the cross sectional area of the plunger, the permeability of the plunger, and the flux density within the plunger. If that is correct, then it seems that the shielding doesn't really affect the plunger, only the reluctance (and thus the inductance) of the overall system. If I were to remove the shielding, it seems that I could expect a very low inductance when there was no core, so I would have to be careful not to burn out my coil, but other than that it seems like the system should be largely unaffected. Am I understanding things correctly? * * * It seems like in practice there is a lot of effort taken to minimize the air gap in the system, and random forum posts state that if you don't do this your solenoid won't be as strong - however I have yet to see any math or reason to back this up or to explain how to figure out how much stronger one system is over another. I'd be very grateful if someone could help clear this up!


title: Energy required to reach 1 wavelength

text: I was curious if there was a forumla to find the energy required to reach 1 wavelength in a given substance. (or a vacumn if that's too hard). I am also wondering if this number can tell us anything about the way the wave acts? My knowledge of electromagnetic radiation is pretty small... Maybe these things don't really matter?


title: Was the universe a black hole at the beginning?

text: Big bang cosmology, as far as I understand it, says that the universe was super hot and super dense and super small. It looks like that all the current matter, seen and unseen, were compressed to infinitesimal distance, which means it was a black hole. 1- Is the big bang, and our universe expansion in this case, hence is nothing but a black evaporation via Hawking radiation? 2- Are we living inside that primordial black hole explosion?


title: What happens to sound waves?

text: I apologize if this is a naive question, but I never really learned about this. I'm curious as to what happens to sound waves after they are "used"? For example, if I say something to you verbally, then a sound wave is transmitted and picked up by your ears, but what happens to the wave after that? Does it float away into space? And if sound waves are never destroyed (not saying that is the case, but if it is), does this theoretically mean we can reproduce or attain all sound waves from the history of man, including every word ever spoken?


title: On Flatness problem, Inflation etc

text: I have a couple of naive questions from the topic of the title.   1. We know \begin{eqnarray} \Omega-1=\frac{k}{a^2H^2}-\frac{\Lambda}{3H^2} \end{eqnarray} Now I read that from the standard big bang (SBB) model $\frac{1}{aH}$ increases with time and in recent time $\Omega\approx 1$. So, $\Omega$ has to be fine tuned to stay close to 1. I guess its because as we go back in time $\frac{1}{aH}$ decreases in SBB, and for fixed $\Lambda$ this drives $\Omega$ away from 1. I guess that's o.k as $aH$ decreases faster than $H$ alone in the second term above. But why do we want $\Omega\approx 1$ in earlier times?  My confusion deepens after reading how inflation solves this problem. In "Inflation", it is argued that $\frac{1}{aH}$ decreases with time. So I thought to myself As before going back in time resulted in decrease in Hubble length (comoving), so in the above equation the 1st term was large that is effectively with non-zero $k$. But now as going back in time increases $\frac{1}{aH}$, the first term decreases and it acts as if $k$ is nearly zero which is the criterion for flat universe. So my confusion boils down to the question on Why do we want $\Omega\approx 1$ in earlier times? Also how does Inflationary era solve the whole flatness problem? What about when inflation ends and SBB begins? Moreover, the above equation is valid for every case (inflation and SBB). So, even if inflation kills the problem, SBB should revive it yielding non unity of $\Omega$ now!   1. Also I came to know that as long as $\dot{\phi}^2<V(\phi)$, inflation takes place and this is generally the case when potentials are flat enough (with $\phi$ of course). How to see that? Related to that, I learned in Hybrid Inflation, since $\phi$ is driven to zero for $\psi>1$ (Why??), the potential in $\psi$ direction is flat and satisfies slow-roll conditions, so that $\psi$ is considered inflation. How can we say potential in $\psi$ direction is flat?


title: Why does gravity need to be quantised?

text: The electroweak and strong forces seem to be completely different types of forces to gravity. The latter is geometric while the former are not (as far as I'm aware!). So why should they all be described in the same way? - Why are gravitons needed? Alternatively, I suppose my question is why a theory of everything has to be some form of quantum gravity. Is there a reason why a theory of everything requires gravity to be quantised? Is it possible for the quantum world and gravity to be described by some overarching theory which does not require gravity to be quantised? Or is there some reason why this is not the case?


title: References on the non-compositeness of the known elementary particles

text: What paper(s) or theory(s) describe or prove that the elementary particles that we have determined today cannot be made up of smaller more fundamental particles?


title: Consciousness and quantum mechanics

text: Quantum mechanics is very mysterious. Consciousness is often brought into play to explain quantum phenomena. Is this only a matter of convenience, or is consciousness inherent to interpreting quantum mechanics? What is the role of the mind in affecting the wave function? What counts as a conscious being? Is the wave function all in our minds, and can we change it just with our thoughts?


title: Has Cosmological Natural Selection been disproved?

text: I've been reading Lee Smolin's Life of the Cosmos. Great book and it makes a lot of sense that the conditions in black holes are the same as conditions at the big bang. Question is, has his theory about Cosmological Natural Selection been disproved as the wikipedia article states?


title: CMB curly B-modes and dark matter

text: I raised a question a while ago regarding weak gravitational lensing of galaxies and the CMB. With all the fuzz with the BICEP2 data, I think it is time to raise even more questions about this amazing subject. One of the assumptions being applied is that if we remove all the gravitational lensing happening to the CMBR, then we are only left with the "non-lensing" CMBR, and any B-mode polarization left over **must** be primordial gravitational waves What is not clear is why can't be assumed that all the the remaining B-mode polarization is due to weak gravitational lensing of unseen dark matter. **Note:** Remember that, given the question I referenced at the beginning, we use gravitational lensing already to 'measure' dark matter (well, at least extra-galactic dark matter distributions)


title: What are the uses of carbon nanotubes?

text: I read somewhere about carbon nanotubes (CNT). What is the state of the research about CNT today? Are they used for some practical purposes?


title: What is a good reference for the mechanical properties of materials at cryogenic temperatures?

text: I want to research various the properties of various materials, namely tensile strength at cryogenic temperatures (~20K). I was wondering if a freely available database of material properties exists.


title: total cross section and contribution

text: Since in electron electron scattering if initial energy is quite large then muon antimuon production process can also take place which also contributes thus increases the total cross section. What does increased cross section mean physically? Does it mean there will be more scattering events or anything more? And How is this a helpful tool while detecting new particles?


title: Understanding fields and their correlation to forces

text: I seem to be confused between the concept of a "force", and a field. Now let's assume there is a magnetic field of $1$ $\mathrm{Tesla}$, what does that mean in relation to force? Finally, if field is $1$ $\mathrm{Tesla}$ does that always mean, the force at that field is always the same? Example a magnetic field source (From Solenoid) of $1$ $\mathrm{Tesla}$ can apply a force of $10,000$ $\mathrm{Newtons}$, magnetic field source (Permanent Magnet) generates the same field strength, at the same conditions does it produce the same force?


title: Alternate solutions to Resistance of a Conical Frustum

text: ![enter image description here](http://i.stack.imgur.com/UmMCc.jpg) Since for a cylinder R=p(length)/(Area) I assumed an equation of radius of this frustum radius=a+((b-a)/length)*x and then integrated to get the answer ![enter image description here](http://i.stack.imgur.com/TwsOo.png) ![enter image description here](http://i.stack.imgur.com/TVK8H.png) **Are there other ways to find the Resistance without assuming an equation of radius** (although it is not that difficult to assume such an equation using details given in the problem)


title: Does the mass of an object change as it moves away from the earth?

text: The mass of a helium nucleus is less than the mass of two isolated protons and two isolated neutrons. When the component hadrons are assembled, this mass is lost as energy ($E=mc^2$). This makes it (at least sort of) seem like mass is a kind of potential energy. Matter and antimatter can annihilate each other, releasing energy ($E=mc^2$). This also makes it (at least sort of) seem like mass is a kind of potential energy. If I have a mass at approximately sea-level on Earth, will flying it away from Earth increase its mass? (If so, is this related to relativistic mass?) EDIT: The original question doesn't really ask what I mean to ask. Suppose that, after the mass has been flown into space, it is stopped relative to Earth. (I think that would require a geosynchronous orbit.) Would its mass be different than it was before it left Earth?


title: Relative Synchronicity

text: Einstein said that the synchronization of two clocks is dependant on the velocity of the observer. But I feel a conceptual contradiction can be made: There are two observers A and B. Observer 'A' faces direction X, and will be labeled "stationary." Another observer B faces direction X and is travelling rapidly in that direction as well on a collision course with 'A'. Both observers are holding two clocks; One in each hand, with hands held perpendicular to direction X. Both observers hit a "synchronization" button on the clocks before colliding. My expectation in this case is that when the moving observer B halts to greet observer A - both observers will agree the B-pair clocks are synchronized and the A-pair clocks are synchronized (though all four clocks are not necessarily synchronized with eachother, and is not at issue in this question). Bottom line: what was considered "synchronicity" by the speedy individual is accepted by the stationary individual. This seems to contradict special relativity. Now if my scenario were modified slightly, then I believe special relativity would apply. If observer A were to hold the A-pair clocks with one held out before herself and the other held out behind herself (instead of the original left and right perpendicular angles), then finally I would expect there to be disagreement between the two observers when they stop to meet eachother. All this suggests that position is an unaccounted for primary component of relativity, but from what little I know of SR, it doesn't hardly factor in at all. Can someone explain what I'm missing?


title: Pressure Inside an Ideal Gas

text: A non-relativistic ideal gas exerts a pressure at the surface of its container $p = \frac13 \rho \langle v^2 \rangle$ where $\rho$ is the mass density of the gas and $\langle v^2 \rangle$ is the average square of the Maxwell velocity distribution. This is the relation for the pressure at the boundary of the vessel containing the ideal gas. However, if one were to place an infinitesimal "test" area inside the boundary of the vessel the momentum flux across that area would be 0 since the distribution of velocities is symmetric. That is, as many particles would cross one way across the area as cross the opposite way. This suggests that the pressure inside an ideal gas is 0. In general relativity an ideal gas is usually presented as an example of a perfect fluid, that is one with stress energy tensor equal to $T_{\mu \nu} = \left( \begin{array}{cccc} \rho & 0 & 0 & 0 \\\ 0 & p & 0 & 0 \\\ 0 & 0 & p &0 \\\ 0& 0 & 0 & p \end{array} \right) $ Since the stress energy tensor should be a local function it seems strange to assign to $p$ (in the frame in which the velocity distribution is isotropic) in the above equation the value of the pressure at the boundary of the vessel. I can see why this is done: one wants the stress energy tensor to be a smooth function, and also it should be that a gas at finite temperature should gravitate more than a gas at zero temperature (dust)... however this is point is not articulated, in for instance MTW. Perhaps I am missing something elementary?


title: Showing that a given matrix provides the desired Lorentz transformation

text: I am working on problem 5.12 in Halzen and Martin’s _Quarks and Leptons_. We are asked to show that the matrix $$ S = 1 - \frac{i}{4} \sigma_{\mu \nu} \varepsilon^{\mu \nu} $$ represents the infinitesimal Lorentz transformation $$ \Lambda^\mu {}_\nu = \delta^\mu {}_\nu + \varepsilon^\mu {}_\nu , $$ in the sense that $$ S^{-1} \gamma^\mu S = \Lambda^\mu {}_\nu \gamma^\nu . $$ I have already proven that $S^{-1} = \gamma^0 S^\dagger \gamma^0$, so I can begin with the left-hand side of this third equation: $$ \begin{align} S^{-1} \gamma^\mu S &= \gamma^0 S^\dagger \gamma^0 \gamma^\mu S \\\ &= \gamma^0 \left( 1 + \frac{i}{4} \sigma_{\mu \nu} \varepsilon^{\mu \nu} \right) \gamma^0 \gamma^\mu \left( 1 - \frac{i}{4} \sigma_{\mu \nu} \varepsilon^{\mu \nu} \right) \\\ &= \gamma^0 \gamma^0 \gamma^\mu - \gamma^0 \gamma^0 \gamma^\mu \frac{i}{4} \sigma_{\mu \nu} \varepsilon^{\mu \nu} + \gamma^0 \frac{i}{4} \sigma_{\mu \nu} \varepsilon^{\mu \nu} \gamma^0 \gamma^\mu - \gamma^0 \frac{i}{4} \sigma_{\rho \tau} \varepsilon^{\rho \tau} \gamma^0 \gamma^\mu \frac{i}{4} \sigma_{\mu \nu} \varepsilon^{\mu \nu} \\\ &= \gamma^\mu + \frac{1}{16} \gamma^0 \sigma_{\rho \tau} \varepsilon^{\rho \tau} \gamma^0 \gamma^\mu \sigma_{\mu \nu} \varepsilon^{\mu \nu} \\\ &= \gamma^\mu + \frac{1}{16} \left( \sigma_{\rho \tau} \varepsilon^{\rho \tau} \sigma_{\mu \nu} \varepsilon^{\mu \nu} \right) \gamma^\mu . \end{align} $$ Remember, we want this to be equal to $$ \Lambda^\mu {}_\nu \gamma^\nu = \left( \delta^\mu {}_\nu + \varepsilon^\mu {}_\nu \right) \gamma^\nu = \gamma^\mu + \varepsilon^\mu {}_\nu \gamma^\nu . $$ The first term is there already, but I have no idea how that second term is going to work out to $\varepsilon^\mu {}_\nu \gamma^\nu$. Can anyone give me a hint, or tell me what I’ve done wrong?


title: Measuring a Rod in Motion with two Synchronized Clocks

text: An explanation of special relativity I'm struggling with, goes like this: A rod traveling by a "stationary" observer has its length measured by use of two stationary synchronized clocks (synchronized from the perspective of the observer). The resulting length will appear "shorter" than if the rod were stationary and measured more conventionally. I don't even understand the premise. How would two stationary clocks be used to measure the length of a moving rod? Instead I can imagine using a single clock with a "split" metric. That is, capture time when the head of the rod passes the clock, and capture the time when the tail of the rod passes. If the velocity is known, the length can be determined. But my formulation only requires one clock, and isn't pertinent to the point of the original presentation. Can someone explain to me how two stationary "synchronized" clocks can be used to measure the length of a rod in motion?


title: Converting Notes to Milliseconds

text: Given a note duration (whole, half, quarter, etc.), a tempo (in beats per minute), and a time signature, how long does that note last in milliseconds?


title: How to compute the heat flow for a specific material for some given boundary temperature?

text: Assume I have a bounded material with heat sources inside. The material is known (i.e. I know heat capacity and all relevant data) and the temperature of the boundary is fixed. I solved the (steady state) heat equation and hence know the temperature distribution. How do I compute the heat flow through the boundary? I expect something like $$ \int_\Gamma k\cdot \nabla T $$ where $\Gamma$ is the boundary and $T$ the temperature. Is this correct? If so, what value for $k$ do I have to use?


title: If all conserved quantities of a system are known, can they be explained by symmetries?

text: If a system has $N$ degrees of freedom (DOF) and therefore $N$ independent1 ~~conserved quantities~~ integrals of motion, can continuous symmetries with a total of $N$ parameters be found that deliver these conserved quantities by means of Noether's theorem? I think this is not exactly the opposite of Noether's theorem since I don't ask whether for _each_ conserved quantity _a_ symmetry can be retrieved, I ask about a connection between the _whole set_ of conserved quantities and symmetries. * * * 1) or $2N-1$, or $N$, depending on definition and details that are irrelevant here. But let me expand on it anyway... I consider the number of DOFs equal to the number of initial conditions required to fully describe a system in Classical Mechanics. That means, velocities (or momenta) are considered individual DOFs, and not that each pair of coordinate + velocity make up only one DOF. Time is no DOF however, it is a _parameter_. Please discuss this in this question if you disagree.