title: Heat transfer to a cube from one of the faces

text: Heat Flux= 10 MW Inlet water temperature = 28 degree centigrade for cooling purpose through a tube passing through the centre of retangular block of length 50 mm,height 30 mm and width 30 mm inner diameter of tube=10mm and outer diameter=12 mm tube is made of copper. Find out the heat transfer coefficient of water at 42 bar and given temperature Find out Nusselt number and Reynold's number.


title: Colliding bubbles in hyperspace

text: Assuming the following   1. A universe is the surface from a bubble in hyperspace. Inside a bubble there is nothing, only the surface represents a universe. The size of the bubble is time.   2. Dark matter is from bubbles different then our own bubble that only shares gravity.   3. The big bang are bubbles colliding, creating a other bubble. My problem is if bubbles do only share gravity why would they have a collision, I expect that they would just pass trough each other without creating a big bang?


title: Is it possible to deduce the Archimedes' law of the lever using only the laws of conservation of the physics?

text: Is it possible to deduce the Archimedes' law of the lever using only the laws of conservation of the classical mechanics? I never saw (which is strange), but I think that it's possible.


title: Renormalizability of the Polyakov Action

text: I was told today that the Polyakov action for a $p$-brane is (superficially) re-normalizable iff $p\leq 1$. Of course, when I went to check for myself, I screwed up my power-counting, and I'm having trouble seeing why. We work in units with $c=1=\hbar$, so that $L=T=M^{-1}$. In these units, any action must have dimension $1$, so from looking at the Nambu-Goto action, $$ S_{\text{NG}}:=-T_p\int d\sigma ^{1+p}\sqrt{-g}, $$ we see that $[T_p]=L^{-(1+p)}=M^{1+p}$. From the Polyakov action, $$ S_{\text{P}}:=-\frac{T_p}{2}\int d\sigma ^{1+p}\sqrt{-h}h^{\alpha \beta}\partial _\alpha X^\mu \partial _\beta X^\nu G_{\mu \nu}(X), $$ we see that the the coupling constant of the interaction of of the scalar fields $X^\mu$ with $h_{\alpha \beta}$ is precisely $\frac{T_p}{2}$, which has dimensions $M^{1+p}$, and so is going to be (superficially) re-normalizable iff $1+p\geq 0$ . . . But this, of course, is not the result I was looking for . . . Where is my mistake?


title: Does a universe experiencing "heat death" have a temperature?

text: As defined by Wikipedia: > The heat death of the universe is a suggested ultimate fate of the universe > in which the universe has diminished to a state of no thermodynamic free > energy and therefore can no longer sustain processes that consume energy > (including computation and life). Heat death does not imply any particular > absolute temperature; it only requires that temperature differences or other > processes may no longer be exploited to perform work. Does it even make sense to describe temperature in the system described? If so, would it be a very cold system or a very hot system?


title: A Question From Jackson Electrodynamics

text: I have a question regarding Jackson's Classical Electrodynamics. Consider the equation $$\varphi \left ( x\right )=\tfrac{1}{4\pi\epsilon _{0}} \int_V \frac{\varrho ( x )}{R}d^{3}x+\tfrac{1}{4\pi} \oint_{\partial V} \left(\frac{1}{R}\frac{\partial }{\partial n}\varphi -\varphi \frac{\partial }{\partial n}\frac{1}{R} \right)dS.$$ This expresses the electrostatic potential due to a charge distribution $\varrho$ in a finite volume $V$ with specified boundary conditions. The first integral expresses the charge inside a volume in space. The second integral encodes the boundary conditions on the surface of this volume. My first question: does this determine the total potential completely inside that volume regardless of any charge that you put or remove outside the volume? Or does the change in the charge distribution outside the volume cause changes in the boundary conditions (the potential and its normal derivative at the surface)? My second question: I can understan mathematically that the potential outside the volume should be zero but I can't see why this is so physically. Also, the zero potential outside will change if you put some charge outside the volume, right?


title: Simulating the Interference Pattern of Fraunhofer Diffraction by a Single Slit

text: I'm attempting to simulate the Fraunhofer diffraction pattern due to a single slit. We know that the intensity at an angle $\theta$ is $I(\theta)=I_0 \text{sinc} ^2(\beta)$ where $\beta=k\,b\,\sin(\theta) / 2.$ Considering the setup shown in the image where O is the origin (the precise center of the single slit) and p is some point on the viewing screen I reasoned that $\sin(\theta)=\sqrt{x^2+y^2}/\sqrt{x^2+y^2+z^2}.$ ![Single Slit Setup](http://imageshack.us/a/img23/1835/6vsq.png) So I plugged this into the above equation which gave me $$I(\theta) = I_0 \text{sinc}^2\left(k\,b\,\frac{\sqrt{x^2+y^2}}{2\sqrt{x^2+y^2+z^2}}\right).$$ For my parameters I chose $k={2\pi / 632.8*10^{-9}}$ which corresponds to the wave number for a typical He-Ne laser, $b=0.5\,\text{mm}$ for the slit width and $z=40\,\text{cm}$ for how back the screen was placed. I then ran the following code in Mathematica to try and generate the viewing screen: `DensityPlot[ Sinc[(2482.2950802700643 Sqrt[x^2 + y^2])/Sqrt[ 4/25 + x^2 + y^2]]^2, {x, -8, 8}, {y, -8, 8}, ColorFunction -> GrayLevel, PlotPoints -> 200, FrameLabel -> {"x", "y"}]` Which produced: ![Incorrect Diffraction Pattern](http://img27.imageshack.us/img27/8365/7l1k.png) Pretty psychedelic but not what I was expecting. I was expecting the diffraction pattern to look more like: ![Correct](http://tsgphysics.mit.edu/pics/Q%20Diffraction/Q2-Single-Slit- Diffraction.jpg) So what exactly am I doing wrong and what function should I be doing a density plot of? Thank You


title: The surface area to volume ratio of a sphere and the Bekenstein bound

text: I am trying to relate the surface-area-to-volume-ratio of a sphere to the Bekenstein bound. Since the surface-area-to-volume-ratio decreases with increasing volume, one would surmise that, per unit of volume, a small space is richer in information than a large one. How can this be and how can this bound work for black holes of various sizes? Thank you very much Mr. Rennie. I appreciate and have investigated your answer. It turns out that I am familiar with the AdS/CFT correspondence and have sufficient understanding of the math (just barely) to be intrigued with the conjecture and, of course, the holographic theory. If the correspondence only works for a certain diameter black hole, the conjecture seems, to me, weak because of the changing surface-area-to-volume-ratio of a sphere. For myself, it would appear to be, likely, a mathematical curiosity or fluke. However, if, through some aspect that I do not understand, the correspondence holds for varying diameters, in fact, all diameters of black holes, then it seems quite astonishing, indeed. After searching for some time, I have once seen the amount described as trivial and possibly in another instance, that it may have something to do with informational redundancy. I’m afraid I cannot site these references as they were far too brief to be of any help.


title: Conformal fields on compactified manifolds? An apparent paradox!

text: I would appreciate it if someone tells me how a cft on a compactified manifold (e.g. by means of periodic boundary conditions) can be meaningful? The global conformal invariance is broken due to the scale over which the manifold is compactified (e.g. the period). The local conformal invariance of course still classically exists, but for the simple case of a field on a cylinder for instance, the trace of the stress-energy tensor becomes non-zero (in proportion with the central charge); hence apparently compactification of the space-time manifold is in contrast with having conformal symmetry.


title: EM wave function & photon wavefunction

text: According to this review > Photon wave function. Iwo Bialynicki-Birula. _Progress in Optics_ **36** V > (1996), pp. 245-294. arXiv:quant-ph/0508202, a classical EM plane wavefunction is a wavefunction (in Hilbert space) of a single photon with definite momentum (c.f section 1.4), although a naive probabilistic interpretation is not applicable. However, what I've learned in some other sources (e.g. Sakurai's Advanced QM, chap. 2) is that, the classical EM field is obtained by taking the expectation value of the field operator. Then according to Sakurai, the classical $E$ or $B$ field of a single photon state with definite momentum p is given by $\langle p|\hat{E}(or \hat{B})|p\rangle$, which is $0$ in the whole space. This seems to contradict the first view, but both views make equally good sense to me by their own reasonings, so how do I reconcile them?


title: Supergroup action on $AdS_5XS^5$

text: In the context of the AdS/CFT correspondence I was trying to understand how the symmetry group of the underlying space $AdS_5 X S^5$ comes out to be the supergroup $SU(2,2|4)$. I can see how the bosonic subrgoup $SU(2,2)XSU(4)_R$ crops up as the group of isometries of $AdS_5XS^5$, since $SU(2,2)$ is a double cover of $SO(2,4)$ and this preserves the signature (+ + - - - -)space from which $AdS_5$ arose. Moreover the group of R symmetries $SU(4)_R$ bears an astonishing resemblance to $SO(6)$ which preserves the $S^5$ metric. So far so good in bosonic land. However, what about the fermionic parts of $SU(2,2|4)$ ? How do they act on $AdS_5XS^5$ ? Something to do with the branes I guess, but I'm not sure....


title: Zeta regularization and Renormalization group

text: Is there a physical method to prove for example when the zeta regularization of a series $$ 1+2^{k}+3^{k}+............= \zeta (-k) $$ gives the correct result: Casimir effect, vacuum energy and when does it 'fail'? For example we plug the zeta regulator inside the renormalization group equations and this group tells us if zeta regularization fails or give exact results.


title: What's the best strategy to fully fill the fridge with beer bottles and have them all cooled?

text: I'm having a party. Suppose I'd like to have a fridge _full_ of cold ($6~^\circ\text{C}$ or below) beer bottles, _in as short a time frame as possible_. The fridge indicates that it is targeting (and presumably currently at) $4~^\circ\text{C}$. All the bottles are currently at $30~^\circ\text{C}$, which is the temperature outside the fridge, and together the bottles will fill the fridge completely (as in: no further bottles could be fitted in). What is the best strategy to achieve this aim? (Should I put in all bottles at once? Should I put the bottles in at different times? And, if so, should I make them touch, or keep them initially apart as much as possible? Should I even consider taking out some bottles at some time and putting them back in later? (That would be really weird.) If so, should I have those bottles cool other bottles that weren't in the fridge yet?) * * * NB 1: I do not have a freezer available. NB 2: Assume that I know how to get as much bottles into the fridge as possible (without breaking any). * * * _Measurements:_ 1 bottle of beer: $0.61~\text{kg}$, 1 empty bottle (with cap): $0.28~\text{kg}$, 1 empty bottle (without cap): $0.28~\text{kg}$, contents of 1 bottle: $0.33~\text{l}$. My guesstimate is that I can get 72 bottles into the fridge.


title: Collision between a photon and a massive particle

text: Just a small question regarding collisions. Imagine a head-on collision between a photon and a particle with mass that moves with a non-relativistic speed, the particle was on its ground state, completely absorbs the photon, and moves to its next energy level. Is it always the case that the particle ends up with a non-relativistic speed after the collision? Something more specific: > To study the properties of isolated atoms with a high degree of precision > they must be kept almost at rest for a length of time. A method has recently > been developed to do this. It is called “laser cooling” and is illustrated > by the problem below. In a vacuum chamber a well collimated beam of Na23 > atoms (coming from the evaporation of a sample at 103 K) is illuminated > head-on with a high intensity laser beam (fig. 3.1). The frequency of laser > is chosen so there will be resonant absorption of a photon by those atoms > whose velocity is v0. When the light is absorbed, these atoms are exited to > the first energy level, which has a mean value E above the ground state and > uncertainty of (gamma). Find the laser frequency needed ensure the resonant > absorption of the light by those atoms whose kinetic energy of the atoms > inside the region behind the collimator. Also find the reduction in the > velocity of these atoms, ∆v1, after the absorption process. Data E = > 3,36⋅10-19 J Γ = 7,0⋅10-27 J c = 3⋅108 ms-1 mp = 1,67⋅10-27 kg h = > 6,62⋅10-34 Js k = 1,38⋅10-23 JK-1


title: WolframAlpha wont reckognize a second derivative inside an integral

text: I know that _WolframAlpha_ questions are off topic but as I cannot find a Q&A site for WA I decided to ask here. It should be a piece of cake for you guys as I think it is a fairly simple question. I have been trying to calculate my derivative in WolframAlpha by inputing this:               A=0.921/10^(9),      a=1*10^(-9),      h=1.055*10^(-34),      m=9.109*10^(-31)           int_((-pi)/(2*a))^((pi)/(2*a)) A cos^2(x/a)*(-h^2/(2*m))*d^2/dx^2(A*cos^2(x/a))dx      Well what I got was a wrong interpretation and therefore a weird result. I have noticed that if I only remove the **second derivative** like this:               A=0.921/10^(9),      a=1*10^(-9),      h=1.055*10^(-34),      m=9.109*10^(-31)           int_((-pi)/(2*a))^((pi)/(2*a)) A cos^2(x/a)*(-h^2/(2*m))dx      the interpretation looks fine but is missing a second derivative. Why isn't the second derivative reckognized? How can i fix this? If it can't be fixed could anyone please calculate this in mathematica? I just need an numerical value of this integral **(values can be found in the first code snippet where with $h$ I meant $\hbar$)** : \begin{align} \int\limits_{-\tfrac{\pi}{2}a}^{\tfrac{\pi}{2}a}A\cos^2\left(\tfrac{x}{a}\right)\left[-\tfrac{\hbar^2}{2m}\tfrac{d^2}{dx^2}\left(A\cos^2\left(\tfrac{x}{a}\right)\right)\right] \,dx \end{align}


title: Calculating states of entangled and disentangled qubits

text: I'm writing a quantum computer simulator (about 8 qubits) and I know most of the basics (i.e. how to calculate the effect of a quantum gate on a qubit). But I have hit a wall. Is it possible, with two qubits of $ a |0\rangle + b|1\rangle $ and $c|0\rangle + d|1\rangle$ to calculate the superposition state of the two entangled? (i.e. $\alpha|00\rangle + ... +\delta|11\rangle$) and vice versa? Also, if I have a pair of entangled qubits, and pass one through, for example, a Pauli-$x$ gate, what effect will that have on the overall entanglement?


title: Length in polar coordinates

text: Say we are in 3 dimensions and use $(-++)$. If we have the metric $$ds^2=-dt^2+dr^2+r^2df^2(t),$$ then what is the third coordinate if the first two were $t$ and $r$? $$X^iX_i=-t^2+r^2+?$$


title: How to determine satellite position in J2000 from latitude, longitude and distance from Earth?

text: Due to my task of writing orbit prediction routines I am trying to understand the reference frames better and how to use them ( particularly for Earth orbits ). I think I get the idea of what ECI (Earth centered inertial) is about. But then there are couple of things unclear about J2000. Am I right thinking that J2000 is an ECI frame, just with added time variable ? If that is the case, how do you present a particular satellite position in a given moment in J2000 frame, if you know its position relative to the Earth's surface ( latitude, longitude and distance from Earth's surface/center ) ? Apart from the general description I would also appreciate to know the coordinate transforms and any other computation necessary to perform the task.


title: Ferris wheel and projectile

text: Imagine there's a little girl/boy sitting on one of the seats of a Ferris wheel. She/he throws out a stone and sees that it's experiencing the velocity **v**. Meanwhile, another observer standing on the ground sees that the stone is thrown with a horizontal velocity, **u**. What's the connection between **u** and **v**? (I hope I explained what's on my mind well enough. )


title: Solar neutrino problem in 1968 and experimental verification of neutrino oscillation in 2001. Why the huge delay?

text: Solar neutrino deficit was first observed in the late 1960's. And theory of neutrino oscillation was developed in 1967. But,in 2001, the first convincing evidence of solar neutrino oscillation came in SNO. Why did it take nearly 35 years to verify the neutrino oscillation? reference: http://en.wikipedia.org/wiki/Neutrino_oscillation


title: Formula for a ball rolling down an Inclined Plane

text: Suppose we set up an experiment where we have an inclined ramp, and a spherical basketball. If we were to assume the ball to be perfectly round, and rolls down in a vertical manner and the situation friction less. The simplified equation that would be used would be $\frac{2}{3} G x \sin\theta$. I'm wondering why is the $2/3$ the constant in the equation. Could it be the force of gravity vs the force of the ramp pushing the ball up? or could it be that spherical objects follow a constant k rate?


title: Calculation of Commutation in constraint analysis

text: During analysis the constraint from a theory, suppose my canonical Hamiltonian is $$H_c=P^A\dot{A}+P^B\dot{B}-L$$ where $P^A=\frac{\partial L}{\partial \dot A}$ and $P^B=\frac{\partial L}{\partial \dot B}$ In this case does the commutation of $[P^A,P^B]=0$?


title: Simplifying the explanation of a low-entropy Big Bang

text: The claim that the young universe was in a low-entropy state seems at odds with   * maximal entropy being thermal equilibrium, and   * the young universe being in thermal equilibrium. I've looked at some other answers and they're too technical for me, but I think I've understood the reason to be basically this: "Entropy was lower because the universe was smaller." Is this right?


title: Practical issues with Superconductivity

text: Well, Is it really possible to maintain such low temperatures required for super-conductors (taking High-temperature superconductivity into account) over _large distances_? What I say is - Even if we were able to pass current through superconductors, we need to constantly cool them for maintaining the zero resistance. Hence to cool, we need power. Then, superconductors wouldn't be necessary in this manner if they don't have an advantage..? Or, are there any new approaches to overcome these disadvantages?


title: quantum field description of squeezing

text: Following with a series of questions regarding quantum squeezing, let me add another one: quantum squeezing of vacuum is a real propagating state of the field, it can be switched on and off, squeezing can be altered and information can be sent modulating it. So, there must be real degrees of freedom in the QED field description that account for the squeezing. But squeezing does not affect the field itself, but the associated uncertainties. The electromagnetic quantum field is usually described as quantum oscillators over a wavenumber $k$ and a polarization number (either -1 or 1). so the question is: where are the degrees of freedom that describe a squeezed field? are they simply missing? This question follows up discussion from these questions: here and here


title: Could sphaleron-induced proton decay also cause vacuum decay?

text: I will say right away that I don't mean standard-model sphalerons, I mean the sphalerons of some extension of the standard model. The reason to even think about this is last year's paper by Frampton and Hung (discussion), which proposes that the Higgs mass might be 126 GeV "because" the timescales for vacuum decay and for instanton-induced proton decay are the same. More precisely: the timescale of vacuum decay is unknown, but if it were the same as the timescale for the spontaneous occurrence of a sphaleron in a proton, that would indicate a Higgs mass near the observed mass. (This is not as remarkable as it may sound: the Higgs mass is right on the edge of making the vacuum genuinely stable, so _any_ extremely long lifetime for the vacuum corresponds to a Higgs mass near the value that we see.) They don't have a coherent causal model. But one way for it to work, would be if proton decay _caused_ vacuum decay. This ought to make for problems with early-universe cosmology, but put that to one side for now, maybe there's a way around that. What I would like to know is whether the idea of proton decay causing vacuum decay even makes sense. What I envisage is a standard model extension with new scalars that appear in the sphaleron action _and_ in an extended Higgs-sector potential. Perhaps the new scalar has a VEV of its own, the proton-destroying sphaleron action is minimized when that VEV changes, but the new VEV will in turn destabilize the existing Higgs VEV and drive it into a new, true minimum. The effect of an extra scalar on electroweak vacuum stability is a current topic of research, and section 4 of this paper shows sneutrinos nominally contributing to the sphaleron action in an extension of the MSSM (though here their contribution is negligible).


title: Work Done by Rockets in Orbital Motion

text: A weather satellite ($m_s = 4350$ kg) is in a stable circular orbit around the Earth ($m_E = 5.97 \cdot 10^{24}$ kg). It completes an orbit once every 2 and a half hours. (I'm sure about these 2 answers) At what distance from the center of the Earth does the satellite orbit? $r_i = 9.35 \cdot 10^6$ m What is the angular velocity of the satellite? $\omega_i = 6.98 \cdot 10^{-4}$ rad/s (I'm having trouble getting this part:) The satellite operators decide to fire maneuvering rockets and move the satellite into an orbit with a 5% larger radius. If the initial magnitude of the satellite’s mechanical energy was $E_{m,i} = 9.26 \cdot 10^{10}$ J and it continues at the same speed, how much work was done by the rockets in moving the satellite to the higher orbit? I calculated the larger radius to be $r_f= 9.86 \cdot 10^6$ m. Using $v = \sqrt{\frac{GM_e}{r}}$, I found $v_i = \sqrt{\frac{GM_e}{r_i}} = 6529.7$ m/s. Likewise, $v_f=6371.5$ m/s. Using the work-energy theorem, I know that $W_i+K_i+W_{other}=W_f+K_f$. Because the total mechanical energy is given, $E_{m,i}+W_{other}=W_f+K_f$. The only work done on the object is by potential energy due to gravity, so $E_{m,i}+W_{other}=-\frac{GM_em_s}{r_f}+\frac{1}{2}m_sv_f^2 \implies W_{other}=-\frac{GM_em_s}{r_f}+\frac{1}{2}m_sv_f^2-E_{m,i} = -1.80 \cdot 10^{11}$ J, which is clearly the wrong answer. Can somebody spot where I'm messing up?


title: charge moves if you scuff the rag with your shoes

text: Why is that when you scuff with your shoes on, charges move (since electrometer moves back and forth), but if you don't have your shoes on, the electrometer doesn't move. Here's the corresponding video detailing the event. http://www.youtube.com/watch?v=cJSp8v0YJrA It is at about 47 min of video from beginning. I don't get the logic behind it.


title: Clarification on Wald's book

text: I have a question concerning the Wald's book: General Relativity. In the appendix E, he derived the Einstein equation by considering the surface term (GHY). I do not understand what he said after the equation (E.1.38). Actually he considers that $h^{bc}\nabla_c(\delta g_{ab})=0$, because we fix $\delta g_{ab}=0$ on the surface, but therefore why the other term in (E.1.38) is not null, the term $h^{bc}\nabla_a(\delta g_{bc})$. They look the same for me, and after some algebra, where we replace the covariant derivative by the one compatible with the metric on the surface we should have a total derivative term on the surface that we can integrate away. Thanks in advance


We know that electron trapped by nuclear, like the hydrogen system, is described by quantum state,and never fall to the nuclear. So is there any similar situation in the case of electron near the black hole but not fall into it? And what is "falling " in gravitation mean when considering quantum mechanics? What does the equivalence principle mean in quantum cases?


title: Spherical harmonics

text: Given the following potential: $$V(\theta,\phi)=\frac{Q}{a}\left(\sin\theta \cos\phi+\frac{1}{2}\cos^2\theta\right)$$ on the surface of a sphere of radius $a$ I am trying to solve Laplace's Equation outside the sphere (where there aren't any charges). I know the general solution to Laplace's Equation outside the sphere is given by: $$\phi(r,\theta,\phi)=\sum_{l=0}B_l r^{-l-1}P_l(\cos\theta).$$ I am not quite sure how to proceed as am very new to spherical harmonics. Does the next step involve expressing the given potential as a Legendre polynomial? I'd appreciate some guidance.


title: Are conformal, Killing and homothetic vector fields the same in pseudo-riemannian manifolds?

text: I work in the Lorentzian manifolds, more generally in pseudo Riemannian manifolds and applications to general relativity. I know the definitions of conformal, Killing and homothetic vector fields in Riemannian hypersurfaces. Are these quantities defined in the same way in pseudo riemannian hypersurfaces? What is the physical significance of these quantities?


title: Imaginary part of Poynting vector

text: When I am studying the total reflection phenomenon, I calculated the Poynting vector of the transmitted wave, which can be written as $S_t=A(k_{x}\hat{x}+i\alpha\hat{z})$ A is some constant. I choosed $z=0$ as the interface, light incident from the region $z>0$, If total reflection occurs, the z-component become imaginary, for some reference the imaginary part is regarded as "reactive power" like in AC circuit. In Hecht's text, stated that the energy is circulating across the interface. But how can I see it from mathematical expressions?


title: Complex polarizability of a dielectric sphere in a homohenious electric field

text: It is well known that complex polarizability of uniform dielectric sphere with radius $r$ and complex permittivity $\hat\epsilon_{in}(\omega)$ placed in a medium with complex permittivity $\hat\epsilon_{out}(\omega)$ under homogeneous electric field with circular frequency $\omega$ is defined by (in the CGS system of units): $$\hat\alpha(\omega)=r^3 {\hat\epsilon_{in}(\omega)-\hat\epsilon_{out}(\omega)\over \hat\epsilon_{in}(\omega)+2\hat\epsilon_{out}(\omega)}$$ This relation is derived for the static case in many textbooks on electrostatics (see here related demonstration). What about the dynamic case?


title: Does the magnetic field lie in the Wave-Particle duality?

text: There is Wave–particle duality. According to this theory, light is a wave and a particle at once. What about magnetic field? Can it be so, that it is also a wave and particle, but this particle has not yet been discovered? Is magnetic field discrete? ![enter image description here](http://i.stack.imgur.com/SMLlc.png)


title: How Does Lead Block Radiation

text: How is it that lead can block radiation, and things are lead lined. In the Indiana Jones 4 movie he climbs inside a lead-lined fridge and he somehow survives the blast and radiation?


title: Damping Coefficient for a Hydraulic-Controlled Door

text: I am not very good with physics terms, so please treat me as an ignorant. I am trying to calculate a damping coefficient dynamically for a hydraulic- controlled door that opens and closes due to hydraulic pressure (opening/closing). The formula where I need my damping coefficient is: viscous_fric_mom = $C \times \omega \times 2/\pi$; The $\pi/2$ division is because the maximum angle that the door can be opened at is $\pi/2$ (i.e. 90°), $\omega$ is the angular velocity of the door which is in $\rm rad/s$. And $C$ is the damping coefficient, which I need to calculate dynamically. The system specifies that my damping coefficient unit is in $\rm N m s$! I thought it would be $\rm N s /m$, because usually it is `Force*time/distance`. Apparently I am wrong. Could someone suggest what I should consider for calculating this damping coefficient? I am really bad at math and do not know any better of doing it. **UPDATE** I am trying to create a software model of a hydraulic-operated door. The door will open given that the effective hydraulic jack pressure have been applied. Same goes true when the door is closing i.e. an effective hydraulic jack retraction pressure must be applied. I use two part integration (integration of acceleration and velocity) to get the current angular position of the door, i.e. from the locked position. My current operating assumption is that the door will have either $\pi/2$ or $-\pi/2$ acceleration (i.e. opening or closing). If I integrate that, I get the velocity and double integration will give me the position. If I take the angular position and feed it back to my damping coefficient calculator, that should work, right?


title: Single mode fibers

text: Is it possible to focus white light into a single mode optical fiber? I thought no because in order to focus it should be a solution to the Helmholtz equation but I am not too sure about it. Also since the equation features the wave number, shouldn't it be impossible?


title: Sign and Four Acceleration Special Relativity

text: If $ use $(+,-,-,-)$ sign convention then four position, four velocity become positive but four acceleration becomes negative! $x_{\mu}x^{\mu}=\tau^2c^2,$ $U_{\mu}U^{\mu}=c^2,$ $a_{\mu}a^{\mu}=-(a\gamma^3)^2,$ in other hands If I use $(-,+,+,+)$ sign convention then four position, four velocity became negative but four acceleration becomes positive! $x_{\mu}x^{\mu}=-\tau^2c^2,$ $U_{\mu}U^{\mu}=-c^2,$ $a_{\mu}a^{\mu}=(a\gamma^3)^2,$ Isn't it true!?


title: Produciton of EM waves with differing wavelengths

text: Sun is the major source of electromagnetic radiation. Then if the source is the same, how are different EM waves with differing wavelengths produced?


title: Does anybody know of any good sources that explain (generically) how we form Lagrangians/Actions/Superpotentials for different field content?

text: I regularly find that I'll understand where the field content in a particular physics paper comes from, but then a Lagrangian or action or superpotential is stated and I don't know how it's derived. Is there a set of general rules for building a Lagrangian/action/superpotential if you already know the field content of the theory? Any suggestions of sources that explain how to do so would be very welcome as I'm having little trouble finding much that helps.


title: Where did this equation come from ∠I+ ∠E = ∠A+ ∠D?

text: $\angle I +\angle E=\angle A+\angle D$ Angle of incidence + angle of emergence = angle of prism (Normally $60^\circ$) + angle of deviation. If their sum is not equal,we made personal error in doing an experiment with prism. Please make sense of this equation.


title: What keeps galaxies united like a solar system?

text: Blackholes may be really strong but they act in a very short range. For example if the sun was a black having the same mass, it will be dark but we will still be revolving around it. It wont engulf us. Also I hear that the outer stars in a galaxy rotates around the galaxy with same speed as the inside stars? This defies the law of gravity. Is this still a mystery? Does anybody know what is the pull on a star by a galaxy? And is this pull uniform throughout the galaxy? Related Question: Evidence of dark matter in our galaxy


title: Why is $SU(3)$ chosen as the gauge group in QCD?

text: Why is $SU(3)$ chosen as the gauge group. Why not $U(3)$? Why does it even have to be unitary?


title: What is stopping us from stick building a space station?

text: I want to understand why we do not build space stations in a similar way that we build a home, piece by piece. Instead we construct modules on the ground and fly them up. Are there some technical limitations other than money that make this impossible? Why don't we fly up raw materials, prefabbed metal panels, structural steel and any other material and slowly construct a space station that is suitable for somewhat normal living, normal sized rooms, ceiling heights, etc.? I'm wondering if any plans exist or working groups are exploring this idea. Or is it a technical limitation, for example: not being able to ensure a complete seal between the exterior pieces? Is what I am wondering clear?


title: How can Y-dwarf stars have such a low temperature?

text: A recent article from NASA said they found some stars with temperatures "as cool as the human body." How is this possible? Does fusion still occur in these stars?


title: Faulty Uncertainty Calculations for a Ground State Particle in an Infinite Well

text: For the infinite well: $$U(x)=\quad\infty : x \leq 0\quad 0 : 0 < x < L\quad \infty : x \geq L$$ $\psi_n=$$\sqrt{\frac{2}{L}}\sin{\frac{n\pi x}{L}}$ Find $\Delta x_n$, the uncertainty in position for some arbitrary eigenstate psi.n So the attempt I made at doing this was to find using $\Delta x_n=\sqrt{<x^2>-<x>^2}$ I went through and found $$<x^2>=L^2(\frac{1}{3}-\frac{1}{2\pi^2})$$ and $$<x>^2=\frac{L^2}{4}$$ This led to the final result of $$L\sqrt{\frac{2\pi^2-12}{24\pi^2}}$$ When I went on to the next part of the question and found $\Delta p_n=\frac{\pi\hbar}{L}$ and then used this with $\Delta x_n$ to verify the uncertainty principle, I failed. What have I done incorrectly, I can't see it. I used my book to verify the integrals.


title: Is that a result of thin-film interference?

text: Several years ago, I was laying on my bed and had a CD shaped transparent plastic disk (which was covering a 100 CD stack), basically a transparent CD. I don't know why but I took my phone and took a picture of the light bulb in my room through the hole of that plastic disk. Here is the result: ![Light bulb through a disk](http://i.stack.imgur.com/dQFl4.jpg) Why does it appear like that? does it have anything to do with Thin-film interference? And would it look the same if there was no hole in the middle?


title: locality vs non-locality

text: Suppose we have a circular loop of wire, and we put a long perfect solenoid inside it which is connected to an AC voltage source so that the magnetic field inside it starts to vary by time, does this varying magnetic field induce an emf in our loop according to Faraday's law of induction? (suppose that the radius of the solenoid is much smaller than that of the circular loop) Does this show some kind of non-locality like the Aharonov-Bohm effect? Or am I just misunderstanding the concept?


title: Is quantum field operator $\psi$ same as quantum field $\psi$?

text: So in QFT, quantum field operator $\psi$ is there. $\psi$ seems to take the role of wavefunction in QM, which now acts upon vacuum state. Then, in lagrangian of various quantum field theories, $\psi$ appears, but now it is called quantum field. So is quantum field operator no different from quantum field here? If it is not different, then how can $\psi$ can have scalar $|\psi|$ in any assumption as it only operates upon vacuum state? Assuming that vacuum state is represented by some $n \times 1$ vector (let us forget about infinite-dimension for now), operator should be of the form $n \times n$.


title: Electrodynamics and the Lagrangian density

text: Could anyone tell me what equations can I obtain from the Lagrangian density $${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times A|^2-\rho\phi+J\cdot A$$ by the Euler-Lagrange equations?


title: Partially filled orbitals and strongly correlated electrons

text: Interesting behavior of strong correlation between electrons occur in metals with partially filled d or f orbitals (transition metals). Why these strong correlations do not appear with elements with incomplete p or s orbital for example ?


title: Do nuclear reaction cross sections depend on the angle between incident beam and target-crystal?

text: Shouldn't the absorption rate of a beam of particles strongly depend on the angle between the beam and the target material's crystal-axis (if the target material is a monocrystal)? At certain angles, all the nuclei will be stacked behind each other, offering a very small cross section, whereas other orientations will expose all of the nuclei without any shadowing. However, I don't see any mention of this in cross-section tables, so I guess it doesn't matter. Why is this?


title: A curious issue about Dyson-Schwinger equation(DSE): why does it work so well?

text: This question comes out of my other question "Time ordering and time derivative in path integral formalism and operator formalism", especally from the discussion with drake. The original post is somewhat badly composed because it contains too many questions, and till today I finally get energetic enough to compose another question that hopefully clarifies what was asked in that post. I have no problem with all the textbook derivations of DSE, but after changing a perspective I found it very curious that DSE actually works, I'll take the equation of motion(EOM) of time-ordered Green's function of free Klein- Gordon(KG) field as an example and explain what I actually mean. The EOM of free KG T-ordered Greens function is $$(\partial^2+m^2)\langle T\\{\phi(x)\phi(x')\\}\rangle=-i\delta^4(x-x')\cdots\cdots(1).$$ The delta function comes from the fact that $\partial^2$contains time derivatives and it doesn't commute with T-ordering symbol. In general for Bosonic operators $$\partial_t \langle T\\{A(t)\,B(t')\\}\rangle=\langle T \\{ \dot A(t)B(t')\rangle+\delta (t-t')\,\langle [A(t),B(t')]\rangle \cdots\cdots(2),$$ $(1)$ can be derived from $(2)$ and the equal time canonical commutation relation of the fields. However $(1)$ isn't very obvious from path integral approach: $$(\partial^2+m^2)\langle T\\{\phi(x)\phi(x')\\}\rangle=(\partial^2+m^2)\int\mathcal{D}\phi e^{iS}\phi(x)\phi(x')\\\\\quad \quad \quad \qquad \qquad \qquad \qquad =\int\mathcal{D}\phi e^{iS}[(\partial^2+m^2)\phi(x)]\phi(x')\cdots\cdots(3).$$ Now if we formally and naively think $$\int\mathcal{D}\phi e^{iS}[(\partial^2+m^2)\phi(x)]\phi(x')=\langle T\\{[(\partial^2+m^2)\phi(x)]\phi(x')\\}\rangle\cdots\cdots(4),$$ **with the notation $\langle\cdots\rangle$ always denoting expectation value in operator approach**. Then the final result will be 0(due to the field equation) instead of $-i\delta^4(x-x')$, and a result like equation(2) cannot be obtained. As drake has pointed out, this is because of the ambiguity in the definition of the equal time operator product when time derivative is present in the path integral, it's very important(e.g. CCR in path integral) to define clearly the time derivative on time lattice, that is, the discretization. There are 3 possible definitions of $\dot \phi$(omitting the spatial variables): (a)forward derivative $\dot \phi(t)=\frac{\phi(t+\epsilon^+)-\phi(t)}{\epsilon^+}$; (b)backward derivative $\dot \phi(t)=\frac{\phi(t)-\phi(t-\epsilon^+)}{\epsilon^+}$ (c)centered derivative $\dot \phi(t)=\frac{\phi(t+\epsilon^+)-\phi(t-\epsilon^+)}{2\epsilon^+}=\frac{1}{2}(\text{forward}+\text{backward})$ These different time discretizations will lead to different equal-time operator orderings(see Ron Maimon's answer in this post ), respectively they are: (a)$\int\mathcal{D}\phi e^{iS}\dot \phi(t)\phi(t)=\langle \dot \phi(t)\phi(t)\rangle$ (b)$\int\mathcal{D}\phi e^{iS}\dot \phi(t)\phi(t)=\langle \phi(t)\dot \phi(t)\rangle$ (c)$\int\mathcal{D}\phi e^{iS}\dot \phi(t)\phi(t)=\frac{1}{2}[\langle \dot \phi(t)\phi(t)\rangle+\langle \phi(t)\dot \phi(t)\rangle]$ With these in mind, we can now get equation $(1)$ from path integral(I'll just show it for the point of equal time, because for $t\neq t'$ there isn't any inconsistency): first I take definition (c) for $\dot \phi$, but define $\ddot\phi$ using forward derivative(which I agree is contrived), so we have $\int\mathcal{D}\phi e^{iS}\ddot \phi(t)\phi(t)\equiv\int\mathcal{D}\phi e^{iS}\frac{1}{\epsilon^+}[\dot \phi(t+\epsilon^+)-\dot \phi(t)]\phi(t) =\frac{1}{\epsilon^+}\\{\langle\dot \phi(t+\epsilon^+)\phi(t)\rangle-\frac{1}{2}\langle \dot \phi(t)\phi(t)\rangle-\frac{1}{2}\langle \phi(t)\dot \phi(t)\rangle\\}\\\ =\frac{1}{\epsilon^+}\\{\langle \dot \phi(t+\epsilon^+)\phi(t)\rangle-\langle \dot \phi(t)\phi(t)\rangle+\frac{1}{2}\langle [\dot \phi(t),\phi(t)]\rangle\\}\\\ =\langle \ddot \phi(t)\phi(t)\rangle+\frac{1}{2\epsilon^+ }\langle[\dot \phi(t),\phi(t)]\rangle=\langle \ddot \phi(t)\phi(t)\rangle+\frac{1}{2\epsilon^+ }\delta^3(\mathbf{x}-\mathbf{x'})\cdots\cdots(5)$ Now we can formally think $\lim_{\epsilon^+\to 0}\frac{1}{2\epsilon^+}=\delta(0)$ because $\delta (t)= \lim_{\epsilon^+\to 0}\,{1\over 2\epsilon^+}\,e^{-\pi\,t^2/(4\,{\epsilon^+}^2)}$. So $(5)$ becomes $$\int\mathcal{D}\phi e^{iS}\ddot \phi(t)\phi(t)=\langle \ddot \phi(t)\phi(t)\rangle+\delta(0)\delta^3(\mathbf{x}-\mathbf{x'})\cdots\cdots(6)$$ The rest is trivial, just apply the spatial derivatives, add it to $(6)$ and apply the field equation, then $(1)$ will be reproduced. The above derivation is mostly due to drake, in a more organized form. Now it's clear that carefully defining time-derivative discretization is crucial to get the correct result, a wrong discretization won't give us $(1)$. However the derivation of DSE makes absolutely no reference to any discretization scheme, but it always gives a consistent result with the operator approach, why does it work so well? Many thanks to who are patient enough to read the whole post! **UPDATE:** Recently I had a lucky chance to communicate with Professor Dyson about this problem. His opinion is that neither these manipulations nor DSE is true math, because of the lack of mathematical rigor of the underlying theory, so there could be situations where DSE might just fail too, but unfortunately he couldn't immediately provide such an example. Although not very convinced( _in the sense that even there's such an example, I still think the "degrees of naivety" of different approaches can be discerned, DSE is clearly more sophisticated and powerful than a direct application of $\partial^2+m^2$_ ), I'd be partially satisfied if someone can provide a situation where DSE fails .


title: A nice overview (and maybe derivation) of the Poincaré transformations of the Vector Spherical Harmonics

text: With $Y_{lm}(\vartheta,\varphi)$ being the Spherical Harmonics and $z_l^{(j)}(r)$ being the Spherical Bessel functions ($j=1$), Neumann functions ($j=2$) or Hankel functions ($j=3,4$) defining $$\psi_{lm}^{(j)}(r,\vartheta,\varphi)=z_l^{(j)}(r)Y_{lm}(\vartheta,\varphi),$$ what are representations of the Poincaré transformations applied to the Vector Spherical Harmonics $$\vec L_{lm}^{(j)} = \vec\nabla \psi_{lm}^{(j)},\\\ \vec M_{lm}^{(j)} = \vec\nabla\times\vec r \psi_{lm}^{(j)},\\\ \vec N_{lm}^{(j)} = \vec\nabla\times\vec M_{lm}^{(j)}$$ ? Does any publication cover all Poincaré-transformations, i.e. not only translations and rotations but also Lorentz boosts? I'd prefer one publication covering all transformations at once due to the different normalizations sometimes used.


title: Proof for angar speed equation

text: I'm struggling to find a solution to a project for college. I have looked through my textbook countless times and googled for days, but I just can't seem to figure it out. The question is that we need to prove the angular speed of a hanging rotating weight is given by the expression: W = root(g/Lcos.theta) Please can you help me or push me in the right direction. Any help would be appreciated. Thanks in advance


title: Calabi-Yau manifolds and compactification of extra dimensions in M-theory

text: I just finished learning M(atrix) theory and the basics of the compactification of extra dimensions. The extra 6 dimensions of superstring theory can be compactified on 3 Calabi- Yau manifolds (because 6 real dimensions means 3 complex dimensions). However, when it comes to M-theory, one cannot compactify on 3.5 Calabi-Yau manifolds, so after compactifying 6 dimensions, where does the extra 1 dimension go? Is it just compactified on a circle, or something like that?


What energy changes take place when you operate a jet-ski?


title: Coordinate and conformal transformations of the FRW metric

text: I'm considering a metric of the following form (signature $(+,-,-,-)$): $$ds^2 = (F(r,t)-G(r,t))dt^2 - (F(r,t)+G(r,t))dr^2 - r^2(d\Omega)^2$$ where $F(r,t)$ and $G(r,t)$ are arbitrary scalar functions. I am trying to find a coordinate and/or conformal transformation to one of the 'standard' Robertson-Walker forms, e.g. $$ds^2 = dT^2 - a(T)^2/(1-kR^2)dR^2 - R^2(d\Omega)^2$$ for any $k=0,-1,+1$, or show that there isn't one. Any tips?


title: How to find Electrostatic Potential Difference?

text: I have a really simple doubt about finding the potential difference in electrostatics. Well, first of all, the definition of potential difference is very clear to me: we take a path between the points of interest and we sum the tangential components of the electrict field $E$ along the path. In equation: $$\Delta V=\int_\gamma \left \langle E\circ \gamma, \gamma' \right \rangle$$ Where $\gamma$ is the path. Well, my problem is just that I'm not really understanding how to use this to calculate for example the potential difference of, for instance, two charged parallel planes a distance $l$ away one from the other. My first step in such a case was to find the electric fields of both planes using Gauss' law. But now what? I have to calculate the potential of each of them doing the trick of using a reference point at infinity, and then subtract? Or I should sum them up and integrate the total field along the path between the planes? I think that this will apply to any charge configuration. Is really the procedure always like this? Thanks very much in advance.


title: Stabilizer formalism for symmetric spin-states?

text: This question developed out of conversation between myself and Joe Fitzsimons. Is there a succinct stabilizer representation for symmetric states, on systems of _n_ spin-1/2 or (more generally) _n_ higher spin particles? By a "stabilizer representation", I mean that:   * every symmetric state (or some notable, non-trivial family of them which contains more than just product states) is represented as the unique +1-eigenstate of some operator or the unique joint +1-eigenstate of a list of operators, where   * each element of this set of stabilizing operators can be succinctly described, as an operator on the larger Hilbert space ( _i.e._  not only as a transformation restricted to the symmetric subspace itself), and    * where the stabilizing operators transform in a nice way in the Heisenberg picture under symmetric local unitaries ( _i.e._  unitary transformations of the form _U ⊗n_). Ideally, one would be able to efficiently describe all sorts of transformations between various symmetric states; but one cannot have everything. The constraint of being a unique +1-eigenstate of the list of stabilizing operators could also be made subject to the constraint of being a symmetric state. (For instance, many states on _n_ spin-1/2 particles are stabilized by a σz operator on a single spin, but exactly one symmetric state is stabilized by that operator. Not that I would expect such an operator necessarily to arise in the formalism...) Does a representation with the above properties (or one close to it) exist?


title: Gauge invariant scalar potentials

text: * If $\Phi$ is a multi-component scalar field which is transforming in some representation of a gauge group say $G$ then how general a proof can one give to argue that the potential can only be a function of the G-invariant function, $\Phi^\dagger \Phi$?  This issue gets especially more confusing when one looks that the situations where $\Phi_{[ij]}$ is being thought of an anti-symmetric rank-2 tensor. Then I think the claim is that the only possible form of the potential is, $V = \frac{m^2}{2}\Phi^{*ij}\Phi_{ij} + \frac{\lambda}{32}(\Phi^{*ij}\Phi_{ij})^2 +\frac{\lambda'}{8}\Phi^{*ij}\Phi_{jk}\Phi^{*kl}\Phi_{li}$   * Is the statement that the above is the only potential that is $G-$invariant for any $G$ and such a $\Phi$?  {..the closest thing that I could think of is that the space of all anti- symmetric rank-2 tensors, $\Phi_{[i,j]}, i,j = 1,2,..,N$, supports a natural representation of $SU(N)$ group..but so what?..}


title: Introduction to neutron star physics

text: I enjoy thinking about theoretical astrophysics because I want to understand black holes. Given that no one understands black holes, I like to ponder the nearest thing to a black hole: a neutron star! I have searched around the web for pedagogical discussions of the structure of neutron stars such as this link from NASA: http://heasarc.nasa.gov/docs/objects/binaries/neutron_star_structure.html, but none seems to be at an advanced enough level for my liking. The problem is that I do not know what literature I should read in order to learn more. What is the current state of neutron star research? What are some good review articles? More specifically, I am curious about theoretical predictions for "starquakes" referenced in the link above, and how they would look to an observer on Earth. I would also be interested in understanding what happens to gas falling into a neutron star -- specifically, if Sol was spiralling to its death by neutron star.


title: How to get started in Astronomy (UK based)

text: I have always been interested in space and astronomy (in my youth - I wanted to be an astronaut). However for various reasons, I never quite got started. I now want to get started - small but steadily. I live in a city, ergo: light pollution is a problem - however, I would like to get a telescope (maybe a second hand one but a good make), maybe join a local astronomy club ? In an ideal world, I will get a "good" telescope which has the following attributes   1. Can be extended to make progressively more powerful   2. Can use one of the opensource astronomy packages (I am a programmer!)   3. Allow me to take photographs  Can anyone provide me with a series of steps to help me finally turn my dream of observing the skies into reality? Note: I am aware that it is very likely that I will have to start with a small, hand held telescope - but I like the idea of a telescope that will "grow with me" - if that is at all possible.


title: Tropical year is 27s/year off from Gregorian year?

text: http://hpiers.obspm.fr/eop-pc/models/constants.html states the tropical year is $365.242190402$ days. The Gregorian calendar's average year is $365.2425$ days (every 4th year a leap year, except every 100 years, except every 400 years). The difference is $0.000309598$ days, which amounts to $26.7493$ seconds. This is much more than the 1 leap second we add every 2-3 years or so. What am I missing?


title: Is there a [set of] rules/patterns that apply to elements

text: > **Possible Duplicate:**   >  Do current models of particle physics explain the chemical properties of > elements/compounds? Is there a rule/pattern, or multiple rules and/or patterns, which describe the properties of an element given the number of protons and neutrons it has. For example a carbon atom which has 6 protons and 6 neutrons, howcan you work out what it will act like, reactivity, if there was a bar of carbon, how could they be arranged and what would its properties be like strength. But the rules would work for any number of protons and neutrons.


title: How are forces "mediated"?

text: I hope this is the right word to use. To me, these forces seem kind of fanciful (except for General Relativity and Gravity, which have a geometric interpretation). For example, how do two charged particles **know** that they are to move apart from each other? Do they communicate with each other somehow through some means? I've heard some people tell me that they bounce together messenger photons. So does one electron receive a messenger photon, go, "Oh hey, I should move in the direction opposite of where this came from, due to the data in it", and then move? Aren't photons also associated with energy, as well? Does this type of mediation imply that electrons give off energy in order to exert force on other electrons? Every electron is repelled by every other electron in the universe, right? How does it know where to send its force mediators? Does it just know what direction to point it in? Does it simply send it in all directions in a continuum? Does that mean it's always giving off photons/energy? I'm just not sure how to view "how" it is that electrons know they are to move away from each other. These questions have always bugged me when studying forces. I'm sure the Standard Model has something to shed some light on it.


title: What are some scenarios where FTL information transfer would violate causality?

text: I've always heard people saying, "Faster than light information transfer can't happen because it would violate causality! Effects can precede their causes!" However, I'm trying to think of a situation where this would happen. I'm sure it has something to do with relativity or something like that. I sort of understand that people going faster perceive time slower. Can someone help illuminate this for me by showing a scenario where causality is clearly violated due to FTL information transfer?


title: What is the mechanism of magnetic core saturation?

text: Why does a magnetic core saturate? What is its actual mechanism?


title: Topology for physicists

text: Which are the best introductory books for topology, algebraic geometry, manifolds etc, needed for string theory?


title: Books for learning Mathematics in Physics?

text: Currently I'm doing Advanced Classical Mechanics courses. I'm finding it hard to understand due to the lack of knowledge in linear algebra, multi variable calculus and other chapters. Can anyone suggest a mathematical book which is dedicated to teaching all the math that is used in physics?


title: Reference request for mathematical physics from an axiomatically rigorous perspective

text: Being a grad student in math, and a rather pedantic one indeed, I was unable to accept many of the things taught to me in undergrad physics courses. I am now trying to learn the applications of geometry to string theory and the applications of probability theory, my main field, to statistical physics. Are there other prominent interfaces between abstract math and theoretical physics? Where can I find these topics explored in a way that would be accepted by a mathematician? (I.e. every object mentioned is a legitimate object or logical statement in ZFC, and every nontrivial claim is proven, no use of unproven conjectures for anything but motivation, and wherever necessary to actually talk about physics of the real world, assumptions that link mathematical ideas (which are merely logical symbols and sets) to what they intend to model are stated in logically precise ways.) In other words I am looking for a "Bourbaki" approach to physics, and wouldn't mind if the book started even as pedantically as to say, for instance, what a physical unit represents in set theory.


title: Mathematical books to become a successful mathematical physicists

text: My understanding of algebraic topology and Riemannian geometry come from Nakahara's _Geometry, Topology, and Physics,_ which I do not think is sufficient. I am first year PhD student, and I want to do string theory at my university. Can you recommend me any other really nice books that I should read over the years.


title: Book for multivariable calculus

text: Hi I want to start learning multi variable calculus specifically for learning electrodynamics. What are some good text books?


title: Prequisite for the Feynman lectures?

text: It obviously requires single- and multi-variable calculus and linear algebra, but what else? And where do you suggest to get that background from?this isn't a duplicate because I'm for the math needed precisely and only for the feynman lectures.


title: Books on representation theory

text: > **Possible Duplicate:**   >  Best books for mathematical background? I'm looking for a textbook on the group/representation theory for a student- physicist. The main questions of interest are representations of SO, SU and the Lorentz/Poincare group in various dimensions (or maybe some other topics that i've missed but important for particle physics).


title: Advice on beginning self learning physics from scratch

text: I am pursuing masters degree in computer applications. I have no formal Mathematics and Physics background but for masters degree entrance examination I have studied senior high school level Mathematics with some introductory college level Mathematics like multi-variable calculus, advance linear algebra etc but that was 2 years back. In my personal opinion computer programming is a monotonous work which is making me bored and from past 2 years (after studying mathematics)and I have a strong urge to self learn Mathematics and Physics. Maths is prerequisite for both computing especially advanced topics (Algorithms, Artificial Intelligence etc) and Physics so I have decided to cover these Mathematical topics first **1.** Linear Algebra by using Introduction to Linear Algebra from Gilbert Strang **2.** Trigonometry by using Trigonometry by Charles P. McKeague and Mark D. Turner **3.** Coordinate Geometry **( _Need Recommendation for book to cover this topic_ )** **4**. Calculus **( _Confused which book to use Thomas' Calculus or Stewart's or some other_ )** And finally Fundamentals of Physics Extended by David Halliday, Robert Resnick and Jearl Walker as my first physics book It will take a lot of time to cover all this therefore I don't want to make any mistake in selecting wrong text for a newB. Can you help me by recommending some good books which i can use with or instead of books mentioned above and a suitable strategy to attain the goal in parallel with my regular studies.


title: Best calculus book for physics

text: Are spivak and apostol calculus book good even from a physics point of view for learning calculus? I have a basic understanding of calculus but want to learn in depth more physics and for this I require more calculus


title: Are there some websites for self learning of advanced mathematics?

text: Are there some websites for self learining of advanced mathematics? For example there is perimeterscholars for self study of theoretical physics, but I haven't found some good websites providing lecture videos of mathematics For example, some great lecture vedios of differential geometry, Lie group , Lie algebra, algebraic topology, partial differential equations and so on.


title: Mathematics for physics resources

text: Looking for book suggestions. I have a good basic understanding of many mathematical concepts but I want to improve to a physicist level. This is mainly because I want to study atmospheric physics (fluid dynamics, gases, quantum mechanics, optics, etc.).


title: Calculus Practice Book for Physicists

text: > **Possible Duplicate:**   >  Best books for mathematical background? I am a college senior looking to apply to graduate school in hopes of becoming a theoretical physicist. One of the things my professor is constantly frustrated with is my ability to do tricky calculations. I'm wondering if anyone out there knows of a good book or online resource that is just basically full of advanced calculus practice problems. Things like messy taylor expansions, gaussian integrals, vector integrals, non-obvious substitutions, etc.


title: Mathematical Physics Book Recommendation

text: > **Possible Duplicate:**   >  Best books for mathematical background? I want to learn contemporary mathematical physics, so that, for example, I can read Witten's latest paper without checking other sources again and again to find some basic definitions and theorems. I know it need a long time and intensive efforts, but are there any good books related so that I can follow them in one or two years? I have learned physics theories that come before the quantum field theory, including general relativity. And I know differential geometry, category, etc.


title: What happens, if a rocket is filled with a vacuum instead of high pressured air?

text: Suppose you put wheels under a compressed air tank ![compressed air tank](http://i.stack.imgur.com/3KYwa.jpg) so that it can move horizontally to the right and to the left. Suppose there is a nozzle on the right hand side of the tank (in the picture on the backside, if you like). If the tank is filled with high pressured air and you open the nozzle, the tank will move to the left. This is how rockets work and one can easily imagine that. **What happens when the tank is filled with a vacuum and you open the nozzle?** My first impression was, that the tank is moving to the right but someone told me, that it would be stand still. Is this true? What is an intuitive explanation for that?


title: Electrode potential of an electrode

text: Suppose we have a voltic cell. In one half cell, we have a zinc electrode (or any other) and in the other we have a hydrogen electrode (or any other). Now, if I say that the electrode potential of zinc is 5 volts, would it mean that it (5 volts) is actually the potential difference between the two electrodes i.e zinc and hydrogen?


title: The probability of finding the electron in the H-atom

text: In the book _Arthur Beiser - Concepts of modern physics [page 213]_ author separates the variables in the polar Schrödinger equation assuming: $$\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$$ then there a statement that the differential od space in the polar coordinate system is: $$dV=(dr)\cdot (d\theta r)\cdot (r\sin\theta d\phi)$$ I understand this, but on the next page there is a statement: > As $\Phi$ and $\Theta$ are normalised functions, the actual probability > $P(r)dr$ of finding the electron in a hydrogen atom somewhere in the > spherical shell between $r$ and $r+dr$ from the nucleus is: $$P(r)dr=r^2|R(r)|^2dr\,\int\limits_{0}^{\pi}|\Theta(\theta)|^2\sin\theta d\theta \, \int\limits_{0}^{2\pi}|\Phi|^2 d\phi=r^2|R(r)|^2dr$$ In this equation i can recognize the differential of volume described above and the wavefunction $\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$. I also know that normalization of the angular functions over the angles returns 1, but I don't understand why there is no integration of the radial part... Can anyone explain a bit?


title: Do eye-glasses decrease the Depth of focus?

text: I was reading up about Depth of Focus and wondered if glasses affect depth of focus. If yes, is it noticeable to the user?


title: Why does a faraday cage protect you from high currents?

text: In an electrostatic case it is clear that that in a space enclosed with a conductor (without charge in it) the electric field is zero. This is often demonstrated in physics shows like on the following image: ![enter image description here](http://i.stack.imgur.com/mKkdX.jpg) However it you have the lighting a current is flowing through the air and through the cage. So wie are not in the electro- **static** situation anymore since we have currents, i.e. moving charges. How can one account in the explanation properly that we have moving charges? Some people say that the fact that the man inside the cage is safe doesn't have to do anything with faradays cage, it's simply because the the cage is a better conductor. Sometimes also the skin-effect is mentioned. So what's true. It would be great do get a detailed and correct explanation of this. Do you have any good references?


title: work done by tension

text: ## The problem statement, all variables and given/known data Consider the following arrangement: ![enter image description here](http://i.stack.imgur.com/Jge7p.jpg) Calculate the work done by tension on 2kg block during its motion on circular track from point $A$ to point $B$. ## The attempt at a solution We know that work done by a force is product of force and displacement. We know the displacement of point of application as 4m. How to find the work done by the tension as it is not constant it is variable! 2nd attempt(calculus approach) The 2 kg block moves along the circle, so its speed is Rdθ/dt. It pulls the string, the length of the string between point O and the block can we obtained with simple geometry at any position θ (ignoring the size of the pulley). The total length of the string is unchanged, so the speed of the 1kg block is dL/dt. http://imgur.com/PbpBpOB Can u help after this


title: How big is an inertial frame?

text: How big is an inertial frame? Consider a huge rod which is rotating about a fixed point in a plane, its length is 1 light year. Thus light from its end closer to the fixed point to the end farther from the fixed point takes one year to reach. Now the angular velocity of the point closer to the fixed point is much slower than the angular velocity of the farther point. Thus the end closer to the fixed point has a relative velocity to the end farther away. At some point in time, the clocks at the two ends are synchronized by sending a light signal to both ends from exactly from the centre of the rod (half a light year from any point). My question is, are the two ends of the rod in the same inertial frame? Is it possible for 1 object to be in two inertial frames simultaneously? A simpler question. A rod is 1 light year long and travelling at a a velocity c/2 along its length. There will be length contraction of the rod by gamma. Now imagine a light source at one end of the rod. The light from one end takes one year to reach the other end (as measured by either end), when the rod is stationary. Now since the distance is contracted when the rod is moving, so must the time be different (as compared to an observer looking at this rod) for the two ends of the rod as light must be measured with the same velocity on both ends. The time must be same at both ends by symmetry, so they are indeed in the same inertial frame. However, if there is length contraction, they will not measure one light year, they should each measure less than one light year. An external observer observing this rod would see the distance as less than one year. But to measure the same velocity of light, must also measure the same time as the ends of the rod, thus implying the observer is in the same frame as the rod? The second part of my question is this. In zero gravity, a person holds a ball in his hand. Thus the person and the ball are in the same inertial frame. Then the person "throws" the ball and as a result, both and ball and the person now acquire a relative velocity to each other (action and reaction). Are the two in the same inertial frame? The third part of my question is this. In zero gravity, can a ship and an observer on the ship be in the same inertial frame? That is, do they share acceleration? Assuming the ship is a plane, when the plane accelerates, the person is floating around, hence the person and the ship cannot share acceleration unless the person is strapped to the ship.Thus in zero gravity, every object must have its own inertial frame?


title: Paraphrasing speed and heat capacity

text: Can we call speed the _change in distance per time_? Further, would you phrase heat capacity as _change in heat per temperature_ or _change in temperature per heat_? The reason for this question is that some people refer to heat capacity by _change in temperature per heat_ and if I were to write down an equation based on that formulation, I would write it down as $C_{[p|V]} = \left( \frac{\partial T}{\partial U}\right)_{[p|V]}$, which is not the way it's usually written.


title: How does quantum world affect us and why should I care about it?

text: We live in a world which is much larger than quantum world. The laws of quantum physics are not valid. While I am pressing the keys on my laptop, I have 100% certainty that I am writing what I really want. Then how is such microscopic world going to affect me? The quantum world is entirely different, perhaps best suited for those Aliens. Then why should I worry about uncertainty and other stuffs happening at infinitesimally small scale?


title: Entropy of a state subject to the action of a set of random unitaries

text: Suppose that we have a known set of unitaries $U_1,...,U_n$ randomly selected from the Haar measure and suppose that each unitary is applied with probability $\frac{1}{n}$ to some input state $\rho$ which is pure and lives in a $d$-dimensional Hilbert space. For $n\rightarrow\infty$ it is clear that: \begin{equation} \lim_{n\rightarrow\infty}H(\frac{1}{n}\sum_{i=1}^nU_i\rho U_i^+)=\log d \end{equation} where $H$ is the von Neumann entropy. However, for small $n$ how would you explicitly compute the entropy of the state? I'll plug some numbers to show an example: if we let $n=2$, $d=2$, this would be equivalent to computing the following average: \begin{equation} E_U\left[H\left(\frac{1}{2} U_1|0\rangle\langle0|U_1^++\frac{1}{2}U_2|0\rangle\langle0|U_2^+\right)\right] \end{equation} I've written $|0\rangle\langle0|$ since by symmetry any pure state will have the same entropy, the average is outside the entropy function because by hypothesis the set of unitaries are known, which means that we can distinguish between each set of unitaries, even if we don't know which unitary from the set has been applied.


title: What is the minimum time period for constellations to change shape?

text: All stars are revolving around the center of galaxy. And so I wonder how long it takes before we can see any noticeable change in the shape of any constellation? What are the factors one will use to find this besides the speed of revolution of the concerned stars? Let us say a noticeable change corresponds to about 30 arc minutes.


title: What is the physical meaning of the Eddington - Finkelstein metric?

text: I want to see a some physical process (experimental) that could explain the many transformations of coordinates into this mathematical procedure. (really two transformations, but i think that is a big number here)


title: Majorara mass and fermion number violation

text: How can it be shown that the Majorana mass violates the fermion number by two units? Can even a Noether charge be defined in presence of Majorana mass term?


title: Could hydrogen liberated from water provide lifting energy which exceeds the energy it took to liberate it from water

text: I was thinking about Hydrogen balloons and that large ones which are used for weather balloons which sometimes go up to 100,000 ft (approx 30km). Then I was wondering, how much potential energy has the balloon gained with the balloon and the weight it carries to get up to 100,000 ft. It seems the object would have a lot of potential energy at that height. If the object was rolled down a ramp from that height, it would generate a lot of energy going down a 30km height ramp. Then how much energy was used to get it to lift, to produce the hydrogen in the first place? So my question is, could there be any situation where the potential energy the balloon and its cargo gained exceed the energy it took to make the hydrogen in the first place? Then, if so, how could a cycle be set up where the lifting energy of the hydrogen is used to liberate more hydrogen and produce energy. Here is another idea, what if the balloon started at the bottom of the ocean, a Electrolysis device is separating hydrogen and oxygen from the water down there. A balloon collects the hydrogen and oxygen and pulls upwards. The balloon is attached to a string which it pulls up and turns a pully (wheel) at the bottom as it goes up. Could the rotation of the wheel gain more energy than the cost to extract the hydrogen. I guess the weight of the string would be a factor to consider as well. My thought is that all of this is very unlikely, as it seems like a perpetual motion device, as the hydrogen and oxygen could be re-combined and it would fall back downwards as water and the cycle would be repeated. The question would be, where does the energy come from? it has to come from somewhere, so this seems very unlikely. I cannot think of where the energy comes from. But can anyone work out the calculations even for a very basic calculation?


title: Besides water, which substances are less dense as solids than as liquids?

text: You can read everywhere about water's extraordinary property of _expanding_ when frozen, thus the reason ice floats on liquid water. What other substances do this? There are claims of mercury, silica, germanium, bismuth, and antimony, but I've had trouble tracking down the data to back these up.


title: charged oil drop in electric field

text: I am currently doing coursework for my A2 physics course. I am dropping a charged oil drop in a horizontal electric field and I was wondering how to calculate how much the droplet would deviate given that the voltage across the plates is 5500 volts. The height I am dropping the drop from is 22 cm, the distance between the plates is 8 cm and I am dropping the drop from the center of the 2 plates. The mass of the drop is 0.01 g and the voltage put through the drop is the same voltage on the plates. Help would be appreciated.


title: Books to understand what's theoretical physics about

text: I'm starting university, but I've not made up my mind yet: I like both physics and maths. I pretty much know what mathematical research is about, but I've no clue about physics. Can anyone suggest some reading (easy stuff) to get an idea of what theoretical physics is all about when it comes to research?


title: $\Delta^+$ decay in GZK process

text: The dominant channels in the GZK process are $$p+\gamma_{\rm CMB}\to\Delta^+\to p+\pi^0,$$ $$p+\gamma_{\rm CMB}\to\Delta^+\to n+\pi^+.$$ According to the pdg, $\Delta\to N+\pi$ makes up essentially 100% of the branching ratio (BR). It doesn't, however, say which process is favored: the proton and neutral pion or neutron and charged pion. My instinct is that they should each contribute about 50%, but I am not sure. So my question is, what are the BRs for each of the processes described above?


title: Derivation of proper acceleration in terms of rapidity

text: In the Wikipedia page for proper acceleration, an equation for proper acceleration in terms of rapidity is given as $\alpha = \frac{\Delta \eta}{\Delta \tau}$, where $\eta$ is the rapidity of the moving frame, and $\tau$ is the proper time, (the time as measured in the moving frame). Does anyone know of a reference that contains a derivation of this? Thanks!


title: Reflected electromagnetic wave relation

text: If incident electromagnetic wave is given as: $$\begin{align*}E_i&=A_e \cos(\omega t + bz)\\\ H_i&=A_h \cos(\omega t + bz)\end{align*}$$ What would be relation for REFLECTED wave? Does it go like this? $$\begin{align*}E_r&=A_e \cos(\omega t - bz)\\\ H_r&=A_h \cos(\omega t - bz)\end{align*}$$


title: A simple question on $SU(2)$ gauge transformations in Wen's papers on projective symmetry group (PSG)?

text: Recently I am studying the projective symmetry group (PSG) and the associated concept of quantum order first proposed by prof.Wen. In Wen's paper, see the last line of Eq.(8), the local SU(2) gauge transformation for spinor operators is deﬁned as $\psi_i\rightarrow G_i\psi_i$, where $\psi_i=(\psi_{1i},\psi_{2i})^T$ are fermionic operators and $G_i\in SU(2)$. Why we define it like this? Since as we know, the Shcwinger fermion representation for spin-1/2 can be written as $\mathbf{S}_i=\frac{1}{4}tr(\Psi_i^\dagger\mathbf{\sigma}\Psi_i)$, where $\Psi_i=\begin{pmatrix} \psi_{1i} & -\psi_{2i}^\dagger \\\ \psi_{2i} & \psi_{1i}^\dagger \end{pmatrix}$, and $G_i\Psi_i$ which is the same as the above transformation $\psi_i\rightarrow G_i\psi_i$ is in fact a spin rotation of $\mathbf{S}_i$, while $\Psi_iG_i$ does _not_ change spin $\mathbf{S}_i$ at all. So in Eq.(8), why we define the SU(2) gauge transformation as $G_i\Psi_i$ rather than $\Psi_iG_i$?


title: Can gravitational potential energy be released in a fire?

text: If one takes a bundle of wood up high to the mountains so its potential energy increases, would there be obtained more heat by burning it?


title: What does it really mean that particle has a spin of up/down? And how is spin actually meassured?

text: I been reading some physics articles (related to the recent discovery of the particle that could be a Higgs boson) posted online and it was talking about electron spin and how it can only have values of either up or down and that always confused me. I know directions of up and down are really arbitrary because in just space there be no up and down. So unless spin orients itself depending on the nearest gravity source, spin of up/down must mean something different then in ordinary English language. I also been confused by the fact that the article claims that you can have right/left spin as a result of a spin measurement: > _Suppose you do measure an electron as spin up, and then try to measure the > left-right spin. Common sense would tell you that that number would be zero, > since you know that the electron is spin up, not left or right, but I warned > you about common sense before. It turns out that a) half the time you'll > measure the electron to be left and the other half you'll get right, and b) > whether it's left or right is completely random._ I probably would understand what is meant by up/down spin if I knew how a spin of a particle is actually measured. (I think i could handle a detailed and precise explanation but a crude explanation will suffice if it gives insight to why spin is up or down and why it can come off as left and right in measurements) Is up down just a name given by physicists to two different types of spins? Or does it have something to do with the actual directions? **Related** What is spin as related to particles


title: Literature on the time reversal operator

text: Time reversal symmetry seems to be a very useful concept and is mentioned in a good number of papers I recently came across. Most of the time people claim that a certain system or Hamiltonian is time reversal invariant and deduce certain properties without going further into details. I have a hard time grasping the entire time reversal symmetry thing and would like to read more on the subject in general. So I was wondering whether anybody had good literature references? Preferably with a lot of applications and examples. I know the mathematical definition, but its applications usually elude me.


title: Calculate Magnetic Flux Density between Two Disc Magnets

text: If I have two disc-shaped magnets (radius r=0.05m, width w=0.03m, Remanance Br=1.06 T) separated by a distance d, how can I calculate the magnetic flux density somewhere between them? I found this webpage but I get a tiny value for B (10^-4 T) and I also have no idea where they get the formula from and whether it is trust-worthy.


title: Can we make any substance that will produce ions at low temprature

text: I am talking about thermal ionization, Is to possible to make any material or is there any element that can be ionized at let say 20 degree centigrade Temperature? I am a computer engineer and into science that much but it is just curiosity, Please correct me If I am talking nonsense. **EDIT :** As per I know a filament of a bulb produces photons when heat applied. My point is can we make any material that will produce photons at less than a room temperature and use photoelectric effect to capture energy of photon and convert it to electricity.


title: Reference for understanding characteristic length and time scales in a system (in particular electronic transport)

text: I am working on the transport properties of two dimensional electron gas in semiconductor heterostructures and am interested in the characteristic length and time scales of the system like elastic scattering time and length, phase coherence length, thermal length, etc. Kindly suggest a good review paper on explaining the significance of each of these scales in relation to fermi wavelength and their effect in gauging the electronic transport properties as a function of the dimensions of our system (like [ballistic (XOR)diffusive] (AND) [classical (XOR) quantum regimes]). As any analysis of a particular property of a **condensed matter system** involves **characteristic length and time scales** , I would be grateful if you could suggest a reference which deals with the problem of finding the scales in a unified framework. else even a reference which deals satisfactorily the electron transport problem also would do good.


title: Determining the decay constant for a damped wave

text: My question is short and simple. If a damped, travelling wave (say on a string) could be described as $y\left( x,t\right) =Ae^{-\gamma x}\sin \left( kx-\omega t\right)$ how could/would one determine the decay/dampening constant $\gamma$ mathematically?


title: Will the siphoning effect help a system pump water upwards if the water's entry and exit points are at the same height?

text: I am looking to pump water from a pool up to a roof for solar heating (black plastic tubing) and then back into the pool with the original source water. Does the gravitational force of the water flowing back down the pipe into the pool assist the pump and therefore decrease the pumps required strength? I have been told that the strength of the pump needed would have to be the same regardless of the exit point's height. i.e. If the water was being pumped into a tank on the roof instead of flowing back to the pool.


title: If you spin a magnet in space, far from any magnet field, would it spin forever, being able to produce electricity forever?

text: This is of course a purely theoretical question and it would take energy to get the magnet moving in the first place but once it's moving in the vacuum of space, with no gravity or magnetic field nearby, could it spin nearly forever (as in billions of years) producing a magnetic field from which you could get electricity? If this wouldn't work, why not?


title: Same momentum, different mass

text: The question is: if   * A bowling ball and ping pong ball    * are moving at **same momentum**   * and you exert **same force** to stop each one   * which will take a longer time? or some?    * which will have a longer stopping distance?  * * * So I think I can think of this as: $$F = \frac{dp}{dt} = m \cdot \frac{v_i - 0}{\Delta t} = \frac{p_i}{\Delta t}$$ Since both have same momentum, given same force and momentum, time will be the same? Is this right? * * * Then how do I do the stopping distance one?


title: Applications of the Linearized Einstein Field Equations (EFE)

text: Look up _linearized Einstein field equations_ anywhere and the first thing you'll see will be a discussion of gravitational waves. Using the linearized EFE's is pretty handy when studying gravitational waves, but it doesn't seem like they are used anywhere else! Is this true? If not, what are the other applications?


title: Nuclear Interaction Stopping Power

text: Hello again question board. I'm in need of some help with my b) question for homework I have. Following question is verbatim: "How thick should a wall of shielding iron be to absorb a 10 GeV/c pion beam. Use the PDG table and the lecture notes to find the necessary parameters. a) Compute the thickness if the ionization loss would be the only source of energy loss. (Hint: make a simple model or use plots from the lecture.) b) The pion may lose energy also via nuclear interaction. The nuclear interaction length is $\text{132.1 g/cm}^2$. Compute the thickness for pure nuclear interaction effects. (Use an intensity reduction of $10^9$.)" I have been struggling with this assignment for the past few days, and for the life of me I can't find any information (aside from it being a real thing, and that the nuclear interaction stopping power being far lower than the ionization stopping power) on how exactly to answer the question, meaning, I can't find any sort of formula to use. Any hints or tips would be much appreciated!


title: Nodal Analysis of an electrical circuit

text: I have several doubts about solving circuits.   1. Can any circuit be solved using Nodal Analysis?   2. If some circuit can be solved using Nodal Analysis, can it be solved using Mesh Analysis too?   3. Why do we need these techniques to solve circuits?


title: How to compensate ray displacement caused by refraction in glass slab

text: I need a nudge in the right direction, i guess (this is not a homework question). I want to calculate the total length of a ray from an emitter to a target which passes through a slab with known properties. Given:   * Position of Emitter and Target $P_\text{Source}, P_\text{Dest}$   * Refractive indices of the slab and surrounding medium $n_1, n_2$   * position and thickness of the slab $d_1$, $d_2$, $d_3$ ![Double refraction on glass slab](http://i.stack.imgur.com/6RHfd.png) Question:   1. What angle of incidence $\theta_i$ is required for a ray cast from $P_{source}$ to intersect $P_\text{dest}$?   2. How long is the path the ray actually takes? I know the incident ray is displaced parallely depending on angle of incidence and refractive indices. I have also found some equation for the determiantion of the offset, but i am still not sure how to apply it to my problem: $$ \begin{equation}\tag{1} \Delta y = d_2 \tan \theta_i \left( 1- \frac{\cos \theta_i}{\sqrt{n^2 - \sin^2 \theta_r}}\right) \end{equation} $$ where $\Delta_y$ is the offset of the ray emerging from the slab. Could you give me a few directions?


title: Finding at a distance from the Earth speed of satellite

text: A satellite at 8000 km from Earth where gravity is 6.4 m/s^2. What is the velocity of satellite? I don't the formula to find speed of satellite.


title: Understanding the Ampere's Law

text: We want to study the magnetic field at point $P$. So, from the figure we take that: ![enter image description here](http://i.stack.imgur.com/xWx3I.png)   1. $\oint_{L_1} B\cdot dl=\mu_0 I_1$   2. $\oint_{L_2} B\cdot dl=\mu_0 I_2$   3. $\oint_{L_3} B\cdot dl=\mu_0 I_2$ The magnetic field contribution of the current $i_1$ at the point $P$ is: $B_1=\frac{\mu_0I_1}{2\pi r}$. And the magnetic field contribution of the current $i_2$ at the point $P$ is: $B_2=\frac{\mu_0I_2}{2\pi r}$. Then, the resulting magnetic field at point $P$ is: $$B = \frac{\mu_0(I_1+I_2)}{2\pi r}$$ But, my question is what happen if I take into account the line $L_3$? Because it also has a contribution $B_3=\frac{\mu_0I_2}{2\pi r}$ at point $P$. Would be erroneous to say that $B = B_1+B_2+B_3$. Does the problem is that $L_3$ is in the same current that the $L_1$ line? If it is so, what happen if $i_1=i_2$ and both wires are in the same circuit? would it be wrong to separately calculate contributions from $L_1$ and $L_2$? I'm a little confused about it.


title: Expanding Universe Balloon Analogy - Anything Similar for Time?

text: It is difficult to imagine the infiniteness of space and how it itself is expanding rather than the universe expanding into something else. A helpful analogy is that of drawing little dots (representing galaxies or some other sub-universal structure) onto a deflated balloon and then blowing it up. The surface expands in all directions, with each dot moving away from every other dot. Although the analogous surface (the outside of the balloon) is effectively 2 dimensional, it's possible to imagine its translation into 3 dimensions. As for time, though, I have a hard time picturing its "before / during / after" states, and I realize those words aren't even accurate. Time supposedly began at the Big Bang and may end at the Big Crunch. But I'm wondering if anyone knows of an analogy for time, similar to the balloon analogy that applies to space. Is there a way to imagine time in some comprehensible way?


title: How would you make 360 degree vision glasses?

text: Animals that have an eye on each side of their head have 360 degree vision so just like with the inverted vision glasses you can buy I'm wondering how you make 360 degre e glasses? I'm thinking of a half periscope setup with a lense on the end on each eye.


title: Quantum chaos in interacting discrete time quantum walk?

text: I have situation where I am simulating discrete time quantum walk (DTQW) for various graphs. I have two quantum walkers on the graph and they can interact with each other by the fact that where the two walkers are co-located on the same node of the graph a relative phase can be introduced. I then measure the entanglement of the two quantum walkers using the Von Neumann entropy. What you find is that two non entangled walkers become entangled over time however the degree of entanglement varies over time in a complex manor. I am investigating if there is any 'quantum chaos' exhibited by the system. So I have been trying to read ' _Quantum Signatures of Chaos_ 'by Haake. As I understand it there will not be any exponential sensitively to initial conditions as this is Quantum Mechanics. There could however be such a sensitivity to the phase of the interaction since this is changing the Hamiltonian. So my question is, what would be an appropriate measure or tool to determine if this system exhibits any quantum chaos in relation to the interaction phase as the parameter of the Hamiltonian which is varied? Here is one of the many papers which explains the background framework of DTQW: http://arxiv.org/pdf/quant-ph/0504042.pdf


title: Can an Ergodic dynamical system approach equilibrium?

text: An ergodic dynamical system $(\Omega,\phi^t,\mu)$ is such that the time average $\bar{f}$ of every function $f\in L_1(\Omega,\mu)$ equal the _space_ average $\langle f \rangle_\mu$, i.e. the system densely cover all the phase space ($\mu$-almost everywhere). Another equal condition of ergodicity is that the only invariant sets ($\phi^t(B)=B$) are the trivial ones (no way of partitioning the phase space), or looking at the $L_1$ space, the only invariant functions ($f\circ\phi^t=f$) are the constant functions. Moreover, we have a stronger property than ergodicity, namely mixing that implies the former. A system is said to be mixing if $$\mu(\phi^{-t}(A)\cap B)\rightarrow\mu(A)\mu(B),\qquad\text{as }t\rightarrow\infty.$$ At the end we have the recurrence, i.e. the system pass through all the points of the phase space infinitely many times. My question arise because in my mind for a system that approaches the equilibrium, there exist a time $T>0$ such that for all $t>T$ the system will spend its future time in a smaller region of the phase space, i.e. there exist a partition of $\Omega$ and then the system cannot be ergodic.


title: Transitions in a magnetic refrigeration

text: The graph below (see attached) shows the measured magnetization against temperature at room pressure for the material Gd and for another material for use in a magnetic refrigerator at room temperature. 1)Calculate the expected change of temperature of a thermally isolated piece of Gd when the field in which it is located slowly reduced from an induction of $H_1$ = 1.2T to $H_2$ = 0.8T starting at a temperature 300K. You may assume that the $M$ versus $T$ curve does not change appreciably with $H$ for $H$ in the range 0.8-1.2T. Additionally, assume that the molar specific heat capacity of Gd is $C_p = 3R J/K/mol$ of atoms, independent of temperature and field. The formula mass of Gd is 157.25g/mol. In a previous question, I showed that $$dT = - \frac{T}{C_{P}} \left( \frac{\partial \mathcal{M}}{\partial T}\right)_{H,P} dH,$$ where $\mathcal{M}$ is the magnetic moment. So, given $C_p$ I need to find the final temperature of the material and also the quantity $\partial \mathcal{M}/\partial T$. The assumptions in the questions indicate that the gradient of the M versus T curve is approximately constant, but I am not sure how to find this value. We are also to assume that $\mathcal{M} = MV$ The graph shows $M/\rho$ vs $T$ which is equivalent to $\mathcal{M}/m$ vs $T$. Many thanks![enter image description here](http://i.stack.imgur.com/Qrd3K.jpg)


title: Who foots the (magnetic) energy bill?

text: Gravitational attraction and electrostatic attraction/repulsion are intrinsic properties of matter, any particle (electron, proton) for some unknown reason can produce KE at a distance. But magnetic attraction/force is not an intrinsic property of matter, a charged particle generates a magnetic field/flux and a magnetic force only when it is moving: higher velocity = much higher force. The definition of KE says that it is _'work done to accelerate an object'_ , energy spent only to make it move, and does not mention the generation of other forces/energy or doing 'extramural' work. _[Electrons moving in a current produce magnetic induction that makes an electric appliance do work, who/what is spending the necessary energy to produce such work? Voltage (the difference of potential) coming from the mains provides the energy to accelerate the electrons, not the energy to blend your fruit. Same voltage would produce equivalent v/Ke if the electron is accelerated in a vacuum (such as in a synchrotron, where there is no fruit). But this is difficult to prove.]_ **Edit** : I will not reply to any comment. They are attributing to me statements I never made. Now, to avoid technical complications ( _voltage_ , wattage etc,) that could trick me, forget the previous example, **let's consider another, simpler case:** An electron is travelling at high speed (say,0.9 C). If is moving near another electron, (proton, positron or a live wire) _it can make anything move, acquire KE_ , it **can do work**. When v approaches c, the attractive magnetic force gets so great that it _equals the huge electrostatic repulsion._ All the issues you have raised (intrinsic spin, magnetic field, electromagnetism etc., some comments have been deleted) are irrelevant here. If those properties exist they exist even when the electron is at rest. When the electron is at rest, it still has spin, nevertheless it is **not able any more** to do work. If this is an irrefutable fact, then, how come it can do work when it is moving, where is the necessary energy coming from?


title: What is it that undulates in a particle?

text: When there is a wave, something is undulating. In the example of a rope, the rope is what undulates. In the case of a ripple on a pond, the water is undulating, and when a sound wave propagates, the air is undulating. The question is: in the case of a particle, what undulates?


title: Degree of ionization and Saha equation

text: Say you want to calculate degree of ionization for different gases in atmosphere of a star with abundances similar to those in Sun (let's assume you only have hydrogen, helium and sodium) over the temperature range (from 2000 K to 45000 K for example) using Saha equation: $$\frac{n_{i+1}}{n_i}=\frac{g_{i+1}}{g_i} \frac{2}{n_e} \frac{{(2\pi m_e)}^{3/2}}{h^3} {(k_B T)^{3/2}} e^{-\chi /k_B T}$$, which you write down for all three elements and of course next to abundances and temperature you also know ionization potentials $\chi$ for each element. How can one calculate electron density in that case and how does it change? I understand, that at lower temperatures number of electrons is equal to number of ionized sodium atoms since it is the easiest to ionize (and in general $n_e=n_H^1+n_{He}^1+n_{Mg}^1$, where 1 means first level of ionization) but that doesn't help much. And additional question: should higher levels of ionization be included, given the temperature?


title: Why does the gas get cold when I spray it?

text: When you spray gas from a compressed spray, the gas gets very cold, even though, the compressed spray is in the room temperature. I think, when it goes from high pressure to lower one, it gets cold, right? but what is the reason behind that literally?


title: Why can't a piece of paper (of non-zero thickness) be folded more than $N$ times?

text: Updated: > _In order to fold anything in half, it must be $\pi$ times longer than its > thickness, and that depending on how something is folded, the amount its > length decreases with each fold differs._   >  – Britney Gallivan, the person who determined that the maximum number of > times a paper or other finite thickness materials can be folded = 12. Mathematics of paper folding explains the mathematical aspect of this.   I would like to know the physical explanation of this. Why is it not possible to fold a paper more than $N$ (=12) times?


title: Are the cosmic horizons observer-specific?

text: It is known that all observers will agree on the position of the black hole event horizon. But what about the cosmic horizon of the de Sitter space? Can one say that the horizon of scientist1 is different from the horizon of scientist2? If so, it turns out that the scientists are researching different universes: the information available for scientist1 is forever lost for scientist2. This may lead to the information loss paradoxes if the observers can communicate. This question was sparked by the answers to this question: Can matter leave the cosmic horizon?


title: What is a non-linear capacitor?

text: I'm new here. I have a (maybe dumb) question: What are non-linear capacitors? I'm given a circuit including a capacitor and the question says > _The given capacitor is non-linear with the characteristic equation > $g=v^3$._ But I don't know what this equation means.


title: What is the event in history where iterated functions became appropriate for modeling physics?

text: Wolfram as well as Aldrovandi and Freitas 1 maintain that iterated functions $f^t(x)$ are a valid alternative to PDEs for modelling physics. Instead of just citing 1, I want to be able to cite the initial paper and author who justified using iterated functions in physics. I do not mean simply modeling a problem in physics, I mean modeling physics itself. I study the mathematics and structure of $f^t(x)$. It is my contention that if $f^t(x)$ has universal properties, then those properties must occur in physics. Schroeder wrote Über iterirte Functionen, the first paper on dynamical systems in 1871, but this appears to be a paper of pure mathematics. Poincare is the first person I think used the dynamical systems of iterated functions to study physics. R. Aldrovandi and L. P. Freitas, Continuous iteration of dynamical maps, J. Math. Phys. 39, 5324 (1998)


title: Design a quantum circuit from a matrix

text: I have unitary matrix and I would find the quantum circuit associated. There are 3 qubits input so it's a 8x8 matrix but it's not a simple operation. The number of gates is not specified. Is there a universal method ? Matrix decomposition with a software ? Thank you!


title: Why does the speed of light within a solid depend on frequency?

text: Different frequencies of light travel at different speeds through solids, which along with Snell's law allows for rainbows. Has this phenomenon of variable speeds been predicted through derivations? What does it tell us about the interactions that occur when light travels through a solid?