title: Classical and quantum probabilities in density matrices

text: In textbooks, it is sometimes written that a mixed state can be represented as mixture of $N$ (I assume here $N<+\infty$) **quantum** pure states $|\psi_i\rangle$ with **classical** probabilities $p_i$: $$\rho = \sum_{i=1}^N p_i |\psi_i \rangle \langle \psi_i|\quad (1)\:.$$ Above $p_i \in (0,1]$ and $\sum_i p_i =1$ and a do not necessarily assume that $\langle \psi_i|\psi_j\rangle =0$ if $i\neq j$ but I require that $\langle\psi_i |\psi_i\rangle =1$ so that $\rho \geq 0$ and $tr(\rho)=1$. (There is another procedure to obtain mixed states using a partial trace on a composite system, but I am not interested on this here). I am not sure that it makes any sense to distinguish between **classical probabilities** embodied in the coefficients $p_i$ and **quantum probabilities** included in the pure states $|\psi_i\rangle$ representing the **quantum** part of the state. This is because, given $\rho$ as an operator, there is no way to **uniquely** extract the numbers $p_i$ and the states $|\psi_i\rangle$. I mean, since $\rho = \rho^\dagger$ and $\rho$ is compact, it is always possible, for instance, to decompose it on a basis of its eigenvectors (and there are many **different** decompositions leading to the same $\rho$ whenever $\rho$ has degenerate eigenspaces). Using non orthogonal decompositions many other possibilities arise. $$\rho = \sum_{j=1}^M q_j |\phi_j\rangle \langle \phi_j|\quad (2)$$ where again $q_j \in (0,1]$ and $\sum_j q_j =1$ and now $\langle \phi_i|\phi_j\rangle =\delta_{ij}$. I do not think there is a physical way to decide, _a posteriori_ , **through suitable measurements of observables** if $\rho$ has been constructed as the incoherent superposition (1) or as the incoherent superposition (2). The mixed state has no memory of the procedure used to construct it. To pass from (1) to (2) one has, in a sense, to mix (apparently) classical and quantum probabilities. So I do not think that it is physically correct to associate a classical part and a quantum part to a mixed state, since there is no a unique physical way to extract them from it. Perhaps my impression is simply based on a too naively theoretical interpretation of the formalism. I would like to know your opinions about this issue.


Edit: Why do people look different in a photo and in a mirror? What is more accurate of the two? P.S. I've edited this question and I suppose it is no longer opinion based.


title: Having trouble with a homework problem involving rotation

text: This is for a past homework assignment so it's already been solved. > _We wrap a light, nonstretching cable around a 9.00kg solid cylinder with > diameter of 34.0cm . The cylinder rotates with negligible friction about a > stationary horizontal axis. We tie the free end of the cable to a 14.0kg > block and release the block from rest. As the block falls, the cable unwinds > without stretching or slipping._ > > _How far will the mass have to descend to give the cylinder 470J of kinetic > energy?_ **Attempt** $K=I\omega^2$ $\sqrt{\frac{K}{mr^2}}=\omega$ $\sqrt{\frac{470}{9*.17^2}}$=42.51 $v=\omega r$ $v=42.51*.17$ $v^2=2a(x)$//x is ($x-x_0)$ where $x_0=0$ $\frac{v^2}{2a}=x$ $x=\frac{7.23^2}{2*9.81}=2.66$ Actual answer 14.1m Perhaps someone can correct the error of my ways?


title: Do neutrinos of any flavor get trapped in black holes?

text: This question has been bothering me a bit. I know that neutrinos have super small mass and they interact via the weak force. Since they have a non-zero mass, they should be affected by black holes and their paths should be affected by them. Suppose we have a neutrino of any flavor traveling directly to the coordinates of the singularity of a black hole... or its cross sectional impact includes the black hole coordinate. Basically, its going straight towards a black hole... Given that a black hole has so much mass and is so dense, it surely must be able to interact with a neutrino, right? What are the conditions for neutrinos to get trapped in a black hole, or not?


title: Possible to generate an electromagnetic field from moving an object through a magnetic field?

text: Is it possible to generate an electromagnetic field from a stationary rare earth magnet with a hole in it by passing an object through the hole? By definition, a Lorentz Force is the force on a particle which moves with velocity through an electric field and magnetic field. Would it be some how be possible to instead move a particle with force through a magnetic field to generate an electric field? (Where the magnetic field were not changing with time such as a stationary rare earth magnet with a hole in it)


title: Geodesic distance in de Sitter space

text: Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for simplicity. Given two points in de Sitter space (denoting de Sitter coordinates by lower case $x$, as opposed to capitalized Minkowski coordinates $X$) we define the so-called hyperbolic distance $$P(x,x')=g_{\mu\nu}x^\mu x'^\nu$$ It is often (between eqn. 32 and 33, between eqn. 2.2 and 2.3, equation 3) said that this is related to the geodesic distance $$ D(x,x')=\int_x^{x'}d\lambda\sqrt{g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx'^\nu}{d\lambda}}$$ by $P=\cos D$. This is independent of the specific coordinates one chooses on de Sitter space. However, I cannot seem to understand how to show this. Can anyone here perhaps enlighten me? Any help would be much appreciated.


title: Why don't we have more elements?

text: By looking at the number of subatomic particles there seem to exist, there should be thousands of element configuration combinations possible. But we have found just over hundred elements to exist. What is the explanation for this?


title: Detecting absolute motion with Doppler (reconciling receiver frequencies)

text: Suppose a transmitter emits a pulse of light every $T$ seconds. The spacial distance between pulses is $cT$. Suppose the receiver is approaching it with speed $v$. ![enter image description here](http://i.stack.imgur.com/M2EGq.png) Because, after receiving the first pulse, the next pulse is at distance $cT$ and it will be covered by both light and receiver approaching each other at speed $(v+c)$ so that the next pulse will be detected after time $$t_1 = {cT \over v+c}$$. Particularly, when receiver is moving at v=c, we have $t_1 = T/2$ -- the receiver detects twice the frequency emitted. Suppose that light source is moving instead ![enter image description here](http://i.stack.imgur.com/a7bof.png) Now, at a time the first pulse reaches the receiver, the next pulse is closer, by distance $cT-vT$ because the transmitter has traveled $vT$ meters when light traveled $cT$. This distance, $cT-vT$, will be closed by light in $$t_2 = {(c-v)\times T \over c}$$ seconds. Particularly, when transmitter speed is equal to the speed of light, v=c, the observer detects infinite frequency ($t_2 = 0$). By measuring the frequency we can detect who is moving, receiver or transmitter. Do you know that this contradicts to the principle of relativity and Michelson-Morley experiment which both say that we must not be able to detect who is moving? Einstein has corrected this by time dilation. Can you show how Lorentz arises here naturally for the Doppler correction? I can guess that time dilation can be modeled by scaling the time period of moving body. That is, when receiver is moving, we can have the observed frequency of $t_1 = {cT \over (c+v) } \times {1 \over f_1(v)} $ and when transmitter is in motion then true observed period $t_2 = {(c-v) T\over c} \times f_2(v)$. I have placed $f_1(v)$ into denomitator because receiver slowdown can be considered as transmitter's speedup. Now, receiver must observe the same frequency regardless of who is moving, $${c \over (c+v) } \times {1 \over f_1(v)} = {(c-v) T\over c} \times f_2(v)$$ or $$f_1(v) \times f_2(v) = {c^2 \over c^2-v^2}$$ which looks suspiciously identical to the square of the Lorentz factor squared. Should I guess that $f(v) = f_1(v) = f_2(v) = \sqrt{1 \over 1 - v^2/c^2}$?


title: How to capture electomagnetic radiation/waves?

text: If I wanted to find out what kind of electomagnetic waves "travel" through my room at which frequency, what kind of equipment would I need? Suppose I want to view frequencies from 0 Hz to 6 GHz.


title: Smooth trajectory on a smooth manifold

text: Physicists talk about a smooth trajectory of a particle on a smooth manifold and they label it as q(t) where q_1(t)....q_n(t) are component functions coming from the homeomorphism. I don't see how we can meaningfully talk about the whole trajectory this way as it might happen that the particle moves from one point to another point on the manifold and it might happen that the coordinate system at this point is different from that of previous point. How do we ensure that these two patch up and we can meaningfully talk about q(t) independent of the location of particle?


title: Is there a way to create an artificial solar eclipse?

text: I heard this story, where they celebrated the birthday of the now defunct North Korean dictator Kim Il-sung in the 1970s and as a birthday present they created through some very complex artillery maneuvers an artificial total solar eclipse over Pyongyang. At that very moment, the dictator stepped out of his palace, in front of the crowd in a suit covered with reflecting material and had giant reflectors directed at him, so he practically 'outshone' the sun... While this seems plausible in view of the megalomania and extreme personality cult we all know about, I still wonder whether that is technically feasible. (I'm not looking for an answer whether the story is true or not.) So my question is whether there is any possibility to have an artificial, man- made total solar eclipse and if so, how?


title: How can a Population III star be so massive?

text: How can a Population III star have a mass of several hundred solar masses? Normally the limit is about 100 solar masses.


title: Determining energy of gamma-rays after alpha-decay of Am-241

text: So it turns into Np, and electrons just falling into 'free new' levels and emmiting, right? ![enter image description here](http://i.stack.imgur.com/b6vyZ.jpg) Give me a link where to read, please, if it's very easy to answer.


title: Glass pipe cutting

text: I want to know how to quickly create the **straightest possible breaks in glass pipes** **I apologise** if this is only borderline suitable for a physics forum - I just hope experts with a lot of experience in stress, strain, thermal expansion, material science and similar topics might have some insight into. **The glass being cut** : in short, all kinds. Varying quality, some tempered and/or annealed. Varying thickness, varying diameter, varying types - lime soda, borosilicate. Typical diameter 20mm to 40mm, thickness 1-2mm. **So far, I've had most success** simply using a glass scoring tool which I use to manually score round the outside. Then I apply a bending force at that cut. I have less than 50% success rate. **I found videos on youtube where amateur glass-workers** use various combinations of scoring, heating over flames, dunking in water hot or cold, applying ice. But the results seem variable, and I have had even worse success applying these methods. **I've heard of professional glass tube cutting machines** that use a flame and water. I don't know if they also score the glass. I couldn't find any such machines on the net, let alone how they work. How would you design such a machine to work? I presume the key factors are glass tolerates higher compression than tension, and glass is not a good conductor of heat. For example, would it make more sense to apply heat evenly around the tube in a narrow band, while next to it, applying water in a narrow band? Or applying one followed by the other? Or perhaps heating on one side of the tube and cooling on the other? Thanks! **Addition:** After seeing this post: **Why does glass break at the line where you score it?** Perhaps it would make sense that heat is applied at the score line, equally and simultaneously around the circumference? If so, where would the water be applied? I'm clutching at glass straws with this one. **Further addition:** This PDF on glassworking, with references to M P Groover, “ _Fundamentals of Modern Manufacturing_ ", explains that tubes are made in extremely long lengths, and implies they are cut by scoring and then breaking along the score line. But it doesn't say how exactly the breaking is done. I should see if I can find a copy of that book.


What is the mass of the LEGO figurines being launched with spacecraft Juno? How much additional fuel will be needed to get them to Jupiter?


title: How does the Luminosity Function relate to the tristimulus sensitivity function?

text: In colorimetry, the irradiance spectrum is weighted with the luminosity function to obtain the perceived luminosity, and the tristimulus sensitivity functions to obtain the perceived RGB-representation. How do these functions (just one scalar for each wavelength) relate to each other? I only found these weighting functions (as numerical arrays) in the matlab package pspectro. There however, the sensitivity function for gamma (= green) is completely identical to the luminosity function, which seems odd. Is it correct?


title: when to consider linear kinetic energy and when to use angular kinetic energy?

text: I saw a problem about a pivoting rod online (http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_RotationalDynamicsPivotingRods.xml), I am thinking the problem if we initially hold the rod horizontally with one end hinged on the wall without friction. When I let go, the rod rotate all the way to the vertical position (downward). If we want to consider the instant speed of the center of mass of the rod when it rotated to vertical position downward. In this case, the energy conserved since no friction in the pivot and we ignore the air resistance. So $$G.P.E = \frac{mv^2}{2}$$ But in that webpage, it consider the angular kinetic energy instead. But in the text, it said that I should consider both linear and angular kinetic energy at center of mass for a rotational object, $K.E. = \frac{MV_{CM}^2}{2} + \frac{I_{CM}\omega^2}{2}$. It is confusing to me because when the rod vertical, the speed is pointing to the right so the speed of the center of mass is linear. So which one is correct?


title: Propagator of a scalar in position space

text: In his lecture on Supersymmetry and Grand Unification, Leonard Susskind "derives" the propagator for a scalar field from dimensional analysis. He says for a particle going from $x$ to $y$ (where x and y are four-vectors), the (massless) propagator is: $$ \qquad\quad \left\langle0\right|\phi(y)\, \phi(x) \left|0\right\rangle \propto \frac{1}{|x-y|^2} \qquad (1) $$ I'm a bit confused about this. I know in momentum space, the propagator is $$ G(p) = \frac{1}{p^2-m^2+i\epsilon}\,. $$ His expression is probably just in position space, but the expressions I've found for the position space propagator are much more complicated (e.g. Wikipedia). Is equation (1) wrong or am I missing something? (I know the first one is massless, and the second one massive. But isn't he missing at least an integral?) Background: I am trying to formulate a short explanation of renormalization, and I like his overall argument and would like to follow it (its for the theory part of an experimental thesis, so it can be general and sketched, but should be correct). Susskind looked for a term with the correct units ($L^{-2}$) that you could construct from the available variables, and that makes sense physically (the amplitude for detecting a particle at $y$ is higher the closer it is to where it was emitted, $x$). The result is simple, but seems not correct enough to wright it down (e.g. into a thesis). Is there a way to replace (1) with something more correct, but still keep it simple and intuitive?


title: Do gamma matrices form a basis?

text: Do the four gamma matrices form a basis for the set of matrices $GL(4,\mathcal{C})$? I was actually trying to evaluate a term like $\gamma^0 M^\dagger \gamma^0$ in a representation independent way, where $M,M^\dagger$ are $4\times 4$ matrices.


Can special/general relativity be derived from the standard model? For example the time dilatation in strong gravitation? My feeling is yes, but I am not quite sure.


title: Lagrangian formulation for relativistic quantum fields

text: The Lagrangian for a real scalar field is: $$\mathcal{L}=\frac{1}{2}\eta^{\mu \nu}\partial_{\mu}\phi\partial_{\nu}\phi-\frac{1}{2}m^2\phi^2 $$ How can I derive the dynamics of this field from this Lagrangian?


title: There is no such thing as magnetism?

text: Here's an interesting "proof" that there is no such thing as magnetism. I know the answer but I love this so much I had to ask it here. It's a great way to confuse people! As we all know, $$\nabla \cdot\vec{B} =0$$ Using the divergence theorem, we find $$ \iint_S \vec{B} \cdot \hat{n} \, dS = \iiint_V \nabla \cdot \vec{B} \, dV = 0$$ Since $\vec{B}$ has zero divergence, there exist a vector function $\vec{A}$ such that $$\vec{B} = \nabla \times \vec{A}$$ Combining the last two equations, we get $$\iint_S \hat{n} \cdot \nabla \times \vec{A} \, dS = 0$$ Applying Stokes' theorem, we find $$\oint_C \vec{A} \cdot \hat{t} \, ds = \iint_S \hat{n} \cdot \nabla \times \vec{A} \, dS = 0$$ Therefore, $\vec{A}$ is path independent and we can write $\vec{A} = \nabla \psi$ for some scalar function $\psi$. Since the curl of the gradient of a function is zero, we arrive at: $$\vec{B} = \nabla \times \nabla \psi = 0,$$ which means that all magnetic fields are zero, but that can't be! **Can you see where we went wrong?**


title: Which physics subjects should a math major follow if s/he's interested in Smart Grid Networks?

text: I study mathematics and I would like to work on Smart Grid Networks in the (near) future. I would like to do so by applying optimization theory, percolation theory, Markov chains and more to problems that are related to Smart Grid Networks. However, I don't know anything about physics. Would it be useful for me to learn about a couple of physics subjects that are related to Smart Grid Networks? If so, which ones?


title: Gravitational binding energy and integrated potential energy not the same?

text: Before looking up the formula for the gravitational binding energy of a uniform sphere, I simply figured that the general formula for binding energy of an arbitrarily-shaped mass distribution would be $\left\langle V,\rho\right\rangle $, where $V$ is the potential as a function of space due to the distribution, $\rho$ is the density distribution as a function of space, and $\left\langle ,\right\rangle $ is the inner product (ie, integral over all space). Going ahead for the special case of a uniform sphere of density $\rho$ and radius $R$, I used the well-known result for the potential inside of a sphere of uniform density, $$V(r)=\frac{2}{3}\pi G\rho(r^{2}-3R^{2})\mbox{ for }r\leq R. $$ I then computed the inner product, $$\left\langle V,\rho\right\rangle =\int_{0}^{R}r^{2}dr\int_{0}^{\pi}\mbox{sin}(\theta)d\theta\int_{0}^{2\pi}d\phi V(r)\rho=-\frac{32}{15}G\pi^{2}R^{5}\rho^{2}=-\frac{6GM^{2}}{5R}, $$ which is twice the correct result, $\frac{-3GM^{2}}{5R}$. (The last equality follows from $\rho=\frac{M}{4/3\pi R^{3}}$). I fully understand the geometric proof that the binding energy of a sphere is $\frac{-3GM^{2}}{5R}$ that proceeds by successively moving shells in from infinity, but was a bit confused when the inner product approach gave an extra factor of 2. My question is as follows:   * Is the extra factor of two in $\left\langle V,\rho\right\rangle$ due to double-counting the interaction energies?   * If so, is the correct formula for the binding energy of an arbitrary mass distribution $U=\frac{1}{2}\left\langle V,\rho\right\rangle$? I am trying to estimate the total energy released when two planets which are just barely touching each other collapse to form a single large sphere, and in the course of the derivation this issue sprung up. Any help explaining the extra factor of 2 would be greatly appreciated!


title: Where does gravity get its energy from?

text: I would like to know where gravity gets its energy to attract physical bodies? I know that the law of conservation states that total energy of an isolated system cannot change. So gravity has to be getting its energy from somewhere, or else things like hydropower plants wouldn't be able to turn the power of the falling water into a spinning rotor. Just to be clear, Lets create an example: Lets say we have two objects with equal mass close to each other. So gravity does its job and it pulls each other closer, this gets turned into kinetic energy. This is where I'm lost. According to the law of conservation energy can't be created or destroyed and the kinetic energy comes from the gravitational pull so where does the gravitational pull gets its energy. If that energy isn't being recycled from some where else then that means you have just created energy, therefore breaking the law of conservation.


title: What causes electron to orbit the nucleus in an atom?

text: What causes the electron to orbit the nucleus? Which is the force that causes it to do so? Is it related to the Electro - Magnetic force? .


title: Where can I find a device or how can I make a device that measures only Alpha particles?

text: Are there special muller tubes that only measure alpha for example?


title: Controllable faster-than-light phase velocity

text: This is not another question about faster-than-light travel or superluminal communication. I totally appreciate the speed limit capped by physical laws (or theories.) Just curious, since there is no limit for phase velocity, is there any way to generate a wave with controllable phase velocity higher than speed of light?


title: Potential functions

text: Can someone please explain what a potential is? Example. velocity potential in ideal flows, acoustic potential (gradient of which gives the particle velocity in a sound wave). Whenever I see potential functions complex analysis is applied to compute integrals, complex functions for conformal mapping. I vaguely understand that potential functions are independent of path and in complex plane the integration around a contour is independent of path as well (the integration depends only on the end points, hence in a closed curve say region $Z$, if function, $f$ is analytic then integration of $f$ over $Z$ is 0). Can you please explain on this?


title: Bose-Einstein condensate in 1D

text: I've read that for a Bose-Einstein gas in 1D there's no condensation. Why this happenes? How can I prove that?


title: Do symmetries increase the number of conserved quantities?

text: Let us consider a classical mechanical system of N particles in a constant external field. We have 3N coordinates and 3N velocities, so totally 6N unknown variables. We have 6N ordinary differential equations of the first order for them or 3N equations of the second order. It is known that such a system has 6N-1 conserved quantities, see Landau-Lifshits, V. 1, Classical Mechanics, Chapter about Conservation Laws. In absence of symmetries these conserved quantities are rather complicated analytical expressions. In case of some symmetries one can construct conserved quantities **additive on particles**. Everybody knows about total energy, momentum, and angular momentum conservation laws. But the number of conserved quantities remains to be 6N-1. It means the symmetries may help us construct "less messy" integrals of motion than in general case. We obtain simplification of analytical expressions but not **new** integrals of motion in case of symmetries. The question I wrote in title has, in my opinion, the following answer: **Symmetries do not lead to _additional_ conservation laws but to _simplification_ of existent ones.** To a great extent it is due to simplification of equation system in case of symmetries. An example of integrals of motion in 1D case: ![1D Integrals of motion](http://i.stack.imgur.com/Nw5Su.jpg)


title: CFT on a torus and diagonal modular invariants

text: Suppose we have a CFT which is sigma model with a torus target $T^2$ at a rational value of the moduli. Does it always give rise to a diagonal modular invariant?


title: Can electrons coincidentally flow along a circuit to cause current?

text: My understanding of circuits which are not supplied an e.m.f. is that the electrons randomly just flow about in random directions, and since there's so many of them, probability dictates that any forwards or useful movement is cancelled almost perfectly by the negative or unwanted movement. If this understanding is correct, is it theoretically possible for the electrons to, under an extremely low probability, mostly flow in the correct direction, and generate a current, perhaps lighting up a lamp? I'm talking even probabilities like 1x10^-1000, just wondering if it is at all possible. This seems wrong to me and if anyone could explain why this is not possible, or the flaw in my logic, that would be greatly appreciated. Apologies if there's some huge hole in my logic, or I'm being extremely stupid, I'm a student studying Physics below university level and thus know little more than basic outlines of Physical theories.


title: requirements for hydrogen fusion

text: What are the requirements for hydrogen atoms to go through fusion? Is it a ratio of heat to pressure or are there specific heat and pressure values that must be met (per atom or per mole?) Are there other requirements?


title: Inflation in a closed universe or a stage 1 multiverse?

text: With the discovery of gravitational waves, Max Tegmark has been using this to promote his level 1 multiverse in that the universe is open (non-compact) and everything duplicates. My question is, are there any inflation models for a closed (compact) universe or do they all lead to what Tegmark is saying? An open self-repeating stage 1 multiverse? Does the universe have to be infinite in size for inflation to work?


title: Potential energy of an infinitesimal length of elastic rod

text: I am having an embarrassingly hard time with the derivation for the potential energy of an infinitesimal element of an elastic rod of area A. The picture shown below is an element of the rod that has been extended by $du$ by the force $F$. ![enter image description here](http://i.stack.imgur.com/O7cCF.png) I've tried this derivation several times and have yet to obtain the factor of $\frac{1}{2}$ in $$dU=\frac{1}{2}AY\big(\frac{du}{dx}\big)^2dx$$ which is given in my lecture notes. Here is my best attempt so far: From the stress strain relation, $\sigma=Y\epsilon$, where $Y$ is Youngs modulus we obtain: $$\frac{F}{A}=Y\frac{du}{dx}$$ I asked a similar question a few days ago, and based on that response I've assumed that the work done in extending the rod element from length $dx$ to $du+dx$ is $$dW=F\big[ (du+dx)-dx\big]$$ $$=YA\frac{du}{dx}du$$ And I can make it look more like the answer given in my lecture notes if I divide and multiply by $dx$: $$dW=YA\big(\frac{du}{dx}\big)^2dx$$ And I am assuming that $dW=dU$ here ($F=-\frac{dU}{du} $ but forget about the negative sign) I have tried other approaches but they make even less sense to me. A formula that I think will come in handy is the deflection at section x of a rod: $$\delta(x)=\frac{F}{AY}x $$ and I think an integral will come in to play but I'm not sure what I'm integrating over any more (I'm dealing with an infinitesimal element of the rod). So how do I use the infinitesimal Work to find the infinitesimal change in potential energy here to get that factor of $\frac{1}{2}$ (assuming that it does in fact belong in $dU$)?


title: Steam and Electricity

text: If an electrical conduit with sufficient voltage were cut and lay naked inside a chamber of steam, would an electrical arc occur? As a secondary question, if the steam were subject to a stabilized pressure wave, in what manner, if any, would an arc occur?


title: Water and electricity? Hot or Cold?

text: Is hot water or cold water more conductive for electricity or is it the same regardless?


title: Do spacecraft engines suffer from carbon accumulation the way typical petrol/kerosene engines do?

text: Just wondering whether the spacecraft engines/drives, or their booster rockets accumulate carbon the way car/truck engines do. What about ion/methane drives?


title: Why can one bend glass fiber?

text: Why can one bend glass fibers without breaking it, whereas glasses one comes across in real life is usually solid? Is there also a good high-school level explanation of this?


title: What can be done to increase the strength of a given electromagnet?

text: There's a lot of information online about increasing the strength of an electromagnet with more turns, different cores, etc, but not much about factors in the power supply that affect the strength of the magnet. I've got a commercial electromagnet rated for 12VDC that's supposed to produce 200 lbs of pull. What factors in the power supply will maximize this magnet's strength? Thanks!


title: Is there a general relationship between the conformal weight of a field and its (classical) scaling dimension?

text: A field $\phi(z)$ has the conformal weight $h$, if it transforms under $z\rightarrow z_1(z)$ as $$ \phi(z) = \tilde{\phi}(z_1)\left(\frac{dz_1}{dz}\right)^h $$ The (classical) scaling dimension can be obtained for each field by appearing in the Lagrangian by making use of the constraint that has to be dimensionless, resulting for example in $$ [\phi] = [A^{\mu}] = 1 $$ for a scalar and a gauge field or $$ [\Psi_D] = [\Psi_M] = [\chi] = [\eta] = \frac{3}{2} $$ for Dirac, Majorana, and Weyl spinors. Are these two concepts of scaling dimension and conformal weight somehow related?


title: Are third derivatives of metric perturbations zero?

text: I'm working on a problem related to fluid perturbations of stars. I'm following this paper. They start with the Einstein equation: $$G_{\alpha \beta} = 8 \pi G T_{\alpha \beta}$$ and then perturb the metric, and the stress-energy of the matter (which they assume to be a perfect fluid). The metric is basically rewritten as $$g_{\alpha \beta} = g^0_{\alpha \beta} + h_{\alpha \beta}$$ where $h_{\alpha \beta}$ represents the perturbation. After working through the algebra, they arrive at a coupled set of differential equations that relate the metric perturbation to the fluid perturbations. My questions is: Is there any generic reason why $h'''_{\alpha \beta}$ would be zero? Assuming that $h_{\alpha \beta}$ only depends on $r$ and the primes represent derivatives with respect to $r$. If there is no general rule about this, does anyone know of specific situations where the third derivative of a perturbed metric does go to zero?


title: Biological Themodynamics - What does an endpoint saturated signal mean. How does it relate to equillibrium constant

text: I have had a question that has been bugging me for a couple of years in my graduate school career, and I was wondering if perhaps some physicist could help explain it to me. Given an endpoint assay like this one I've shown below (an ELISA assay, but I assume it could work for any endpoint), how does the endpoint signal (the signal at the highest concentration) relate to binding. And how does EC50 (the concentration between the maximum and minmum signal) relate to the equillibrium constant. ![ELISA](http://structbio.vanderbilt.edu/~willisjr/Screen%20Shot%202013-07-17%20at%2012.19.53%20PM.jpg) For years, biologist have used the EC50 to give a rough approximation for the equilibrium binding constant $K_d$. However, it always bothered me that all curves features on the graph could produce nearly the same EC50, but with different levels of maximum absorbance. For instance two of the curves are saturated at around 1.2 and the others are around 2.5. Do all of these curves have roughly the same $K_d$, or is it worrisome that we don't get equivalence signal for the maximum concentrations. Please note, I was not sure whether this belongs in biology or physics as its definitely a biologic assay but the principals I'm asking about are physics oriented. Thanks


title: Quantum Field Theory: why fields are equal to zero on the boundary?

text: One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is $$ \phi(x)=0\,\text{on the boundary} $$ and this is widely used in many situations (e.g when calculating a surface integral on the boundary). Is there a physical reason for such assumption?


title: Physics behind Wheel Slipping

text: Lets say that I'm in a car and I apply full acceleration suddenly. Now, the wheels would slip and hence the car doesn't displace much. But If I start with some constant acceleration, slipping doesn't appear and the car moves normally. I think that its related to some friction mechanism. But I don't understand why the wheel slips at high speeds and not at low speeds. It's like, when the speed is high, rules are changing. Also, In each step F(s) (friction) should be equal to F (force in other direction). Isn't it? Any physical explanations?


title: What does $\psi_j(r_i)$ mean?

text: I have a mean-field Hamiltonian for N electrons. The mean-field potential felt by electron $i$ at position ${\bf r}_i$ is given by $V^{(i)}_{int}({\bf r}_i)=\sum_{j\ne i}|\psi_j({\bf r}_i)|^2$ I can understand why this is the case. However, I need to clear up my understanding of the term $\psi_j({\bf r}_i)$. Is it simply the wavefunction of the $j^{th}$ electron at position ${\bf r}_i$?


title: Inductance - Sign convention problem...

text: My problem is with a circuit containing a resistor of suitable resistance $R$ and a solenoid. At time $t<0$, there was a battery that created a current in the circuit and at $t=0$, the battery is disconnected from the circuit. Now I need to find the current as a function of the time $i(t)$, for which I've used Kirchhoff voltage law. I know that the voltage drop across the resistor is $V=IR$, and the voltage across the solenoid is $V=-L\frac{di}{dt}$ where $L$ is the self-inductance of the coil. Now, I don't know how to determine the sign of voltage across the solenoid. I mean, whether it's positive or negative..?


title: Why is plasma the highest "state" of matter?

text: As far as solid, liquid, gas, plasma go, why is plasma the highest state? Are there any other states of matter?


title: Name of the process that causes ice to melt under pressure and refreeze after

text: I remember a physics experiment from school where a wire with weights on each end was placed over a block of ice. The pressure of the wire caused the ice to melt underneath and refreeze once the wire had passed. Thus the wire passed through the block of ice - keep it whole. I thought the term was "relegation" but am not sure now. Thanks


title: If gauge symmetries are fake, then why do we care if they are anomalous?

text: My understanding is that gauge symmetries are fake in that they are only redundancies of our description of the system that we put in (either knowingly or unknowingly) see Gauge symmetry is not a symmetry?. Moreover it seems like we could in principal work without the gauge redundancy, and things would just be a bit nastier at intermediate stages of a calculation. At the same time, people put a great deal of emphasis that gauge symmetries cannot be anomalous. I understand that if we work with the gauge redundancy then we do indeed need it to be anomaly free so that the unphysical polarizations will cancel. However, what if we work without the gauge redundancy, with just the physical polarizations, what goes wrong then if we don't make sure the would-be gauge symmetry is not anomalous?


title: What is a mass gap?

text: I read that Quantum Chromodynamics is a theory with a mass gap. What is a mass gap in laymen terms? Why some theories have it? Which theories does not have it? **Note: I searched for mass gap before asking, all topics about it assume that the reader knows what it is, or define it in an advanced and technical way. So I'm looking for a simple answer if possible.**


title: Filming light in motion?

text: Regarding this video http://www.youtube.com/watch?v=Y_9vd4HWlVA, which claims to "film" light in its motion. Is it not an absolute nonsense? Even if photons could even be "seen" (meaning, returning light them self), isn't this video look unrealistic? You can see that the area around the "light" is getting brighter, but that absurd.. light is not a flash light... light does not illuminate the area around it, because it does not "emit" more light to all the directions.. Am I missing something?


title: Is the second law of Thermodynamics an immense tautology?

text: Let's imagine for a second a system that is changing constantly from one microstate to another one. It could be a given volume of a gas with its atoms moving and bouncing around, or a deck of cards being constantly shuffled by a monkey. If the starting microstate belongs to a macrostate with very few microstates, chances are that in the next step the system will be in a macrostate with more microstates in it. There is nothing mysterious about this, it is simply a matter of probabilities and how we define them. Now we have the second law of thermodynamics, that says that entropy always increases. It could have been reformulated like: a system that is permanently visiting different states, will spend more time in those which have a higher probability of being visited. Things more probable occur more times. And, since we define probabilities in terms of frequency: Are not we simply saying that things more likely to occur, occur more times? **Isn't it true then, that the second law is simply an immense tautology?**


title: Help with change in specific volume with time in piston cylinder?

text: I have a piston cylinder assembly and I am trying to determine the change of specific volume with time, namely $\frac{dv}{dt}$, due to an inlet mass flow rate. My first thought was to put it in terms of the mass flow rate so... $$\frac{dv}{dt}=\frac{dm}{dt}\frac{dv}{dm}$$ and I know that $\frac{dm}{dt}$ is the inlet mass flow rate. I could then use then use the expression $v=\frac{V}{m}$ to find $\frac{dv}{dm}$. My final expression came out to be $$\frac{dv}{dt}=-\frac{V}{m^2}\dot m$$Unfortunately my professor told me the answer is $$\frac{dv}{dt}=-\frac{V}{m^2}\dot m+\frac{1}{m}\frac{dV}{dt}$$ So I am wondering where I went wrong and why is there that extra term? Is there a chance he made a mistake?


title: Why does the perforated tin foil on a shisha pipe rise when smoking?

text: Imagine this setup (just without the windguard): ![shisha pipe wikimedia diagram](http://i.stack.imgur.com/K5Ci9.png) When applying negative pressure at the hose, I can observe the perforated tin foil separating the charcoal from the bowl rise a few millimeters, which seems odd, because the pressure above it should be greater than below. Why does this happen? Maybe because of vortices forming below it?


title: Electromagnetic fields in daily life

text: I have been reading up on electromagnetism lately, and to gain some intuition I wanted to know what effects electric and magnetic fields would have in daily life if they were generated "without any purpose". So what I tried to figure out was if I made a strong electric or magnetic field in my home, or a fast oscillating electric or magnetic field, what effect would that have on everyday objects like home appliances and circuits and stuff, if any. This endeavour proved more difficult than I first thought, so is there anybody out there who have solved the maxwell equations to figure out these kinds of things? Thanks in advance.


title: Pressure and Volume (SQA 2011 Higher Physics Q23)

text: On this question ![enter image description here](http://i.stack.imgur.com/xpaXH.png) Part bi, the equation to be used is P₁V₁=P₂V₂, so it states that the technician removes 50ml of air from the jar, so I had: P₁=1.01x10⁵ Pa V₁=200ml P₂=? V₂=150ml (since he removes 50) But in the marking scheme it has the value of V₂ as 250ml? I don't understand why? Thanks for any help in advance.


title: Relativistic Time Difference

text: I thought that it might be interesting to calculate the time difference between a clock placed on Earth when I was born and a hypothetical clock placed at the centre of the sun at the same time. I thought that I might use special relativity and the Lorentz factor. However, even if the speed of the Earth were constant (which it is not), the Earth still experiences acceleration as it traverses its (almost) elliptical orbit around the sun. Given there is acceleration, I suppose that I must use general relativity. How might one calculate the time difference experienced between me and my barbecued brother?


title: Normalising a wavefunction where $\psi$ is equal to a sum of functions

text: The wavefunction $\psi(x)$ = $\phi_1(x)$ + $2\phi_2(x)$ + $3\phi_3(x)$ is to be normalised. The functions $\phi_1(x)$, $\phi_2(x)$, $\phi_3(x)$ are normalised eigenfunctions of a Hermitian operator $\hat{O}$ with eigenvalues $\lambda_1=1$, $\lambda_2=5$, $\lambda_3=9$. I know that to normalise a wavefunction you do: $\int$ $|\psi(x)|^2 dx = 1$ But substituting for $\psi(x)$ gives a long sum of a combination of the $\phi(x)$s and I don't see how you can integrate that.


title: Why is the pressure on top of a slab of water greater than the pressure on the bottom?

text: In the image below, my book seems to be saying that if you have a cup of water in complete equilibrium, then if you have a small cube of water inside the cup given by $dm=ρAdy$ there is a downward force of $-(p+dp)A$ acting on the superior surface, a force $pA$ acting on the inferior surface, and $-dw$ which is the weight. What I don't get is why the pressure on top is greater than the pressure on the bottom? Isn't this supposed to be the other way around? If anything, they're deriving Pascal's Law here. ![picture of fluid diagram](http://i.stack.imgur.com/8SkxD.jpg)


title: Quantum Mechanics Lx operator

text: > Show that if the state $ \rvert\gamma\rangle $ is real, then the expectation > value of each component of the angular momentum is zero. Does this imply the > angular momentum is zero? My Work: $$ \langle\ \gamma\rvert l_x\rvert\gamma\rangle =\langle\ \gamma\rvert l_x\rvert\gamma\rangle^* =\langle\ \gamma\rvert l_x^*\rvert\gamma\rangle$$ $$l_x=\frac12(l_+ + l_-)$$ $$l_-^+= l_x + _-^+il_y$$


title: Mean field theory = large-N approximation?

text: Wikipedia entry of 1/N expansion (or 't Hooft large-N expansion) mentions that > _It (large-N) is also extensively used in condensed matter physics where it > can be used to provide a rigorous basis for mean field theory._ I would like reference(s) that reviews this connection between MFT and large-N.


title: In a double slit experiment are any particles lost because they hit the space between the two slits?

text: In its wave-form a particle should pass through every time because it propagates in all directions. So there shouldn't be any losses of particles landing in between the slits, right?


title: How does quantum entropy scales with the size of the sample?

text: Suppose i have a 3D bulk of physical matter with **no black holes** enclosed in a sphere of radius $R$. What is the scaling law of all quantum entropy in function of $R$? If the scaling is not $R^2$, in what sense can we argue that the holographic principle holds in our universe? Under what scenarios quantum entropy of non-black hole matter will scale with the area of the enclosed volume?


title: What is absorption of an electromagnetic wave?

text: Can any one explain the absorption/transmission/reflection of electromagnetic waves in the wave form? It is generally said that the atom absorbs/reflects/transmits photon. But can this phenomena be explained in the wave form of EMR?


title: Is having full information about the resonances of a rigid body equivalent to having full information about its material parameters?

text: Lets say I have a mechanical system whose mechanical resonances (mode shape and frequency) I can measure with perfect accuracy. Is this theoretically equivalent to knowing the materials parameters, including spatial variation, with perfect accuracy? My intuition says that the answer is yes, but I am not sure how to prove it. For concreteness, here is a specific example. Given a right circular cylinder such as the one shown below; will measurements of its resonant modes allow me to reconstruct its spatially non-uniform Young modulus and Poisson ratio? ![enter image description here](http://i.stack.imgur.com/fFUyi.jpg)


title: Can water evaporate when frozen?

text: If an ice cube is stored in a freezer could it evaporate given enough time? Is there a temperature below which water cannot evaporate (even just a little)?


title: Electric field problem

text: First of all I hope I'm doing the right thing by posting this message on the stack exchange site. I know you aren't my personal problem solvers, but I just can't solve it. And maybe this problem is too easy for this forum. Secondly, my first language isn't English and I'm not at all specialized in physics, so I probably will use some wrong words. I'm actually just a 16 year old boy with a physics exam tomorrow. **The Problem** * _Data_ *               Q1      P     Q2     + -----------  -           40.0cm      $Q_1 = +50.0 \mu C$   $Q_2 = -10.0 \mu C$   $d(Q_1, Q_2) = 40.0 cm\ \ \ d(x,y) = distance\ between\ x\ and\ y$ I don't know for sure, it's not in the problem description, but I guess $P$ lies in the middle between $Q_1$ and $Q_2$. **Question** Calculate the electric field size in $P$. **What I've tried** Nothing really, I just don't know how to start.   Thank you in advance, I'm sure this will be far to easy for you guys! **Edit:** As I was asked if I knew how to solve it if one of the electric charges would be zero, I hereby want to tell I do. I know:   $F = k \cdot \frac{|Q_1] \cdot |Q_2]}{r^2}$   $E = \frac{F}{|Q_t|}\ \ \ \ (Q_t = test\ charge)$   $= k \cdot \frac{|Q_s| \cdot |Q_t|}{r^2|Q_t|}\ \ \ \ (Q_s = source\ charge; Q_t = test\ charge)$   $= k \cdot \frac{|Q_s|}{r^2}$ _Note:_ test charge and source charge are a free translation of 'proeflading' and 'bronlading' (Dutch/Flemish).


title: Topology and Majorana bound states

text: I'm working at the moment on Majorana Bound states and their topological properties. Now I have a question about it. The Altland-Zirnbauer symmetry classes says us how many topological different ground states the system have just due to the presence or absence of symmetries and the spatial dimension. Further, in one-dimensional systems with only particle-hole symmetrie (class D) emerges Majorana Bound states at the ends. I can this obtain by solving the Bogoliubov-de Gennes equation. My question is there a "topological" method to obtain whether Majorana bound states emerges in the system in general? The Altland-Zirnbauer classes are the "Can Be"-condition, but at the present to prove the presence of Majorana bound states is to solve the Bogoliubov-de Genes equations for a special system and not in general.


title: Do convection currents under the crust affect Earths motion in the solar system?

text: Whilst browsing through this website I began to wonder whether all of that molten rock underneath the Earth's crust would have a notable effect on how the Earth moves in it's orbit of the Sun. Considering this stuff is forever shifting and readjusting itself and that it's comprised of different materials it seems understandable to think that there should be some reactions


title: Theoretical proof forbidding Loschmidt reversal?

text: In a famous debate, Loschmidt criticized Boltzmann's new theory of statistical mechanics by asking what would happen if the velocities of all the atoms were reversed. Typical objections are that such a reversal would not be possible without a fine detailed control over all the atoms of the system. However, spin echo experiments are a clear counterexample, albeit one restricted to very special cases. Is there any theoretical proof that without a fine detailed control over most of the atoms of a totally isolated system, a Loschmidt reversal would be extremely improbable? Remember such a proof would have to cover all sorts of elaborate complicated contraptions. Are reversals impractical for theoretical reasons, or because of a lack of ingenuity?


title: Canonical transformation problem

text: _(Apologies if HW questions are not allowed -- I couldn't really find a definite answer on this)_ **Question** > _Let $Q^1 = (q^1)^2, Q^2 = q^1+q^2, P_{\alpha} = P_{\alpha}\left(q,p > \right), \alpha = 1,2$ be a CT in two freedoms._ > > _(a) Complete the transformation by finding the most general expression for > the $P_{\alpha}$._ > > _(b) Find a particular choice for the $P_{\alpha}$ that will reduce the > Hamiltonian_ > > $$H = \left( \frac{p_1 - p_2}{2q^1} \right)^2 + p_2 + (q^1 + q^2)^2$$ > > _to_ > > $$K = P_1^2 + P_2.$$ **Attempt** I have shown that $$P_1 = \frac{1}{2q^1} \left( p_1 + \frac{\partial F}{\partial q^1} - p_2 - \frac{\partial F}{\partial q^2} \right), $$ $$P_2 = p_2 + \frac{\partial F}{\partial q^2}$$ is the most general canonical transformation for the momenta, where $F=F(q^1, q^2)$. This is consistent with the solution manual. For part b, however, the answer I get for an intermediate step is inconsistent with the solutions manual, and I don't understand why. Given that the transformation is canonical, all I need to do to find the transformed Hamiltonian K is find the inverse transformation and plug it in to the Hamiltonian H. The inverse transformation is $$p_2 = P_2 - \frac{\partial F}{\partial q^2},$$ $$p_1 = 2q^1P_1 + P_2 - \frac{\partial F}{\partial q^1}.$$ Plugging this into H, and renaming H to K since it's in terms of the transformed coordinates we have $$K = P_1^2 + P_2 - \frac{\partial F}{\partial q^2} + (q^1 + q^2)^2.$$ Since we want K to be $$K = P_1^2 + P_2,$$ this means $$\frac{\partial F}{\partial q^2} = (q^1+q^2)^2 = (q^1)^2+(q^2)^2+2q^1q^2.$$ $$F=q^2(q^1)^2 + \frac{1}{3}(q^2)^3 +q^1(q^2)^2 + C.$$ Plugging this into the general transformation I derived I find that $$P_1 = \frac{1}{2q^1} \left(p_1-p_2-(q^1)^2 \right),$$ $$P_2 = (q^1+q^2)^2+p_2.$$ My equation for $P_2$ is consistent with the solutions manual, but my equation for $P_1$ is not. According to the solutions manual $$P_1=\frac{p_1+p_2}{2q^1}.$$ My question is, is my methodology essentially correct, and if so did I go wrong in the algebra or did I make some sort of mistake in how I solved the problem.


title: There is no electricity at home,I need to light a 15W CFL Bulb.Can I Do it with the help of a hamster?

text: We know that i)avg speed of A Hamster is 30km/hr. ii)Avg mass of hamster is 1.5 kg. From the above info: Kinetic energy=1/2 X mass X velocity^2 So, K.E=1/2 x 1.5 x 30 x 30                 =1/2 x 3/2 x 900            =675      =675 J per hr. In one second,=675/3600 =1/5 j/s but power needed is 15j/s to light a CFL. 75 Hamsters would have done that. if I catch 75 hamsters,and run them for an hr,can I light a bulb [NOTE:-Just applied my 14 yrs old brain...pls correct if I am wrong..also,please tell me why are hamsters used in experiments]


title: Why is the LHC circular and 27km long?

text: The LHC in Geneva is a circular accelerator, 27 km long, why is it like that ?


title: Dielectric slab counter-intuitive formula?

text: For the calculation of force on one of the two equal(in magnitude, opposite in sign) point charges separated by $r$ with a dielectric slab of dielectric constant $K$ and width $d$ in between, the formula presented in many books is:-   $$F=\frac q{4\pi \epsilon_o (r-d + \sqrt{k}d)^2}$$ This means that the force between the two charges without the dielectric slab is reduced in presence of it if $k>1$. This contradicts my intuition. The charges induced on the dielectric will be due to electrostatic induction by the electric field of the two point charges and the induced charges themselves. But that means that the part of the slab towards the positive charge will have induced negative charge and the part away will have induced positive charge. Since the distance between the original charges remain unchanged, all the change in the force has to be brought about by the effect of superposition of the fields (forces) due to the induced charges on the dielectric slab. But since, considering the positive point charge, the induced negative is closer to the induced positive, there has to be a net attractive effect due to the induced dielectric charge and as a result the total force should increase rather than decrease as predicted by the formula. Where am i going wrong? If my intuition is correct, what would the formula for finding the field be(an approximate would do)? on a side note, **would the qualitative answer(attraction increases or decreases) change if the dielectric slab is replaced by a conducting slab?**


title: Breatheability of atmosphere above 3000 meters

text: I would like to offer you a slight correction on your statement that 3000 m is about the limit of breathable atmosphere. Unless I misunderstood you, I need to point out that many people live in Leadville Colorado above 3000 m and it's really quite comfortable unless you are from a sea level altitude and have not had the opportunity to develop the additional Hgb that makes oxygenation easier. As someone trained in Respiratory Technology, I can tell you that it's possible to live at extreme altitudes if you acclimate slowly enough because the body does develop more Hgb--to a point. That's why Olympic athletes train in Colorado Springs and bike from the base of the pass on I70 to Leadville, and from the base of Mount Evans to it's 14,300+ ft apex. It's a killer but it leads to natural packing. Nuff said. I'm enjoying reading your posts on gravity balloons. I am indeed writing a story on living on an asteroid. Adam


title: Are elliptical orbits really elliptical?

text: I have wondered for a long time how elliptical orbits can work. It seems awkward for a freely-moving object to come very close to a source of gravity and then return to the exact point where it started. I started to wonder even more after playing with the Box2D physics engine recently and finding that when I caused one object to be pulled toward another one, it didn't trace out a full ellipse. Instead, when the orbiting body approached the stationary body, it swerved in a different direction and started tracing out a new ellipse over there. The resulting orbit resembled the Treyarch logo, which I now suspect was inspired by physics demos in the company's early history. So what I want to know is whether real-life "elliptical" orbits are really doing this. I suppose that if you apply relativity, it could still be called an ellipse. For the record, I know that Box2D is only a rough approximation of physics.


title: Current density?

text: The current $i$ can be defined as: $$i = \int \vec{J} \dot{}d\vec{A} $$ where $\vec{J}$ is the current density and $d\vec{A}$ is the area vector. Is it possible for: $$i = \int \vec{J} \dot{}d\vec{A} \neq J\times A $$ where $A$ is the area? My book gives the example of when the current is not parallel to the area vector. However, I don't see why the direction of the electron flow matters. If 3 electrons passes through a circle per second, wouldn't the current be 3e/s regardless of whether they pass at 45 degrees or 90, since they pass regardless?


title: What causes polarised materials to change colour under stress?

text: Our physics teacher showed the class a really interesting demonstration. He used two polarised filters in opposite orientations, then he took some antistatic tape and stretched it under the two plates. The resulting image was projected on the wall using an overhead projector unit. Under stress, the originally clear looking tape (as it looked between the polarised filters) turned all sorts of weird colours, and apparently different colors correlate to different levels of stress. What causes this odd effect?


title: Electrons on Stern–Gerlach experiment

text: My questions about spin and negative charge of electrons. Stern-Gerlach experiment is very famous in order to find spin of electron. this video created by paris-sud university really well-explained on this experiment except one thing.watch the video first. http://en.wikipedia.org/wiki/File:Quantum_spin_and_the_Stern- Gerlach_experiment.ogv The thing I confuse second step of experiment they use electrons they goes two different ways. Aren't electrons have negative charge only? How they can go two different ways?


title: Implications of Formula for Stellar Aberration

text: I am studying relativity and was working on deriving stellar aberration using relativity. My derivation is as follows: Suppose that the observer is traveling at a velocity $v$ in the $x$-direction. Consider a light beam coming from a star to the ship's crew, which has velocity $c$ and components $u_x=c\cos\theta$ and $u_y=c\sin\theta$. Using the Lorentz transformations, assuming that hte shit is at rest and that the star is moving in the $x$-direction at a velocity of $-v$, we see that $u'_x=\frac{u_x+v}{1+u_xv/c^2}$ and $u_y'=\frac{u_y}{\gamma(1+u_x v/c^2)}$, where $\gamma=\frac{1}{\sqrt{1-(v/c)^2}}$. Then the new angle is given by $$\tan\theta'=\frac{u_y'}{u'_x}=\frac{u_y}{\gamma(u_x+v)}=\frac{\sin\theta}{\gamma(\cos\theta+(v/c))}.$$ For most angles, this has the desired effect; it makes the angle smaller. However, at the angle $\theta=\arccos(-v/c)$, we encounter a discontinuity, such that the tangent of $\theta'$ is not defined. I am a little hesitant to say that this would thus correspond with $\theta'=\pi/2$, so that $\arccos(-v/c)$ is sent to $\pi/2$. Is this indeed the case? Additionally, after this (i.e. for angles greater than $\arccos(-v/c)$), $\tan\theta'$ becomes negative. Moreover, for angles $\theta$ near $\arccos(-v/c)$, we can choose $\theta$ close enough to $\arccos(-v/c)$ to be arbitrarily large (in magnitude). But since these angles are naturally modded by $2\pi$, it would seem them that the apparent position of the star could be just about anywhere as observed by the observer. This seems very fishy, and occurs as well with angles just below $\arccos(-v/c)$. How should I interpret this? Indeed, how should I interpret the fact that the angles are negative? Does this means that it is reflected about the $x$-axis? Note that I am not making (and do not want to make) assumptions about the relative size of $v$; $v$ can be arbitrarily large (while less than $c$). Thank you for your time.


Will a moving neutron produce a magnetic field around it? I know that neutrons have no charge, so magnetic field should not be produced along it...but neutrons have a magnetic moment. So why can't this magnetic moment help it to generate a magnetic field around it?


title: Can quantum entanglement increase in the semiclassical limit?

text: In the paper > Classical Dynamics of Quantum Entanglement. Giulio Casati, Italo Guarneri & > Jose Reslen. _Phys. Rev. E_ **85** no. 3, 036208 (2012); arXiv:1109.0907, the authors state that the quantum entanglement of a certain bipartite state increases as the system approaches the semi-classical limit. What makes this possible, and why is this not a contradiction?


title: Torque on object

text: I would like to understand why the torque on white object is 0. I know gravitational forces are very low. But the torque must be at 0. I drawn all the study in first image. Blue color is a torus of liquid helium. The white object is vacuum (or gas at very low pressure). I drawn gravitational forces from atoms of helium to atoms of helium in second image, red forces showing gravitational forces on atoms. I drawn details of all forces in third image. Atom attract another atom: f1 and f2 forces   These forces give forces on support fs1 and fs2   Support reply and give -fs1 and -fs2   Sum1 is the sum of forces on atom 1   Sum2 is the sum of forces on atom 2 Like white object can only turn. Sum1 and fs2 are canceled if surface of white object is radial or part of circle. fs1 give a torque to white object $T1 = fs1 * r2$ and atom give a torque to helium $T2 = sum2 * r1$. Torques are not the same, why ? ![enter image description here](http://i.stack.imgur.com/coAH0.jpg) * * * ![enter image description here](http://i.stack.imgur.com/LJzyX.jpg) * * * ![enter image description here](http://i.stack.imgur.com/zHwgj.jpg)


title: What is the magnetic effect on either of the charges moving parallel

text: Consider two electrons moving parallel to each other in the same direction with same constant velocity. Will they experience any force due to either of them?


title: Isn't the Jacobi constant just the Lagrangian times 2?

text: At this wikipedia page the Jacobi constant is expressed as: $$C_J=2\left(\frac{v^2}{2}-U\right)$$ where $U$ is the potential energy and $v$ is velocity. If kinetic energy $T$ is defined (as it usually is) $T=\frac{v^2}{2}$, then this equation can be rewritten: $$C_J=2(T-U)$$ which looks awfully like your run of the mill Lagrangian multiplied by 2. That is: $$C_J=2L$$ So why does the Jacobi constant get all this special attention and notation as something unique and different, when in fact it is basically just a Lagrangian? EDIT: Assuming of course a unit mass $m=1$ so that $T=\frac{mv^2}{2}=\frac{v^2}{2}$.


title: How are neutrons produced from cosmic ray particles?

text: What are the details of how neutrons are produced as a result of cosmic ray particles hitting our planet's atmosphere? For instance, what is the pathway that creates the highest number of neutrons from cosmic ray particles? The article "Single event upset" states: > An SEU happens due to cosmic particles which collide with atoms in the > atmosphere, creating cascades or showers of neutrons and protons. At deep > sub-micrometre geometries, this affects semiconductor devices at sea level. But it does not describe the mechanism. The Wikipedia article on the neutron states something similar: > Cosmic radiation interacting with the Earth's atmosphere continuously > generates neutrons that can be detected at the surface. What are the processes, in detail?


title: Frequency dependence of permittivity -- why not monotonic?

text: I naively thought that most materials were transparent to radiation of frequencies above their plasma frequency, and opaque to radiation below it. The most intuitive (and analyzed lightly in Griffiths' E&M book) reason I've heard is that opaqueness is caused by electrons in the material responding to the incident radiation by getting oscillated by it, in which they produce their own radiation that cancels the incident radiation. However, when the incident radiation is above the plasma frequency, they can't respond quickly enough and it can start to penetrate the material. Mathematically, $\epsilon(\omega) > 0$ for $\omega < \omega_{plasma}$ and $\epsilon(\omega) < 0$ for $\omega > \omega_{plasma}$, and the wave vector $k \propto n \propto \sqrt{\epsilon}$, so when $\omega$ is above $\omega_{plasma}$, $k$ is imaginary and $e^{i \vec k \cdot \vec r}$ decays quickly in the material. But I was recently told that as the frequency keeps rising, the material again at some point becomes opaque to it. What is this called, and what's the physical reason for it?


title: Tire speed dependent friction

text: I have an old, non power steered car. When the car is stationary, the steering wheel is really tough to move, but as soon as I gain very little (0.5 kph or so) speed, the resistance is dramaticly decreased. But at higher speeds, if I wish to make a full steer, the steering wheel will be resisting again. What is going on with the wheel friction?


title: Open problems in special relativity, and non-inertial motion in flat-spacetime, or things that have been discovered recently

text: What classical open problems are there in special relativity, including questions about non-inertial motion in flat-spacetime, but excluding questions about quantum theories. Answers can include things which were open problems until recently. New things in special relativity (and non-gravitational relativity) still seem to be discovered relatively recently: For instance the book "A broader view of relativity" by Jong-Ping Hsu, Leonardo Hsu, contains formulas for transformations between some types of accelerated frames. Abraham Ungar derived formulas for things like proper velocity composition, and for Lorentz transformation composition in terms of velocity and rotation parameters. So it would be good to have a list of things that we still haven't worked out, or have only been worked out recently, to challenge the assumption that special relativity is all figured out. (Due to linear frame-dragging it also seems that the usual saying that GR tends to SR in the limit of negligble gravity should be stated as GR tends to SR for negligble gravity and low acceleration, so any calculations concerning the half-way house of non-inertial relativity between SR and GR would only be valid for low acceleration. Perhaps this should be the definition of non- inertially extended special relativity: acceleration without linear frame- dragging.) Edit: I +1ed the answer on self-force because it was an interesting general issue, but once we are talking about fields and particles then we are getting away from the question which is really about calculations in the theory of special relativity itself. Once we talk about fields and particles then I guess there are lots of problems and an accurate treatment requires quantum theories which this question is not about.


title: Simple three-body-problem?

text: Consider the problem of three bodies two of which having mass _M_ , one of them having mass _m_. Body _m_ is in the middle between the other two, coupled to them by two equal linear springs in rest. Now fix the two bodies _M_ and move body _m_ for a small amount perpendicular to the connection line. Now let loose the three of them. The solution is trivial when we assume _m_ to be finite and _M_ to be infinite (or vice versa), or when the spring constant is 0. But the problem is so symmetric, that there might be hope to get a closed or approximate solution even for finite _m_ >> _M_ , _M_ >> _m_ , or even _M_ = _m_?


title: What is the meaning of "background" in General Relativity?

text: I was reading a book on Topological defects of the very early universe as an example of the fundamental groups, and they say that "in an expanding homogeneous and isotropic universe, the background energy density is a function of time", I do not know what do they mean by "background", are they referring to the spacetime. Could somebody please explain this to me? I am not into physics but I like general relativity. Thanks


title: How to determine the required resolution to view an image at a certain size?

text: If I have several camera specifics, can I determine the required resolution to view an image at the size I want? For example, let's say I want a picture of a square painting to be at least `20 pixels` large. I know the focal length is `7.5 mm`, the painting was `8 m` away from the camera, it is `2 m` tall in real life. I know that the image sensor is `2.4 mm` by `2.4 mm`. Can I determine the required resolution to view the painting at least `20 pixels` large?


title: M2-brane wrapped twice around $S^1$

text: M-theory wrapped around $S^1$ is type IIA, especially in the limit of zero radius. An M2-brane wrapped around $S^1$ once is a type IIA string. The zero mode anyway. In the limit of very small radius, if we project to states with tiny energy, we get a collection of type IIA strings only. What does an M2-brane wrapped around the circle twice correspond to? Its energy is also low. It has to be. Pretend it is an M-theory compactification with twice the radius. Orbifold it over half a periodic translation. It's back to the original. So, is it made up of type IIA strings? Is it two type IIA strings? Or a single type IIA string? Surely it's not a _different_ kind of type IIA string with $1/\sqrt{2}$ times the string scale and $\sqrt{8}$ times the string coupling?


title: Why does the aorta spray blood when atmospheric pressure is higher than blood pressure?

text: Atmospherical pressure is around 760 mmHg, while blood pressure is on average 100 mmHg. Then why do you bleed from cuts, and why does a cut aorta spray blood? The atmosphere should press the blood back in, or at least stop it from spraying.


title: Name for phasor model of light

text: I'm looking for the name of the model of light "exploring" every path to a given point, and reaching that point with a probability proportional to the square of the resultant phasor's amplitude. (Yes, that's why I need something more concise.) I'm thinking that Quantum Electrodynamics is too general, and after some googling, "phasor model" doesn't seem to refer to light specifically. If you can tell me that I'm wrong, or suggest a better name, it'd be appreciated.


title: Which metals can cause magnetic interference (passively)?

text: I am developing an application that uses the magnetometer inside smart-phones to detect orientation w.r.t. the Earth's magnetic field. I have noticed that when the phone is held close to a metal structure, such as Iron/Steel railings, there is a huge deflection in the magnetometer reading. There is no externally-induced current flowing through the structure; it has ~~induced~~ warped the magnetic field by its own. My question is, which types of metals can show this effect? Or more generally which type of elements can show this effect? I suppose Ferromagnetic materials do show this effect. And paramagnetic materials (like Aluminium) will show a very weak effect. What about diamagnetic substances such as copper? **Update** Changed the title to mention _passively_. I understand that a copper coil forced to carry current would induce a magnetic field that interferes with the Earth's magnetic field. But does the coil distort the Earth's magnetic field when _no_ EMF is applied?


title: Why does reentry from space tend to result in such great heat?

text: Let's pretend for a moment that the atmosphere had sea-level density, pressure, and temperature all the way up to, say 500km high, and then would abruptly end in a complete vaccum. In such a situation you could have a glider orbiting at 501km high which could do a very graceful, low temperature reentry by simply slowing down the angular velocity and then using aerodynamic lift at, say, a 1:30 gliding ratio to drastically reduce the rate in which potential energy gets released. Or even have a completely vertical entry using a simple parachute.. With our real atmosphere though it seems that all reentries are at very steep angles and at very high radial velocities. Why? Is this a direct consequence of the low density at high altitudes, which necessitates a far higher velocity to reach the same lift/drag, and that high velocity contributes to increasing the temperature far more than the low density contributes to decreasing the temperature?


title: Probablistic problems in physics?

text: So I have an opportunity to do math research with a probabilist. I would like to propose to him a project that relates to physics, as it would be a good way to learn about another field. What are some open probabilistic problems in physics? Thanks!


title: Symmetry argument about degeneracy of graphene energy band at Dirac point

text: This question is very related to the thread here. In the answer given by @BebopButUnsteady , the statement is that as long as the inversion and time-reversal symmetry are respected, the Dirac points will exist. I would like to know a more detailed explanation about this argument, is this degeneracy related to Kramer pairs? Or to small groups?


title: The Opera Neutrino Experiment and the Supernova 1987

text: So this probably stems from my massive ignorance about post-Newtonian physics but the supernova results of 1987 which measured neutrinos arriving 3 hours before the light from the supernova have been presented as a non-trivial objection to the Opera result. However if the Opera result is confirmed, then doesn't that weaken the supernova objection since star mechanics relies heavily on relativity and such a result might imply that relativity is not the complete picture which in turn could imply different star mechanics than the one we understand? Thanks Edit: To clarify, I'm asking whether the supernova objection may not apply given that this experiment seems to challenge relativity which is what has been used to understand the behavior of stars, supernovae and such.


title: Explanation for the power of quantum computers

text: I have seen various explanations for the power of quantum computers: Quantum computers perform operations in parallel universes ![enter image description here](http://i.stack.imgur.com/WupzF.png) Quantum computers can use quantum tunneling to reach a global extremum of a function ![enter image description here](http://i.stack.imgur.com/P2cKX.png) Quantum computers can manipulate quantities of information smaller that 1 bit independently and perform logical operations on such quantities. ![enter image description here](http://i.stack.imgur.com/AVUYx.png) Constant entropy of unitary evolution allows quantum computers to roll back in time, when the answer is wrong, so to perform multiple calculations during the same time interval. ![enter image description here](http://i.stack.imgur.com/ohUns.png) Which of these explanations is more correct or do they supplement each other?


title: Two important misconceptions in Quantum Mechanics

text: I'm reading an article that talks about general misconceptions in QM. It says in its abstract: > Two deep-seated misconceptions are responsible for the interpretation > difficulties associated with quantum mechanics: the notion that the spatial > and temporal aspects of the world are adequately represented by sets with > the cardinality of the real numbers, and the notion of an instantaneous > state that evolves in time. The latter is an unwarranted (in fact, > incoherent) projection of our apparent “motion in time” into the world of > physics. Equally unwarranted, at bottom, is the use of causal concepts. Would you help me in other words what is trying to tell ? The article is > What Quantum Mechanics Is Trying To Tell Us. U Mohrhoff. _Am. J. Phys._ > **68** no. 8, pp. 728-745 (2000), arXiv:quant-ph/9903051.


title: Newton's laws of motion

text: According to Newton's laws, if net force is zero on a particle then the particle is at rest or in uniform motion, and if it is not zero then it is accelerating. So when a car moves on the road, friction helps it to accelerate. If the acceleration is zero, (i.e) it is moving with constant velocity, the net external force must be zero, so friction is zero. Then with friction equal to zero how is the car moving on the road?


title: What is the height of breeze/wind?

text: How high does a breeze/wind blow? (If you are out in the open and can feel the breeze blowing, till how high is this breeze felt?)   And what are the factors that affect it?


title: How far can the human eye see? Any ending point or infinite?

text: How far can the naked human eye see if unobstructed? (straight ahead on perfectly flat land). Is there a stopping point or is it infinite when you look in the sky? Is there any situation that the human eye can see infinite? What are the factors that determines how far we can see? The photon flux density and...? Physics and biological point of views will both be interesting to discuss.


title: Good explanation of a real image?

text: Okay well I've started to study phys chem in school recently and I honestly can't get my head around what a real image actually is I've asked my teacher to demonstrated it but she's quite lazy, and then I got this sudden flashback of something I learned about renaissance art in primary school. Its the camera obscura painters used to use it or something I don't know but I just wondering does this explain what a real image is or am I just a idiot, here is a picture : http://upload.wikimedia.org/wikipedia/commons/a/a2/Camera_obscura_1.jpg


title: Mathematical description in GR

text: I have heard a phrase somewhere, which can be reduced to the following two points: 1) There exists a handy and underused mathematical apparatus applicable to GR, comparing to which tensor calculus is obsolete. 2) The apparatus is related to graphs. Does anybody have an idea, what could this apparatus be?


title: Symmetrical Spinors and Symmetrical Tensors

text: In Quantum Electrodynamics by Landau and Lifshiz there is the following: > The correspondence between the spinor $\zeta^{\alpha \dot{\beta}}$ and the > 4-vector is a particular case of a general rule: any symmetrical spinor of > rank $(k,k)$ is equivalent to a symmetrical 4-tensor of rank $k$ which is > irreducible (i.e. which gives zero upon contraction with respect to any pair > of indices). L&L also writes out this for a 4-vector $$ \zeta^{1\dot{1}}=\zeta_{2\dot{2}}=a^3+a^0 ,\quad \zeta^{2\dot{2}}=\zeta_{1\dot{1}}=a^0-a^3, $$ $$ \zeta^{1\dot{2}}=-\zeta_{2\dot{1}}=a^1-ia^2 ,\quad \zeta^{2\dot{1}}=-\zeta_{1\dot{2}}=a^1+ia^2, $$ Surely there must be an established method to do this in general just like it says above. I would like to know this method, so if someone would be kind enough to show me or refer me to a reference I would be grateful, (e.g. suppose I would like to know the components for $\zeta^{\alpha\beta\dot{\gamma}\dot{\delta}}$ in terms of the symmetric traceless rank-2, 4-tensor). Thanks,


title: Best Materials Science Introduction Book?

text: Why is this here? > Sorry, I know that this isn't the best place to put this however there does > not seem to be any other stack exchange specific to this so I thought this > would be the best place since it seemed the most related. Question: > What would you suggest as a good introduction to materials science? (Prior > usage and examples would be wonderful, my particular focus is neutron > scattering) What I've Found So Far: >   * Materials Science and Engineering: An Introduction by Callister (Seems > to have good reviews) > Thank you for the help. Note: I didn't see anything related on the book request wiki.


title: What do spacecraft have in common with atmospheric aeroplanes?

text: Science fiction depicts spacecraft as both deep-space & surface capable. Is this feasible? I would have imagined a vessel constructed for space travel to have little in common with operating characteristics/requirements of a vessel to operate in atmosphere. What operational parameters/characteristics do spacecraft have in common with aero-planes? EDIT: What I have in mind, for instance, is the fact that an atmospheric craft would necessarily need to be aerodynamic. At the same time, an atmospheric craft would operate with some air-pressure without instead of a vacuum - hence it could have view-ports instead of camera/screen/radar. An atmospheric craft may rely upon moving surfaces to control flight instead of jets/gravity. Stuff sort-of like this but these are what are different; I'm looking for similarities.


title: Second Quantization - Texts

text: I am trying to familiarize myself with the ideas of Second Quantization. However, the literature that I can find online seems only to outline the tools of this formalism of quantum mechanics. There is very little description about the origin of this formalism and how it connects to other problems in physics. For example, I know that I have solved the Harmonic Oscillator problem in QM using ladder operators but I do not understand why the mathematics of the Quantum Harmonic Oscillator should be the same as the mathematics I use to describe many body systems. Are there fundamental symmetries? Are all objects in the universe oscillators in some sense? I was hoping that someone could recommend a good text for an introduction to this Second Quantization formalism. The other problem is that I am an undergraduate student without a knowledge of QFT, thus I seek a text which does not rely on a detailed knowledge of this area.


title: Question on communication between universes in a level 1 multiverse

text: Can matter, energy, or information travel from one universe to another in a Level I Multiverse? That is, is there any communication between Hubble volumes in an eternal inflation-induced multiverse?


title: Does a thermally expanding torus experience internal stress?

text: I'm trying to learn continuum mechanics and thermo-mechanics. As we know, heating an object increases the mean atomic distance $a_0$ of the atoms in a rigid body. Let's assume it is a linear elastic material and we're well below the melting point. The lattice is perfect (no defects). I'm interested in whether the _topology_ of a body plays a role when it is heated up. I think, the cross section of a torus (topologically different to convex bodies) changes like in the sketch below (A: circumference at initial temperature, B: circumference at higher temperature). ![cross section of an expanded torus](http://i.stack.imgur.com/Lwzgn.png) ### Question 1: Is `B` still a circle or is it an ellipsoid? ### Question 2 (main question): Is there a non-uniform internal stress field in the torus? E.g. is there more stress on the inner rim? How does this compare to the thermal expansion of a convex body (e.g. sphere)? ### Question 3: What is the influence of the crystal structure (FCC, BCC, wurzite) to the internal stress of an thermally expanding body? References are appreciated - especially good books on this subject.


title: References on $C^{*}$-algerbas, $W^{*}$-algebras and Quantum Theories

text: I would like to know some references regarding $C^{*}$ and $W^{*}$-algebras and quantum theories. I'm interested in concrete physical applications, models and problems. Here it is the list of references I already know:   * Dixmier: $C^{*}$-algebras   * Dixmier: $W^{*}$-algebras   * Pedersen: $C^{*}$-algebras and their automorphic groups   * Landsman: Lecture notes on $C^{*}$-algebras and quantum Mechanics   * Araki: The mathematical theory of quantum fields


title: Is there a closed form solution to the Esdale river problem?

text: This is probably not well known problem but it looks like open problem. What kind of methods there are to find a closed form solution to the physical situation? * * * Can you solve this problem? You're passively flowing downstream in the middle of a river that has its fastest flow in the middle. Most places along the riverbank are too steep or too vegetated, but suddenly you spot a perfect location for coming ashore a distance y away (measured along the river bank). Note that y can be zero so that you only spot it when you're already drifting past it; or if you're slower still, y can be negative. Now assume your swimming speed is a constant v, while the river's flow is V in the middle and linearly decreasing towards the shore. What angle should you take, as a function of your distance to the shore (x), to reach the desired location using minimum effort (i.e. shortest journey or, equivalently, shortest time)? ![enter image description here](http://i.stack.imgur.com/ha4VF.jpg) Source and image credit: Hanna Kokko.


title: How to make a black hole?

text: Many Physics discussions I have often conclude with: > Well you will then form a black hole... My questions are:   * Is there a general recipe for making a black hole?    * If not, then can you list the families of black hole causes? This means I can put a more rapid halt to many future Physics discussions.


title: When experimental search for exotic dark matter-like particles began exactly?

text: I am looking for information about :   * **what was the first experiment that claimed to look specifically for non baryonic dark matter particles ;**   * **when occurred the first serious(*) reporting of an experimental result regarding a non baryonic dark matter candidate.** (*: published in a peer reviewed journal)


![setting](http://i.stack.imgur.com/rcorp.jpg) Hi Sir/ Madam Want to achieve maximum magnetic force & find out the max point for this setting, want to know   1. is the strongest magnetic force must in the 'dot' area ( middle poin of setting )   2. would the length of D1, D2, D3 affect the 'dot' location?   3. if add a metal sheet ( material AISI1010 ) between the magnet, would the magnetic force increase? would the thicknes of the sheet D4 affect the force? Magnet material: NdFeB 52 5x10x18mm D1 would be <4mm


title: The Universe as a four-dimensional sphere?

text: I was chatting with my 12yo cousin yesterday and we got to the Universe, its size and stuff like that. Then he came up with the idea (I'll rephrase it), that the Universe could basically be a 4d sphere which looks like 3d, but is warped into the 4th dimension, so it can form a 4d sphere - the same way as the Earth is 3d sphere which looks like 2d when you stand on it, but is warped ito the 3rd dimension, so it can form a sphere (hopefully the analogy makes sense as I seem to lack the proper wording). That would allow the Universe to be both "infinite" and have its size, also questions like what's beyond the edge are not meaningful anymore. So it all looks very logical to him (and I admit, to me too). But I am pretty sure this is incorrect as I don't recall reading anything about 4th spatial dimension (apart from String theory hidden dimensions), but I wasn't able to give him any kind of proof or counterexample. So my question is: Is there a (as simple as possible) explanation/measurement/demonstration I could give/show to him to disprove his idea? Although it's obvious, I confess I am definitely no expert, so please be forgiving to my formulations and assumptions.


title: States of "positronium" with chiral fermions?

text: When I combine positron and electron to form positronium, or generically two spin 1/2 particles, I have four possible spin combinations that arrange into a singlet and a triplet state, which in turn are the trivial and standard representations of SO(3). Now, what does happen if one of the particles, or both, are chiral particles without their corresponding chiral partners? Imagine for the sake of discussion that you want to combine a neutrino and an electron, or two neutrinos, or a pair neutrino antineutrino. Are the combinations part of the SO(3) triplet, the singlet, or none of it? Or instead neutrinos, think for instance mesons with one or two exotic chiral quarks.


title: Are pressure and volume not independent properties in liquid water?

text: Every thermodynamics textbook teaches us that, for a simple compressible substance, any two independent properties will suffice to determine the system state. Those can be pressure and temperature (except in saturation), volume and temperature, pressure and volume or many other combinations. However, the later chapters of Van Wylen's Fundamentals of Thermodynamics present me a diagram similar to this one: ![water specific volume x temperature at 1 atm](http://i.stack.imgur.com/fVFSn.png) That is an isobaric line for water (likely at 1 atm). But $v(p, T)$ is not surjective along that $p = \text{1 atm}$ line (i.e. $v = 1.0001$ could mean $T \approx 2$ or $T \approx 6$). So I conclude that **specific volume and pressure are not independent properties** in intervals that contain $T=4$. Because, if only $p$ and $v$ are given, the thermodynamic state (i.e. $T$) cannot be determined. If this is true, I'm shocked that nowhere on the books or the internet this is pointed out. I admit it's a small interval of non-compliance, and often volume is considered almost constant anyway, but, when teaching independent properties, the only exception ever mentioned is the saturation state, where $p$ and $T$ are not independent so $v$ is needed (or $u$ or $h$ or $s$ or...). I feel that my learning of independent properties was incomplete if this is true. Could you please confirm these thoughts?


title: Electric force between charges in two different media

text: As far as I know, Coulomb's law of electrostatic force is applicable on two different charges situated in same medium. But if two individual charges are in different media (say one charge on a iron surface another on a plastic surface), then how does one calculate the force between them? And if I have wrong conception , please correct me.


title: A Conceptual Problem With the Field Equations of General Relativity

text: I have two questions:   1. Suppose that we have an amount of energy in the form of a perfect fluid in the right hand side of Einstein field equations (energy momentum tensor), this will lead to a gravitational field, the gravitational field itself has energy, and this self energy also produces gravitational field ... in other words the gravity beget gravity !! ... due to this scenario we will have an infinite gravitational field!! ... what's wrong here?! is my reasoning wrong or is it the field equations that are not correct?   2. Has this non-linear behavior of gravity(or maybe graviton!) anything to do with the fact that when we try to quantize gravity we encounter infinities?


title: No local degrees of freedom when connection is flat

text: I was studying Chern-Simons theory and variation of action gives us the flatness conditions $\mathrm{d} A + A \wedge A = 0$. I am wondering how to see that this implies there are no local degrees of freedom. And what precisely does it mean that a degree of freedom is local?


title: Relating theta_QCD to neutron EDM

text: How do I relate the topological $\theta_\text{QCD}$ parameter to the electric dipole moment (EDM) of the neutron? I am very familiar with chiral perturbation theory. I just need to know how to take $\theta_\text{QCD}$ into account. Any good sources?


title: Action and reaction pair problem

text: If I sit on a chair, the first action and reaction pair force is my weight and the force acting on the earth by me. And the 2nd pair is the force acting on the chair by me and the opposite force. According to newton third law, the action and reaction force must be equalI. 'm confused because how come the force acting on the chair by me is equal to normal force? F=gmm/r2


title: Construction of Angular Momentum eigenvectors

text: I have a problem that asks (verbatim) > Carryout the construction of the eigenvectors of total angular momentum and > its z component for $j_1$=3/2 and $j_2$=1/2 I am not completely sure where to start out with this. Our professor has not given the best explanation. The equations I have been trying to use are the following: $$\textbf{L}^2|l,m\rangle =\hbar^2l(l+1)|l,m\rangle$$ $$\textbf{L}_z|l,m\rangle=\hbar m|l,m\rangle$$ I figure I probably want to use the same equations, but for $\bf J$ instead of $\bf L$. I am also confused what the differences between $j_1$ and $j_2$ would represent. I would greatly appreciate any help!


title: Number of wave modes in a cavity

text: I'm trying to calculate the number of acoustic modes that can exist in a room in a certain range of frequencies. I thought of using the Rayleigh-Jeans formula for the electromagnetic standing wave modes possible in a cavity ($\frac{dN}{d\nu}=\frac{8\pi V}{c^3}\nu^2$), dividing by two to account for the fact that longitudinal waves such as sound do not have two different polarizations. I'm not sure that this formula is valid for a non-cubical cavity, though, because the development represents the modes as points in 3d "mode space", and counts them by looking how many of the points are included within a sphere. If the cavity is not a cube, wouldn't there be more modes in a direction than in another, stretching the sphere into an ellipsoid? My book (Eisberg-Resnick, "Quantum Physics") says that the formula is valid for an arbitrary cavity, but doesn't explain that statement. Can someone explain to me why I'm wrong?


title: Physical reason for magnetic mirroring?

text: I understand the mathematical derivation of magnetic mirroring, which usually starts from the conservation of the magnetic dipole moment (e.g. in a plasma). But physically: a mirrored particle is effectively coming to a halt and then starting to move again, in the opposite direction. 1) It loses kinetic energy whilst slowing down - where does this energy go? 2) It recovers it when it is fully reflected - where does this energy come from? where was it stored?


title: Indirect band gap and additional momentum?

text: For indirect band gaps, an electron needs both energy and momentum in order to be excited from the conduction band. I am not sure I understand the momentum requirement. What does it mean physically? We need to "push" the electron forwards? Won't that be equivalent to just shining light onto it and let it recoil?


title: Stokes' theorem in complex coordinates (CFT)

text: I am studying CFT, where I encounter Stokes' theorem in complex coordinates: $$ \int_R (\partial_zv^z + \partial_{\bar{z}}v^{\bar{z}})dzd\bar{z} = i \int_{\partial R}(v^{z}d\bar{z} - v^{\bar{z}}dz). $$ I am trying to prove this by starting from the form of Stokes'/Greens theorem: $$ \int_R(\partial_xF^y - \partial_yF^x)dxdy = \int_{\partial R}(F^xdx + F^ydy $$ and transforming to complex coordinates. The reason I ask this here and not on Math exchange is that in CFT we have the distinction between indices up and indices down: $$ v^z = v^{\tau}+iv^{\sigma} \\\ v^{\bar{z}} = v^{\tau} - iv^{\sigma} \\\ v_z = v^{\tau}-iv^{\sigma} \\\ v_{\bar{z}} = v^{\tau} + iv^{\sigma}$$, with $z = \tau +i\sigma$ and $\bar{z} = \tau - i\sigma$. The substitution is kind of straight forward, but I get: $$ \int_R(\partial_zv^{z} - \partial_{\bar{z}}v^{\bar{z}})dzd\bar{z} = i\int_{\partial R}v^zd\bar{z}+v^{\bar{z}}dz, $$ so I get two relative minus signs wrong. As the calculation is not so difficult, I have the feeling I am missing something crucial here. Does anyone have an idea?


title: Are Classical Field Theory and Quantum Mechanics of a single particle (nonrelativistic or "classical") limits of Quantum Field Theory?

text: Recently I talked about QFT with another physicist and mentioned that the Quantum Field Theory of a fermion is a quantisation of its one-particle quantum mechanical theory. He denied this and responded that he rather sees the single particle QM as the non-relativistic limit of a QFT. He elaborated that the energies encountered are all much smaller than the particles mass, so we can ignore all multi-particle excitations in Fock Space and get an effective Hilbert space consisting of all single-particle excitations. In turn, I asked what the corresponding limit of QED quantum mechanics of the massless photon is, and he of course responded that there can't be a nonrelativistic limit of QED exactly because of the masslessness. But there is classical ED, the classical limit of QED. So is taking the classical or the nonrelativistic limit the same, or does one include the other, or is there some deep difference? The question What does a Field Theory mean? has something to do with it, but does not fully answer my question.


title: how does graphene affect the refractive index of an optical waveguide?

text: Could someone help me find data on the electro conductivity of graphene and its effect on the refractive index of an optical waveguide


title: conceptual doubt in method to find moment of inertia about an axis

text: I asked this question before about whether I can take a component of angular velocity along another axis and say that the body spins about that axis with that component. Now I have another doubt: Consider a rigid body having an inertia $I_0$ and angular velocity $\omega_0$ about some axis. So according to the answer to my question above, I can say that the object has an angular velocity $$\omega_0\cos\theta$$ about an axis inclined at $\theta$. And I can also say that the angular momentum about that axis will be $$I_0\omega_0\cos\theta$$ by taking the component of the angular momentum about the original axis, $I_0\omega_0$ along the axis at $\theta$. So why can't I say that the inertia about that axis will be $$I = \frac L{\omega}=\frac{I_0\omega_0\cos\theta}{\omega_0\cos\theta} = I_0$$ Where is the problem in this?


title: Slicing a surface concentration from a volumetric number concentration

text: Assume I have a given volumetric concentration $c$ of $N=10000$ particles in a qubic box of volume V: $$c = \frac{N}{V}$$ The units of $c$ are $$[c] = \frac{[\\#]}{[m^3]}$$ Now if I introduce an infinitely small path along the $z$ direction: $dz$, so that the concentration in the infinitely small volume becomes: $$dz \cdot c = \frac{N}{V}\cdot dz$$ If I want to reduce a 3D problem to a 2D problem in order to make some numerical studies , however, this is not very helpful since $dz \cdot c$ will approach zero as $dz$ goes to zero. I realize that I can insert an arbitrary $dz$, say $dz = \Delta z = 1$ m. This basially means that the surface concentration is equal to the volumetric concentration. Is that correct? If not, how do I get a surface number concentration out of the volumetric number concentration that I can actually do calculations with? **EDIT:** So what I am trying to model in the end is a fluid flow through a pipe in three dimensions. At the inlet of the pipe, I inject particles which are given as molar concentrations. The next step is to study diffusion and convection phenomena of those concentrations. The reason why I want to do this in 2D first is simply that it saves a lot of computation time.


title: Does photons undergo the process of cyclic absorption and re-emission by virtual particles in vacuum?

text: The process of cyclic absorption and re-emission by electrons in a medium is an explanation for the fact that light appears to slow down in mediums relative to vacuum. But, does light undergo this process due to virtual particles that constitute vacuum? What does it mean in this case to say that the refractive index of vacuum in unity?


title: Formulation of the uncertainty principle for a system?

text: There is a biological system that I can indeed describe by a simple quantum Hamiltonian $H$ having eigenstates $|q\rangle$ labelled by the numbers $q$, and having energies proportional to $f(q)$ - that is a continuous function of $q$ that sends $\Bbb N \rightarrow \Bbb R$. The form is: $$H|X\rangle=E_q|q\rangle$$ with $$E_p=E_0 f(q)$$ While $|X\rangle=|x_1,x_2,x_3,\dots,x_q\rangle$ From here obtain a partition function with $J$ analogue to temperature $T$ and $K$ analogue to $k_B$ Boltzman constant: $$Z(J)=\sum_{i=1}^\infty exp \left( \frac{-E_i}{KJ}\right)$$ I have never done before formulating the uncertainty principle derived from equations like above. May you help me with following questions: _What are the commutators in the above case?_ _How does the formula for the uncertainty inequality look like for the above case?_ _Do I need to use standard deviations or is it possible to use directly certain commutators from the variables in the above case_