title: How to rearrange the fermions in CohFT?

text: A simple question about notation of Moore Nekrasov and Shatashvili which makes me confused. Page 3, the authors rearranged the action into a novel form. For D=3+1,5+1,9+1 respectively, the path integral is $$ I_D=(\frac{\pi}{g})^{\frac{(N^2-1)(D-3)}{2}} \frac{1}{{\rm{Vol(G)}}}\int d^DXd^{\frac{D}{2}-1}\Psi e^{-S} $$ where $S=\frac{1}{g}(\frac{1}{4}\Sigma {\rm{Tr}}[X_\mu,X_\nu]^2+\frac{i}{2}\Sigma {\rm{Tr}}(\bar{\Psi}\Gamma^\mu[X_\mu,\Psi]))$ The authors rearrange the fields into the following form: $$ \phi=X_D+iX_{D-1} \\\ B_j=X_{2j-1}+iX_{2j} ~~~~~~(\rm{for ~~~j=1,2...D/2-1})\\\ \Psi \rightarrow \Psi_a=(\psi_j,\psi_j^{\dagger}), \vec{\chi },\eta$$ $B_j$ are often denoted as $\mathbf{X}=\\{X_a, a=1,....D-2\\}$ My question is what the rearrangement of fermion field means? For D=4, a=2, j=1 ,$\chi$ has one component, before arrangement, we have a Dirac spinor $\Psi$, and what do we have after arrangement? are $\chi$ and $\eta$ Weyl spinors? If we expand formula (2.4) using nilpotent symmetry (2.3), why no such terms like $\chi^{\dagger}[\bullet,\bullet]$? **Edit:** From some related paper Kazakov Kostov and Nekrasov, the rearrangement is clear while there are some other puzzles. From KKN, first rewrite matrix model into complex fermion form, which is the formula (2.1) of KKN $$\frac{1}{\rm{Vol(G)}}\int dXd\lambda \exp(\frac{1}{2}\Sigma _{\mu<\nu}\rm{Tr}[X_\mu,X_\nu]^2+ )+\rm{Tr}\bar{\lambda}_\dot{\alpha}\sigma_\mu^{\alpha \dot{\alpha}}[X_\mu,\lambda_\alpha]$$ Two complex fermions $\lambda$ can be written as four real fermions $\chi$, $\eta$,$\psi_\alpha$, $\alpha=1,2$, $$ \lambda_1=\frac{1}{2}(\eta-i\chi),\\\ \lambda_2=\frac{1}{2}(\psi_1+\psi_2),\\\ \bar{\lambda}_{\dot{a}} =\sigma_2^{a\dot{a}}\lambda_a^*,~~~s=[X_1,X_2]$$ Using the following nilpotent symmetry: $$ \delta X_\alpha=\psi_\alpha,~~~\delta\psi_\alpha=[\phi,X_\alpha] ,\\\ \delta\bar{\phi}=\eta,~~~\delta \eta [\phi,\bar{\phi}],\\\ \delta\chi=H,~~~\delta H=[\phi,\chi],\\\ \delta \phi=0$$ KKN claims that the action can be written as formula (2.5), $$ S=\delta \left( -i\rm{Tr} \chi s -\frac{1}{2} \rm{Tr}\chi H - \Sigma_a\psi_a[X_a,\bar{\phi}] -\frac{1}{2} \eta[\phi,\bar{\phi}]\right) $$ I found that there is some inconsistence between formula (2.1) and formula (2.5). Look at fermionic part that consist $X_2$ in (2.5) which is proportional to $i\rm{Tr} \chi[\psi_1,X_2] + \rm{Tr}\psi_2[X_2,\eta] $. If we start from (2.1), fermionic part that consist $X_2$ should be proportional to $ \bar{\lambda}_\dot{1}\sigma_2^{2\dot{1}}[X_2,\lambda_2] +\bar{\lambda}_\dot{2}\sigma_2^{1\dot{2}}[X_2,\lambda_1] $. Further using definition of $\bar{\lambda}_\dot{a}=\sigma_2^{a\dot{a}}\lambda_a^*$, we always get terms of form $\lambda_1^*[X_2,\lambda_1]$ and $\lambda_2^*[X_2,\lambda_2]$ which can not consist $i\rm{Tr} \chi[\psi_1,X_2] + \rm{Tr}\psi_2[X_2,\eta] $. Anything wrong here? Some comments and references are welcoming.


title: spectral function in condensed matter physics

text: What is the importance of deriving the results of perturbation theory in condensed matter physics in terms of spectral functions ?


title: Is the Higgs field really disconnected from gravity?

text: I would like to understand better the role of Higgs mass in the gravitational interaction. I read here in some posts, that the Higgs mass has nothing to do with gravitation. Is it justified to say that? Gravitation acts on "energy" rather than mass but it is only mass, among the physical observables, which provides an equivalent to energy in contrast to electrical charge for example. Hadron masses are generated by QCD but doesn`t one need still Higgs-massive quarks for this? If so, planet masses are connected to the Higgs mass. In the picture of general relativity space-time curvature causes gravitation but remembering Kepler`s laws, why should be "Higgs-based" mass unessential to gravitation, where it is the correct input, describing the orbits of planets etc.? Sorry, that I mix a few questions and it is a bit unstructured.


title: Prerequsites for Zee's QFT

text: What would be a good book or books for a sufficient prerequisite for Zee's book QFT in a nutshell? I have had a course in QM and relativistic QM, but I think there are some gaps that needs to be filled. Maybe someone who have read the book can tell me what other books they read or?


title: Confinement of charged tachyons in AdS spacetime

text: It is well known that the negative cosmological constant of AdS spacetime can act like a confining potential. That is, in contrast to asymptotically flat spacetime, in an asymptotically AdS spacetime _massive particles cannot escape to infinity_. However, massless particles can escape to infinity and actually do so in a finite time. **As tachyons travel faster than massless particles, is it true that all tachyons can escape to infinity as well?** If the answer is yes, then I have some trouble understanding the following argument in a paper by Horowitz on holographic superconductivity (see here). Here, the considered action of the holographic dual to the superconductor (the bulk action) is $S=\int d^4x\sqrt{-g}\left(R+\frac{6}{L^2}-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-|\nabla\Psi- iqA\Psi|^2-m^2|\Psi|^2\right)$, i.e., a complex scalar field $\Psi$ and a Maxwell field $A_t$ (electric) coupled to gravity. The effective mass for $\Psi$ following from this action is $m_{eff}^2=m^2+q^2g^{tt}A_t^2$. In constructing this dual theory, Horowitz argues that " _In AdS, the charged particles cannot escape, since the negative cosmological constant acts like a confining box, and they settle outside the horizon._ " (Of course, only for particles for which the sign of the charge is the same as that of the black hole.) However, the case considered subsequently is $m^2=-\frac{2}{L^2}$, which implies that $m_{eff}^2<0$ since also $g^{tt}<0$. Hence they consider tachyons! **Being tachyons, how can these particles settle outside the horizon? Why would they be confined by the cosmological constant rather than escape to infinity?** EDIT: right now I'm actually questioning my claim that all tachyons automatically travel faster than light...


title: How EM waves are produced by accelerating charged particles?

text: 1. How the electro-magnetic waves are produced by the accelerating charged particle? Graphical explanations are most welcomed.   2. Is the explanation given by the below mentioned article correct regarding the movement of electromagnetic waves? http://www.arrl.org/files/file/Technology/tis/Why%20an%20Antenna%20Radiates.pdf


title: How to understand "accelerating charge radiate" using intuition?

text: While I know that accelerating charges produces EM radiations (at least in lots of cases), most discussion about this matter only focuses on _which kind of situation_ will emit EM radiations and which does not, with very little mention of the intuition behind this physical phenomenon. Recently I'm trying to understand why accelerating mass generates gravitational wave (predicted by General Relativity), so I thought the first step is to understand it for charge first (they're very similar, after all), but surprisingly for the discussion I could find there isn't really any explanation about this matter. While mathematics can prove accelerating charges sometimes radiates EM waves, I want **an explanation using intuition that shows why this is true. Please don't use formulas to explain it.** Also, yes, I searched about the topic, and saw some mention of "conservation of energy" and "work done to the particle". But then, It still doesn't explain why the energy is lost in terms of EM radiation. Wikipedia said this kind of behavior has something to do with Special Relativity.


title: Why isn't the wave equation $\nabla^2 \psi - 1/c^2 \partial_{tt} \psi = (\frac{mc}{\hbar})^2\psi$

text: Special relativity was well established by the time the schrodinger equation came out. Using the correspondence of classical energy with frequency and momentum with wave number, this is the equation that comes out, and looks sensible because this is of the form of a wave equation, like the one for sound etc, except with an inhomogeneous term $$\nabla^2 \psi - 1/c^2 \partial_{tt} \psi = (\frac{mc}{\hbar})^2\psi$$ Instead, we have schrodinger's equation which reminds of the heat equation as it is first order in time. **EDIT** Some thoughts after seeing the first posted answer What is wrong with negative energy solutions? When we do freshman physics and solve some equation quadratic in, say, time... we reject the negative time solution as unphysical for our case. We do have a reason why we get them, like, for the same initial conditions and acceleration, this equation tells usthat given these iniial velocity and acceleration, the particle would have been at the place before we started our clock, since we're interested only in what happens _after_ the negative times don't concern us. Another example is if we have areflected wave on a rope, we get these solutions of plane progressive waves travelling at opposite velocities unbounded by our wall and rope extent. We say there is a wall, an infinite energy barrier and whatever progressive wave is travelling beyond that is unphysical, not to be considered, etc. Now the same thing could be said about $E=\pm\sqrt{p^2c^2+(mc^2)^2}$ that negative solution can't be true because a particle can't have an energy lower than its rest mass energy $(mc^2)$ and reject that. If we have a divergent series, and because answers must be finite, we say.. ahh! These are not real numbers in the ordinary sense, they are _p-adics_! And in this interpretation we get rid of divergence. IIRC Casimirt effect was the relevant phenomenon here. **My question boils down to this**. I guess the general perception is that mathematics is only as convenient as long as it gives us the answers for physical phenomenon. I feel this is sensible because nature can possibly be more absolute than any formal framework we can construct to analyze it. How and when is it OK to sidestep maths and not miss out a crucial mystery in physics.


title: Cosmological relativistic effects : misunderstanding between cosmological and relativistic communities?

text: I would like to clarify something that mixes cosmology and relativistic effects. Maybe I'm not understanding something or maybe there a difference of vocabulary between the cosmological and the relativistic people. If you ask a cosmologist at which scale the relativistic effects appears (for example in N-body simulations), he will probably answer you that a problem may occur at the scale of the horizon (so at the scale of the observable Universe). If you ask the same question to a specialist of the backreaction or a specialist of general relativity I suspect that he will answer you that a problem may occur at the scale of matter inhomogeneities (so at the scale of the cosmic web, filaments and voids). My question is : why are there these 2 point of views ? I suspect that is because a cosmologist hypothesizes an homogeneous space-time background and apply a perturbation theory on this background whereas for a people from general relativity there is no such background. Is it the answer or I don't understand something ?


title: What parity has an electron?

text: I couldn't find anything about the parity of an electron. Neither in the german, nor in the spanish and nor in the english version of Wikipedia. I only found one sentence in the parity article of Wiki: > One way to fix a standard parity operator is to assign the parities of three > particles with linearly independent charges B, L and Q. In general one > assigns the parity of the most common massive particles, the proton, the > neutron and the electron, to be +1. - Wiki But I cannot find other sources to confirm it. I do not need it for a special exercise, it's just to understand the whole thing...


title: Is there an equation to calculate efficiency of an optical fiber to transmit sunlight for length of 4 m

text: I want to transmit sunlight over a distance of approx 4 m via optical fiber. Ideally I want to light up the whole house with sunlight. I was reading that the largest diameter for an optical fiber may not be the right way to solve this issue. I was wondering if there some sort of equation where I can insert the length that I would like to carry light over (length is a variable) and maybe the number of cores of optical fiber (also a variable) with the output of this equation being the efficiency or loss in transmission. This way I can integrate all variables in one equation and optimize against the cost to procure.


title: Understanding Elitzur's theorem from Polyakov's simple argument?

text: I was reading through the first chapter of Polyakov's book "Gauge-fields and Strings" and couldn't understand a hand-wavy argument he makes to explain why in systems with discrete gauge-symmetry only gauge-invariant quantities can have finite expectation value. This is known as Elitzur's theorem (which holds for continuous gauge-symmetry). > Polyakov says : _[...] there could be no order parameter in such systems (in > discrete gauge-invariant system) [...], only gauge invariant quantities are > nonzero. This follows from the fact, that by fixing the values of > $\sigma_{\mathbf{x},\mathbf{\alpha}}$ at the boundary of our system we do > not spoil the gauge invariance inside it._ Here $\sigma_{x,\alpha}$ are the "spin" variables that decorate the links of a $\mathbb{Z}_2$ lattice gauge theory. I would like to understand the last sentence of this statement. Could anyone clarify what he means and why this implies no gauge-symmetry breaking ?


title: Homogeneity of space implies linearity of Lorentz transformations

text: In the derivation of Lorentz transformations, the Wikipedia article mentions a couple of times that the linearity comes from the homogeneity of space. I am looking for a thorough explanation on this.


title: Group transformations on $H_2O$

text: In my readings of Mirman (1995), "Group Theory: An Intuitive Approach", on p.35 he asks me to consider a so-called "water group" that has 4 transformations. I'll list them for completeness, but I'm only concerned about two of them.   1. The identity element   2. Reflection in the plane element   3. Rotation by $\pi/2$ about a line through "O" perpendicular to the line joining the two "H"s   4. Reflection through the line described in 3.  Now for some context. This book is primarily a book about group theory, but the author likes to use examples from physics in order to provide examples that yield a concrete picture of what the formalism can and can't describe. Leading up to the example of the water group, I calculated the Cayley table for the symmetry group $S_3$; the dihedral group $D_3$; and then the table for an isosceles triangle as an example of symmetry breaking from the equilateral triangle in the prior example. All of that I get. What I don't understand is how a quarter-turn rotation leaves the figure invariant in the water example. I tried it from two different angles:   1. using cylindrical coordinates, there is only one possibility: namely a 1/4 of a full turn in the plane of the figure which yields a picture that is different than what you started with.    2. or, using spherical coordinates, you can perform the rotation out of the plane but that leaves you with a top-down view and the three "atoms" following in a straight line which isn't what you started with, either.  So, I'll ask again: is there a way to do a 1/4 turn of an isosceles triangle that leaves the original shape unchanged?


title: A simple way of calculating Euler Angles from Rotation Matrix --- help!

text: This is a follow up of this question : I have the rotation matrix $$ \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\\ a_{21} & a_{22} & a_{23}\\\ a_{31} & a_{32} & a_{33}\\\ \end{matrix}\right) $$ I'm using pre-multiplying rotation matrix (that operates on column vectors) for intrinsic rotations (i.e. I make rotations about the axes of the plane that rotates). And since the fixed frame is my reference frame --- $$ \left( \begin{matrix} 1 & 0 & 0\\\ 0 & 1 & 0\\\ 0 & 0 & 1\\\ \end{matrix}\right) $$ My rotation matrix is nothing but the column unit-vectors of the axes of the rotated frame, i.e. $$ \left( \begin{matrix} x_{1} & x_{2} & x_{3}\\\ y_{1} & y_{2} & y_{3}\\\ z_{1} & z_{2} & z_{3}\\\ \end{matrix}\right) $$ So therefore I have the values of a11,a12,a13,a21,a22,a23,a31,a32,a33 as x1, x2, x3, y1, y2, y3, z1, z2, z3. Now if I consider a particular set of rotation (say X first, then Y , then Z), with the corresponding Tait-Bryan angles \--- a,b and c. My rotation matrix will be the following. Rx(a)*Ry(b)*Rz(c) \--- $$ \left(\small{ \begin{matrix} \cos(b)\cos(c) & -\cos(b)\sin(c) & \sin(b)\\\ \cos(a)\sin(c) + \cos(c)\sin(a)\sin(b) & \cos(a)\cos(c) - \sin(a)\sin(b)\sin(c) & -\cos(b)\sin(a)\\\ \sin(a)\sin(c) - \cos(a)\cos(c)\sin(b) & \cos(c)\sin(a) + \cos(a)\sin(b)\sin(c) & \cos(a)\cos(b)\\\ \end{matrix}} \right) $$ Now if I have to solve for the above angles a, b & c (pitch, yaw and roll), I basically have nine equations but three unknowns. Following are the equations ---               a11 =  cos(b)∗cos(c)     a12 = −cos(b)∗sin(c)     a13 =  sin(b)     a21 = cos(a)∗sin(c)+cos(c)∗sin(a)∗sin(b)     a22 = cos(a)∗cos(c)−sin(a)∗sin(b)∗sin(c)     a23 = −cos(b)∗sin(a)     a31 = sin(a)∗sin(c)−cos(a)∗cos(c)∗sin(b)     a32 = cos(c)∗sin(a)+cos(a)∗sin(b)∗sin(c)     a33 = cos(a)∗cos(b)       This is where I learnt about it. Now I am using a non-linear least squares curve fitting method to solve the above set of over-determined equations. There are two major problems that I am encountering   1. The final values of a,b, c change as I change the initial values in the iterative algorithm. I get different results if I start from [50 50 50] and different results with [0 0 0].   2. Secondly I don't think that the values obtained are correct; since the angles of pitch, yaw & roll seem pretty much different in the video. I'm using the lsqcurvefit(click for the question I asked on stackoverflow) command in Matlab. (click for documentation) I have been on this problem of how to calculate pitch, yaw & roll for quite some time now. I think this post will give you all the details of what I have tried. I need your help to know if what I am doing is the best approach to tackle my problem. If so, please point out what is wrong in my method. If you think there are other simpler methods, please let me know about them. I'm sure there has to be a better method, since this seems like a pretty simple thing to do. Should I change my Matlab algorithm? Anyone know any special Matlab/Mathematica toolbox that calculates the yaw, pitch, roll? Thanks!


title: Calculate the weight that a hot air balloon can carry

text: Given a hot air balloon of radius 10 meters and negligible mass, calculate the maximum weight it can carry if the density of outside air is 1.2 $\frac{kg}{m^3}$ and the density of inside air is 0.9 $\frac{kg}{m^3}$. Edit: My attempt: Since the maximum weight the balloon can carry is determined by the relation : $Q=mg$ I somehow need to set bouyancy force equal to $Q$. Is this correct and if not, how to do it correctly?


title: If a planetoid was wet and you spun it would the water move to the equator?

text: If the moon was alone in space and covered in X feet of water and it began to rotate would it displace to a bias along the equator?


title: Kallen–Lehmann spectral representation for an arbitrary spin

text: Let's have Kallen–Lehmann spectral representation for the scalar theory: $$ \tag 1 D(p) = \int \limits_{0}^{\infty} d(\mu^{2})\frac{\rho (\mu^{2})}{p^{2} - \mu^{2} + i\varepsilon}. $$ We can represent $(1)$ in a form $$ D (p) = D_{free}(p, m)Z + \int \limits_{m^{2}}^{\infty}d(\mu^{2})\rho (\mu^{2})D(p, \mu), $$ where $\mu$ refers to the mass of the multiparticle states and $m$ refers to the mass of one-particle free state. From here there is interesting result: it can be showed that $0 \leqslant Z \leqslant 1$. How to get analogous result for the arbitrary spin field (or at least for fermions with spin $\frac{1}{2}$ and for photons)? I know the general structure of the propagator of the free theory (for simplicity I assume massive case): for field $\Psi $ with spin $s$ $$ \hat {\Psi}_{l} (x)= \sum_{\sigma = -s}^{s}\int \frac{d^{3}\mathbf p}{\sqrt{(2 \pi)^{3}2E_{\mathbf p}}}\left( u^{\sigma}_{l}(\mathbf p )e^{-ipx}\hat {a}_{\sigma}(\mathbf p ) + v^{\sigma}_{l}(\mathbf p )e^{ipx}\hat {b}^{\dagger}_{\sigma}(\mathbf p ) \right) $$ it will be $$ D_{lm}(p) = \frac{F_{lm}(p)}{p^{2} - m^{2} + i\varepsilon}, \quad F_{lm} = \sum_{\sigma}u^{\sigma}_{l}(\mathbf p )\left(u^{\sigma}_{m}(\mathbf p) \right)^{\dagger}. $$ For the derivation of spectral representation for the scalar field see the reference above. Here also you can see the problem with this derivation which appears for the case of field with nonzero spin: it is impossible to introduce the scalar density function $\rho (\mu^{2})$. Also there is bigger problem: there was using relation $\langle |[\hat {\Psi}(\mathbf x , t), \frac{d}{dt}\hat {\Psi}^{\dagger}(\mathbf y, t)]|\rangle = i\delta (\mathbf x - \mathbf y)$ for getting relation $0 \leqslant Z \leqslant 1$ (look to the Weinberg's "QFT" (chapter "Kallen–Lehmann spectral representation" of the section "Nonperturbative methods") or to Greiner's "Field Quantization" (pp. 278-282)). But this relation is correct only if one field is canonical conjugated to another (one field is canonical coordinate while the another one is canonical momentum). But for the arbitrary spins the canonical momentums must be chosen "individually".


title: Mass of the particle and gravitational field

text: Which mass of the particle is the source of gravitational field? If we define mass as a pole of the propagator, and calculate loop corrections to the pole we get infinities. Now the way we get rid of these infinities defines what is our renormalized propagator and what is its pole. What is the mass of the particle is dependent on which renormalization scheme we choose. Now, gravity field knows about everything that happens to the particle (as any energy gravitates), all contributions of whatever virtual particles contribute to the mass of particle (up to very short distances).


title: Software to simulate and visualize atoms?

text: Not sure if this is a physics or chemistry question. But if the motion of atoms and it's particles can be described by quantum mechanics, then is there a software that simulate full atoms and it's boundings, in a way you can visualize them, and that can be used, for instance, to throw 2 molecules together and watch them reacting?


title: Gauss's Law vs Newton's Law

text: This is thought experiment. I couldn't get a good answer because I keep getting negative mass. Gauss's Law say that eletric field is proportional to charge, how much charged is enclosed. Newton's gravitational pretty much says the same thing. More mass, strong gravitational strength. So to put it mathematically $$\vec{E} \propto \sum Q_{en}$$ But charge can be negative, a negative sum of charge means the electric field is going _inwards_. $$\vec{g} \propto \sum M_{en}$$ But mass can only be positive, but g is then propotional to the mass enclosed, which means it will go radially outwards. That doesn't make sense because we know gravity is radially inward for a spherical shape (like earth)


title: Simple Harmonic Motion. Why am I wrong? Why is my equation wrong more importantly?

text: **Problem/Solution** ![](http://img221.imageshack.us/img221/4285/20841428g.jpg)! I am deeply confused. B) We know that $x = 2\sin(3\pi t)$. $x' = 6\pi\cos(3\pi t)$ So max _speed_ is $6\pi$ $6\pi = 6\pi \cos(3\pi t)$ $\cos(3\pi t) = 1$ $3\pi t = 2\pi$ (reject 0 since t >0) $t = 2/3$ But it isn't 2/3s. I understand where the solution is coming from, but I don't understand why I am wrong.


title: What is the Physical Significance of Tr(A) w.r.t. Matrix Representations in Group Theory

text: I've seen the post on mathoverflow.SE asking almost the same question, and I have indeed flipped through said answers, but most are in a more general context ie quantum mechanics and do not provide a conceptual answer with physical interpretation. Anyone able to offer any insight, or even an example in the aforementioned context? ( More particularly the theory of representations for symmetry groups. )


title: Why wouldn't this system of equations determine where two balls meet?

text: > A ball is thrown vertically upwards at $5\text{ m/s}$ from a roof top of > $100\text{ m}$. The ball B is thrown down from the same point $2\text{ s}$ > later at $20\text{ m/s}$. Where and when will they meet? Well at first I separated the fact that while ball B falls at say $t$ seconds, ball A's time is given by $t+2$ (due to it being thrown 2 seconds prior to ball B). Given what's given above (the velocity and height)...I wrote down the following equations to find TIME, where lower a and b denote ball A and B: $$\begin{align}s_a &= s_{0a} + u_a(t+2) + \frac{1}{2}a(t+2)^2 \\\ s_b &= s_{0b} + u_bt + \frac{1}{2}at^2\end{align}$$ $S_a(0) = 100$ m, $S_b(0) = 100$ m, $u_a = 5$ m/s, $u_b = 20$ m/s, $a=-9,8$ m/s$^2$ Now plugging those in gives: $S_a = 100 + 5(t+2) + \frac12(-9.8)(t+2)^2$ and $S_b = 100 + 20t + \frac12(-9.8)t^2$ but i tried equalizing the above two equations with all the proper variables replaced by the values provided in the problem, but unfortunately i don't get the right answer.eventually knowing time i can answer to the "where" part of the question. I'm lost, I'm not even sure if I tackled the problem correctly.


title: Surface tension of solutions and mixtures

text: The inspiration for this question is over on cooking.stackexchange, asking more about actual measurements for commonly consumed liquids, but I'm interested more generally as well. What determines the behavior of surface tension for solutions and mixtures with respect to concentration? Of course, I expect that the answer depends on the liquid, since different liquids have different causes of cohesive forces. I would be interested both in quantitative answers (very approximate/general, probably) and qualitative ones. Additionally, what is the dependence of surface tension on temperature? Does that have any interaction with dependence on solution/mixture concentration? (I know this question borders on chemistry, but there's no chemistry stackexchange, and besides, I'm sure at least some surface tension properties admit explanations from statistical mechanics!)


title: Are there hidden parameters in neutron decay?

text: The neutron decay is a spontaneous process. After isolating neutrons the mean lifetime is approx. 15 minutes. The real moment when the neutron decays is not affected by us. That's why, it is allowed to speak about hidden parameters?


title: Difference between various shear forces

text: What is the difference between $\tau_{xy}$ and $\tau_{zy}$; because as far as i know the first character of subscript represents the direction to which the stress is perpendicular and other the actual direction. So a vector perpendicular to $x$ along $y$ and another perpendicular to $z$ along $y$, shouldn't they be the same?


title: Converting two component product to four component notation

text: Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \begin{equation} \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta \end{equation} This is equal to, \begin{equation} \left( \begin{array}{c} \chi ^\alpha \\\ 0 \end{array} \right) ^T\left( \begin{array}{cc} \epsilon _{ \alpha \beta } & 0 \\\ 0 & \epsilon ^{ \dot{\alpha} \dot{\beta} } \end{array} \right) \left( \begin{array}{c} \eta ^\beta \\\ 0 \end{array} \right) = \bar{\eta} _L ^\ast \gamma _0 C \chi _L \end{equation} where I have used some common spinor identites and defined, $ \eta _L \equiv P _L \eta, \chi _L \equiv P _L \chi $ ($\eta $ and $ \chi$ are now four component spinors). I also use the defintion, $C \equiv i \gamma_0 \gamma _2 $. While I don't think anything is particularly wrong with this derivation, I have never seen a term like this in normal quantum field theory. It there a simpler way to reformulate this to correspond to common expression for such mass terms or is my uncomfort with this term due to my ignorance?


title: Calculate the UPS Capacity in amp-hours

text: I am trying to find out the UPS capacity in amp-hours for my HP UPS system. I've already done some calculations based on the UPS information from the HP Power Manager software. ![HP UPS Parametars](http://i.stack.imgur.com/rdvd0.png) Bellow are my calculations but somehow I doubt them and I think I am making a mistake somewhere: Output Power: **1160W**   Output Voltage: **235V**   Run time remaining: **12min** \- Converted to hours that is **0.2h** First I am converting the W to A:   1160W / 235V = **4.936A** Now to find the amp-hours for 12min that are specified in the run time remaining: **4.936A * 0.2h = 0.987Ah** Can someone more experienced in batteries, current and UPS Systems tell me if my calculations are correct? I am not sure that I have taken the correct values into consideration since **my calculations are based upon the output values from the UPS.**   Also as a side note I must tell you that I am not very fond of current and all that stuff and I have only basic knowledge about amps, volts and watts from college.


title: How does one calculate the volume of a nucleus and the volume of an atom (in this case hydrogen)?

text: The hydrogen atom contains 1 proton and 1 electron. The radius of the proton is approximately 1.0 fm (femtometers), and the radius of the hydrogen atom is approximately 53 pm (picometers).


title: Does entropy decrease through measurement?

text: For an electron in its rest frame, we have an entropy $$ S = \log 2, $$ which comes from the 2 possible spin directions along z-axis. If the measurement $S_z$ changes its state to $\left| + \right>$, the entropy goes to zero. Does this violate the second law of thermodynamics?


title: How many years would it take the Pioneer space probe to travel to Proxima Centauri with its current speed?

text: Pioneer space probe moving at a speed of $30km/s$. Assuming its heading for Proxima Centauri, which is situated at $4.2ly$ from earth, calculate how long it would take to get there in years, to the nearest year? Could you please help.


title: Space contraction: what do we see

text: ![enter image description here](http://i.stack.imgur.com/MbcF9.gif) This is my opinion about what we will see. When the pipe arrive at the bar, we will be unable to see some part of it anymore (the pipe will absorb the light emitted by the bar), even if the pipe and the bar didn't appear to us superposed yet. We will not see the white background, because the bar is not transparent. So, we must see nothing (black), even if we know the bar is there. Am I right or wrong?


title: What's so special about AdS?

text: This question is coming from someone who has very little experience with M-Theory but is intrigued by the AdS/CFT correspondence and is beginning to study it. Why is the gauge/gravity duality discussed almost always in the context of anti-deSitter space? What is unique about it? What are the difficulties in studying it in Schwarzschild, deSitter, etc.? References to work done on the gauge/gravity duality in these more physical spacetimes would be much appreciated.


title: Why do we need to find 5 Higgs Bosons to prove the existence of the dark matter?

text: I was recently watching a show that say we need at least 5 Higgs Boson to prove the existence of the dark matter because it will strengthen the concept of symmetry. Why is that so? Because, I am not getting what it says.


title: What's the Noether charge associated with Kaehler invariance of SuGra?

text: What is the Noether charge associated with Kahler invariance of supergravity (SUGRA)? As the question is rather tangential to what I need to do, I have not tried explicitly calculating it myself, but I'm sure that I'm not the first one to wonder.


title: Can special relativity be extended such that the frame of a photon makes sense?

text: Suppose I want to know what the universe looks like from the perspective of a frame of reference moving at $c$ relative to my current frame. As discussed at length in various other questions on this forum, from the perspective of the current established theory of special relativity, the notion of such a frame is more or less nonsense.$^{[1]}$ However... Is it possible to modify the setting of special relativity, by adding dimensions to space-time, or any other hereto unobserved features, such that the restriction of the theory to our 4-D slice of space-time matches special relativity, and such that there is a meaningful way to describe the frame of a photon? [1] In partiucular, the transformation we get by shoving $v=c$ into the usual formulae is not in the Lorentz group (it doesn't preserve volume of space-time and is not invertible).


title: Do We Need Maxwell's Equations Since They Fail to Account for An Experimental Fact at Least in One Occasion?

text: This question is an outgrowth of regarding voltage and emf where @sb1 mentioned Faraday's law. However, Faraday's law as part of Maxwell's equations cannot account for the voltage measured between the rim and the axis of a Faraday generator because $\frac {\partial B} {\partial t} = 0$. It would've been a different story if the derivative were $\frac {dB} {dt} $ but it isn't. A palliative solution to this problem is given by invoking the Lorentz force. However, Lorentz force cannot be derived from Maxwell's equation while it must be if we are to consider Maxwell's equations truly describing electromagnetic phenomena. As is known, according to the scientific method, one only experimental fact is needed to be at odds with a theory for the whole theory to collapse. How do you reconcile the scientific method with the above problem?


title: Time duration for pulse of single electron viewed as a wave

text: Electron as an example has a de Broglie wavelength and could diffract. If it has a single wavelength the time extent of the particle's pulse duration would be infinite .. If it carries a broadband will be finite in time .. my question is how is it determined the duration in time of the electron or it is assumed to be the classical diameter and what is its spectral content ?


title: Inspecting the form of a wavefunction

text: Just a quick check: If given a time-independent wavefunction of the form $$\psi(x) = e^{ikx}f(x)$$, where $f(x)$ any arbitrary function of $x$ but one can't factor out another $e^{i\alpha x}$, $\alpha\in\mathbb R$. Could I then immediately conclude that $k^2= \frac{2mE}{\hbar^2}$? Is there a name for this quantity? It seems to creep up a lot. Suppose the wavefunction is $$\psi(x) = e^{ikx}(\tanh{x}-ik)$$. Am I justified to conclude by inspection that there is no reflection (since there is no $Re^{-ikx}$ term)? What else can I conclude by inspection? Thanks!


title: Unsatisfactory explanation for the EMF measurement of a battery

text: Experimentally, I have seen how hooking up a battery to a simple circuit just with a high-resistance voltmeter raises the voltage reading (allegedly to a level equal to the EMF of the battery). However, I find the explanation for why the reading rises, much less to an EMF, very unconvincing. We were told that the internal resistance and the necessary potential drop is ignored, because there is no current in the said circuit, hence why the voltmeter measures an EMF. How can this make sense? There clearly must be some current, albeit very little, flowing, for the high- resistance voltmeter to even have a reading, and that little current will still experience resistive forces from the internal resistance of the cell - so the EMF should not be attainable. Or is there a mechanism by which, when there is very little current, resistors are ignored, hence no work has to be done to traverse them? Clearly I am wrong, as experimentally I saw the voltage rise in that super simple cell. My point of view suggests that there shouldn't be a difference between the reading in said circuit and the potential difference in a circuit consisting of 3 resistors (the voltmeter in this case measures the drop between these 3 resistors, note there is no other significant source of resistance other than the internal resistance). Really, in my theoretical understanding they should produce an equal reading, but they don't. So, to be honest, not only do I believe that the reading we saw shouldn't have been the EMF, but not even any different from the reading in a normal circuit, as described (the latter belief clearly conflicts with reality). I an eager to know what I am thinking wrongly about. Please ask if I can help clarify anything! Thank you very much :)!


title: Why is all the voltage used up in a circuit?

text: We always assume that all the voltage, in no matter what type of (basic, I guess) circuit we are dealing with, is used up. I can see why this is true. Imagine a circuit with low resistance - and correct me if I am wrong, but from electrostatics, we know that an electric field, similar to magnetic fields, accelerates charges. Now mustn't it be that some charges arrive at the end of the circuit (into the positive charge reservoir) with some velocity, higher than that with which they began. Essentially, if seems to me what we always assume that the electrons always do the maximum that they could, no matter what the conditions. Is it my misunderstanding that such an assumption exists or are there some ideas I am completely oblivious of? Please ask if you want any clarifications.


title: Will a blanket warm you if you are underwater?

text: Suppose a man falls into very cold water and gets their foot stuck under a heavy rock. Fortunately, his head is above water and someone is able to call for help. The paramedics want to keep him warm while they work on freeing his foot. They put a hat on his head. Should they also wrap him in a blanket?


Where can a good treatment of the 'sudden' perturbation approximation be found? A lot of quantum mechanics books have very brief discussions of it but I want to see it in some detail and preferably with as many examples as possible. Is there a book, paper, or some other place that details this approximation?


title: Without gravity, is there still up and down?

text: I'll try to be clear: example: If you send the ISS far enough for it not to undergo the Earth's gravity anymore, then you turn it and the—sleeping—astronauts in it upside down, when they wake up, will they know/feel that they're not the right way up? How?


title: Weird operator and wavefunctions

text: How can one show that $\int_{-\infty}^{\infty}\psi^*(x)(d/dx+\tanh x)(-d/dx+\tanh x)\psi(x) dx=\int_{-\infty}^{\infty} |(d/dx+\tanh x)\psi(x)|^2 dx$, where $\psi$ is normalized?


title: Light and parabola

text: I know that parallel light beams hitting a parabola will be focused at the focus of the parabola (`f = 1/4a`) and a light source at the focus of the parabola will produce parallel light. What will happen if the light was not parallel but came from a light source shorter then the focus of the parabola and at an angle to the axis of symmetry? More general how will dispersement of the light from the parabola be affected with the light source at different angles and lengths from the parabola.


title: How can a conductor be grounded yet there are induced charges on it?

text: A classic example for the method of images is the following, quoted from Griffiths's Introduction to Electrodynamics, page 121: "Suppose a point charge $q$ is held a distance $d$ above an infinite grounded conducting plane. Question: What is the potential in the region above the plane?" Griffiths continued on solving the example using the method of images setting V=0 on the plane as one of the boundary conditions saying "since the conducting plane is grounded". Now, of course there will be an induced surface charge density. My question is, how can this be since the plane is grounded? Does the word grounded have different meanings? sometimes it means not charged and the others it means the potential there is 0?


title: Why is the energy density of the electric field produced by two unlike charges positive, even though their potential energy is negative?

text: Consider two stationary charges, one positive the other negative. Their potential energy is clearly negative. So you would expect that the energy density of the associated electric field would also be negative. But it isn’t. It’s the square of the electric field and therefore positive. Why isn’t the energy density negative like the potential energy?


title: In general relativity (GR), does time stop at the event horizon or in the central singularity of a black hole?

text: I was reading through this question on time and big bang, and @John Rennie's answer surprised me. In the immediate environment of a black hole, where does time stop ticking if one were to follow a 'watch' falling into a black hole?   1. At the event horizon?   2. In the central singularity? If time stops at the event horizon, does the watch get stuck there, or does it keep falling in all the way to the singularity. Guess I know less than I thought.


title: CHSH Inequality: why $\pi/8$?

text: I understand the mechanism how CHSH Inequality works. One thing bugs me is why $\pi/8$. I can also take $\pi/100$ for example and $\cos^2(\pi/100)> \cos^2(\pi/8)$ so much better probability and it doesn't contradict with the explanation of setting up states to suit $\pi/100$. there is nothing special about $\pi/100$ infact i am guessing i can have the angle 0 < angle < $\pi/4$ but we want to get as close to zero as possible to get the highest probability is this correct if not why


title: Does reactive force require the two force involved have to have two different medium for reactive force to occur?

text: Does reactive force require the two force involved have to have two medium for reactive force to occur? I know the fuel-thruster is working on vacuum space, but we human could not use arm to swim in space? For example, two baseball hitting together have two medium


title: Confusion with infinity and time

text: I have some confusion between with resolving the following situation. I know that no measurable quantity can have a value of infinity. For example, I just wrote something out, but clearly this doesn't work, since infinity is not really a number and thus measurable entities can't be quantified as being of infinite amount. > I own an infinite amount of coins scattered on the ground. I give you all of > them so I have none left and you have an infinite amount. > > With the same infinite amount of coins, you then give me all coins showing > heads, and keep all coins that are tails. Now we both have an infinite > amount of coins. > > I then keep £100 worth of coins for myself and give the rest back to you. > > Does that then mean that you have made a net gain of coins, or do you have > the same amount of coins as you had before? I can understand that the above doesn't make sense, however, what if you were to use the same concept with time. For example, if I ask this question: > Is time infinite? I can't understand how the answer to that can be either `Yes` or `No`. Both answers must be wrong. If you respond saying `yes`, and say that time is in fact infinite, then it would mean that up until the writing of this question, that an infinite amount of time has past, and that an infinite amount of time is still yet to pass. However, the fact that I am writing this post now, must mean that time is not infinite, because how can an infinite amount of time have already past, if I am writing this now? Put simply, "now" cannot exist, if time is infinite. Equally, if you were to respond and say "no" time is not infinite, then that would mean that the big bang started time, but then that must also mean that time needs to stop at some point. Otherwise, time would be again be infinite, meaning that "now" could never exist. (Someone feel free to change the title of this question to something more suitable).


title: Hanging a Hammock

text: I have a hammock that I want to hang using a tree on one end and a wooden post set in a bucket of cement on the other end. How would I determine how heavy the cement needs to be so that it would support the weight of a 250lbs person in the hammock? Any ideas would be appreciated.


title: What is Energy made of?

text: We have the famous equation $E = mc^2$, and we also believe that matter is made of particles. Then, What is the energy made of? If the two are interchangeable, there must be some common building block to both for sure. Isn't it? If energy is made of "Nothing", how could it be converted to matter?


title: How to determine the field of view for a pinhole camera with given parameters?

text: I am reviewing some old material I learned years ago and am having trouble figuring this one out. Can somebody confirm that I have done my math correctly, and tell me how I can recover the field of view from these parameters? I have a $3.6$(height) by $4.8$(width) mm sensor, which displays as $640\ by\ 480$ pixels. I take an image of some item that I want to be 50px large in my image. It is $10 m$ away, and $10 cm$ tall in real life. I compute the size of a pixel on the sensor as $\frac{3.6}{640}\ by\ \frac{4.8}{480} mm$ to get $0.006\ by\ 0.01 mm$. I compute the magnification by $\frac{image\\_size}{actual\\_size}$, so I compute that the image size of $50px$ with a pixel height of $0.006mm$ takes up $0.3 mm$ of the sensor. Thus, magnification is $\frac{0.3}{100} = 0.003 mm$. Magnification can also be viewed as $m = \frac{f}{u - f}$, so $0.003 = \frac{f}{100 mm - f}$, which will give us $f = 0.299 mm$. From here, I know that it's possible to calculate the field of view, but how can I do it? I imagine the equation will use the image sensor size and the focal length. Thanks!


title: Nonlinear dynamics beneath quantum mechanics?

text: Yesterday I asked whether the Schroedinger Equation could possibly be nonlinear, after reviewing the answers and material given to me in that thread I feel like my question were adequately answered. However could there still be nonlinear dynamics underneath quantum mechanics that could potentially explain the "weirdness" of quantum mechanics? I know of atleast one serious physicist who is developing an approach in this direction, Tim Palmer with his Invariant Set Postulate. Just like the Liouville equation is linear, but there are "deeper" nonlinear dynamics beneath it, couldn't the Schroedinger Equation be the same? This is atleast one of Tim Palmers motivations for developing his approach and is also what Dirac said way back in the days. I suspect this is what David Zaslavsky meant yesterday when he responded to my other thread (Could the schroedinger equation be nonlinear) when he said: > That being said, there's no reason that the "true" theory underlying QM > would have to be linear. In fact, for exactly the reason you pointed out > (i.e. that general relativity is nonlinear), it's commonly believed that we > will need some kind of nonlinear theory to properly explain the universe at > its most basic level. Any views / opinions / thoughts / theories ?


title: Position dependent speed, how to compute position

text: I can't solve a problem: $ A= 0.5 (ms)^{-1}$, $ x_0 = 0.5 m $, $v(t)= A \cdot x^2 $, I have to compute the position at $t=3$ ($x_0$ is the initial position). So my guess is that I should be able to compute the $x(t)$ formula by integrating $v(t)$: $$ \int^t_0 A \cdot x^2 dt = x_0 + A \cdot x^2 \cdot t $$ So I get: $$ x^2 \cdot At -x + x_0 = 0 $$ Which is a 2nd grade equation with a negative discriminant: $$ \Delta(x) = (-1)^2 - 4 \cdot Atx_0 = 1 -4 \cdot 0.5 \cdot 3 \cdot 0.5 = 1-3=-2$$ My book includes just the solution, but it doesn't say how to get it. The solution is: $$ x(t) = \frac{x_0}{1 - x_0At} $$ If I study it I get: $$ x = \frac{x_0}{1 - x_0At} $$ $$ x \cdot \big( 1 - x_0At \big) = x_0 $$ $$ xx_0 \cdot At -x + x_0 =0 $$ Which is different from the one I got ($x^2 \cdot At -x + x_0 = 0$).


title: Why does the moon not revolve around the sun directly?

text: The sun pulls on the moon with a force that is more than twice the magnitude of the force with which the earth attracts the moon. Why, then, doesn’t the sun take the moon away from the earth?


title: Why has a gravitational wave spin 2? (Group theoretically?)

text: How can I see, using group theoretic arguments, that a the quantum of a gravitational wave has spin 2? How can one show that it is described by a 5 dimensional representation of $SO(3)$? I know the argument from Carroll's book on General Relativity: from looking at the perturbation on the geodesics followed by a perfect fluid, which are invariant under 180 degrees. But that doesn't seems very convincing.


title: Bernoulli equation from energy conservation

text: I have derived the energy conservation equation: \begin{equation} \frac{\partial}{\partial t} \left [ \frac{1}{2} \rho v^2 + \varepsilon + \rho \phi \right ] + \frac{\partial}{\partial x_j} \left [ \frac{1}{2} \rho v^2 v_j + \rho h v_j + \rho \phi v_j \right ]=0 \end{equation} where $\varepsilon$ is internal energy and $\rho \phi$ is the gravitational energy. I was trying to derive the Bernoulli equation from the above equation for time independent flow. It is not clear to me which term is Bernoulli equation term. How can derive the Bernoulli equation?


title: Can double entanglement preserve correlations?

text: We have 2 EPR experiments running in parallel, with Alice having one leg of each (a1,a2) and Bob the other leg of each (b1,b2). Thus (a1,b1) are anticorrelated, as are (a2,b2). Thus also (a1,a2) are uncorrelated as are (b1,b2). Now Alice locally entangles (a1,a2), and Bob measures b1 and b2. After repeating the entire experiment (including setting up the initial entanglements) many times, does Bob see consistent correlation or anticorrelation between his measured b1 and b2? How Alice accomplishes this final entanglement (a1,a2) is either via entanglement swapping, or via the method described in Yurke and Stoler, Phys. Rev. A46, 2229 (1992): "Bell’s-inequality experiments using independent- particle sources". Put another way, it's clear that b1 and b2 will show no correlation if Alice does not entangle (a1,a2), since the two EPR experiments are independent. Will this situation change for Bob as a result of Alice's entanglement of (a1,a2)?


title: Scattering problem: Converting the two-body lab frame problem into a one-body center-of-mass frame problem

text: I'm reading the section on scattering in Goldstein's Classical Mechanics, and I have a rather basic question about this. It says that scattering in the laboratory is a two-body problem because of the recoil of the scatterer. Therefore, we convert the obtained data into center of mass coordinates in order to find the true scattering angle, the angle that we would get if the scatterer didn't recoil. However, I'm having a hard time understanding what exactly this center of mass system is. The figure (3.25) below shows the path of two particles moving towards each other, but it looks like it is simply the laboratory problem shown in the frame of reference where the center of mass is not moving. My question: It still looks like a two-body problem to me, especially since the scatterer is deviating from its path. How does this simply the situation? Figure 3.25 still doesn't show a situation where the scatterer's position is fixed. Neither does figure 3.24. ![enter image description here](http://i.stack.imgur.com/9OSm9.jpg) ![enter image description here](http://i.stack.imgur.com/Fl79e.jpg)


title: Aharonov-Bohm Effect and Flux Quantization in superconductors

text: Why is the magnetic flux not quantized in a standard Aharonov-Bohm (infinite) solenoid setup, whereas in a superconductor setting, flux is quantized?


title: What is the status of the Gennes - Alexander theory of Superconducting Micronetworks?

text: I have started reading the book Connectivity and Superconductivity which gives an introduction to the ideas of de Gennes-Alexander theory. My question is: how is this theory regarded experimentally? Besides the sophisticated math approach,does it give good experimental results?


title: Reversing gravitational decoherence

text: [ **Update:** Thanks, everyone, for the wonderful replies! I learned something extremely interesting and relevant (namely, the basic way decoherence works in QFT), even though it wasn't what I thought I wanted to know when I asked the question. Partly inspired by wolfgang's answer below, I just asked a new question about Gambini et al.'s "Montevideo interpretation," which (if it worked as claimed) would provide a completely different sort of "gravitational decoherence."] This question is about _very_ speculative technology, but it seems well- defined, and it's hard to imagine that physics.SE folks would have nothing of interest to say about it. For what follows, I'll assume that whatever the right quantum theory of gravity is, it's perfectly unitary, so that there's no problem at all creating superpositions over different configurations of the gravitational metric. I'll also assume that we live in de Sitter space. Suppose someone creates a superposition of the form (1) $\frac{\left|L\right\rangle+\left|R\right\rangle}{\sqrt{2}},$ where |L> represents a large mass on the left side of a box, and |R> represents that same mass on the right side of the box. And suppose this mass is large enough that the |L> and |R> states couple "detectably differently" to the gravitational field (but on the other hand, that all possible sources of decoherence _other_ than gravity have been removed). Then by our assumptions, we ought to get _gravity-induced decoherence_. That is, the |L> state will get entangled with one "sphere of gravitational influence" spreading outwards from the box at the speed of light, and the |R> state will get entangled with a _different_ such sphere, with the result being that someone who measures only the box will see just the mixed state (2) $\frac{\left|L\right\rangle\left\langle L\right|+\left|R\right\rangle\left\langle R\right|}{2}.$ My question is now the following: **Is there any conceivable technology, consistent with known physics (and with our assumption of a dS space), that could reverse the decoherence and return the mixed state (2) to the pure state (1)? If so, how might it work? For example: if we'd had sufficient foresight, could we have surrounded the solar system with "gravity mirrors," which would reflect the outgoing spheres of gravitational influence back to the box from which they'd originated? Are exotic physical assumptions (like negative-energy matter) needed to make such mirrors work?** The motivation, of course, is that if there's _no_ such technology, then at least in dS space, we'd seem to have a phenomenon that we could justifiably call "true, in-principle irreversible decoherence," _without_ having to postulate any Penrose-like "objective reduction" process, or indeed any new physics whatsoever. (And yes, I'm well aware that the AdS/CFT correspondence strongly suggests that this phenomenon, if it existed, would be specific to dS space and wouldn't work in AdS.) [Note: I was surprised that I couldn't find anyone asking this before, since whatever the answer, it must have occurred to lots of people! Vaguely-related questions: Is decoherence even possible in anti de Sitter space?, Do black holes play a role in quantum decoherence?]


title: kinetic energy and conservative force field

text: The kinetic energy of a particle is a periodic function in time. Does it imply that the particle is in a conservative force field and there are no dissipative forces acting on it at any instance of time ? **EDIT** (in view of comment by Willie) Please consider the question as "Is the force acting on the particle conservative ?" Also consider the kinetic energy to be periodic with non zero period.


title: Surface charge in a wire?

text: ![enter image description here](http://i.stack.imgur.com/L5thM.png) The image above shows the distribution of the surface charge in a current carrying wire. The surface charges distributes themselves to make sure the field inside the wire is always perpendicular to the surface of the wire. Why is exactly half of the wire covered in negative surface charges and the other half with positive surface charges? I've noticed this in every surface charge distribution I've seen.


title: Why are there some inconsistencies with the underlying principle of center of gravity and rotational inertia?

text: COG: The lower the center of gravity, the more stable and object is. Rotational Inertia: The farther the concentration of mass from the defined axis of rotation, the more resistance the object has to movement. I'm quite confused between these two statements.


title: Gauge symmetry is not a symmetry?

text: I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate calculations. Regarding this I have a few questions:   1. Why is it called a symmetry if it is not a symmetry? what about Noether theorem in this case? and the gauge groups U(1)...etc?   2. Does that mean, in principle, that one can gauge any theory (just by introducing the proper fake degrees of freedom)?   3. Are there analogs or other examples to this idea, of introducing fake degrees of freedom to facilitate the calculations or to build interactions, in classical physics? Is it like introducing the fictitious force if one insists on using Newton's 2nd law in a noninertial frame of reference?


title: How does the quantum path integral relate to the quantization of energy?

text: So, the quantum path integral is a generalization of the classical principle of least action- but here we know that all paths contribute something finite to the probability density. What confuses me is that this doesn't seem to involve the quantization of energy (action) at all. How does this come into play? Is it a separate assumption, only coming into play when we worry about the non-commutativity of certain operators?


title: A question from Srednicki's QFT textbook

text: I have a question in Srednicki's QFT textbook. In order to compute the vacuum to vacuum transition amplitude given by : $$\left \langle 0|0 \right \rangle_{J}~=~\int \left [ d\varphi \right ]e^{i\int dt ~L\left ( \varphi ,\partial _{\mu }\varphi \right )},$$ one has to Fourier transform the field to the momentum space $$\varphi \left ( x \right )~=~ \int d^{4}k~e^{ikx}\phi \left ( k \right ).$$ But what is the motivation to do so? And what other methods that could be used to compute $\left \langle 0|0 \right \rangle_{J}$ in the path integral formalism? I feel that although I understand the derivation, many steps are done in many places in this book but I don't understand what are the motivations for taking them.


title: What mechanism in string theory enforces the consistency of self-couplings of massless vector bosons?

text: I have been reading the stackexchange questions on enhanced symmetries in string theory, the Leech lattice, monstrous moonshine, etc. , and I have a question to ask. An astute commentator pointed out with enhanced symmetries, massless vector bosons have to couple in the Yang-Mills fashion. Only if the massless vectors come in a Lie algebra will that be possible. Imagine bosonic string theory. Compactify 24 spatial dimensions over the Leech lattice or odd Leech lattice. With respect to the uncompactified dimensions (one spatial and one timelike), we get 196560 massless vector bosons, but they can't be part of any Lie algebra. But that's OK because massless vector bosons in 2 dimensions have zero norm. Let's try again. Compactify 23 spatial dimensions over the shorter Leech lattice. There are 2 spatial and one timelike uncompactified dimensions. Over this space, we have 4600 massless vector bosons, but they're not part of any Lie algebra either. But that's also OK because massless vector bosons in 3 dimensions are physically indistinguishable from massless scalar bosons. The reason for this is there is no helicity. If we try to find a similar example over at least 4 uncompactified dimensions, where massless vector bosons exist for certain and aren't equivalent to anything else, we discover all unimodular lattices in 22 dimensions or less are part of a root system. Thus, we always have a Lie algebra. What is the magical mechanism in string theory enforcing this sort of self- consistency? Is string theory only self-consistent because of accidental coincidences?


title: Polarized sunglasses: should the axes in both lenses be parallel?

text: See the pictures below. A pair of sunglasses I recently purchased has the polarization axis in one lens offset about 20 degrees (by eyeball estimation) from the other. I don't have much experience with other polarized sunglasses, but this seems very obviously wrong to me. And it's very noticeable while wearing the glasses. When facing into glare from certain directions, one eye filters our considerably more glare than the other, which is very distracting and uncomfortable. I can see arguments for making the polarization axis angle just about anything (though horizontal or vertical seem most logical), but what I cannot see is any argument for having it different in each lens on the same pair of glasses. Thoughts? ![enter image description here](http://i.stack.imgur.com/TIu4z.jpg) ![enter image description here](http://i.stack.imgur.com/TW0Fd.jpg)


title: Electric charge in string theory

text: The mass of an elementary particle in string theory is related with the way the string vibrates. The more frantically a string vibrates the more energy it posses and hence the more massive it is. My question is how is the electric charge of a particle is described in S.T. How is the opposite charges described? More specifically, I would like to know how a particle and its antiparticle are conceptualized?


title: Purchasing semiconductor substrates

text: I'd like to make a comparison of prices, availability and properties of semiconductor substrate layers like Si, Ge, GaP, AlN etc. I wonder what are the problems related to getting such data, what are the leading companies that sell such things, what's the quality, waiting time and so on. I'm not going to buy one, It's just a little research, that's why I ask here and not the companies directly. Your own experiences (what problems you've encountered and maybe some sample prices or company names?) are much appreciated.


title: Semiconductors: why the mass action law is not valid for very low temperatures?

text: I thought that it was valid for very low temperatures since for it to be valid I think that it is necessary to be in the non-degeneracy condition, which requires $E_G >> k_B T$ (with $E_G$ being the energy gap), that it is satisfied at very low temperatures... But maybe at too low temperatures the non-degeneracy condition breaks for some other reason. And the Ashcroft and Mermin's book only helps to increase my confusion! Could someone help me figuring it out, please? Thanks!


title: What's the point of Hamiltonian mechanics?

text: I've just finished a Classical Mechanics course, and looking back on it some things are not quite clear. In the first half we covered the Lagrangian formalism, which I thought was pretty cool. I specially appreciated the freedom you have when choosing coordinates, and the fact that you can basically ignore constraint forces. Of course, most simple situations you can solve using good old $F=ma$, but for more complicated stuff the whole formalism comes in pretty handy. Then in the second half we switched to Hamiltonian mechanics, and that's where I began to lose sight of why we were doing things the way we were. I don't have any problem understanding the Hamiltonian, or Hamilton's equations, or the Hamilton-Jacobi equation, or what have you. My issue is that I don't understand why would someone bother developing all this to do the same things you did before but in a different way. In fact, in most cases you need to start with a Lagrangian and get the momenta from $p = \frac{\partial L}{\partial \dot{q}}$, and the Hamiltonian from $H = \sum \dot{q_i}p_i - L$. But if you already have the Lagrangian, why not just solve the Euler-Lagrange equations? I guess maybe there are interesting uses of the Hamiltion formalism and we just didn't do a whole lot of examples (it was the harmonic oscillator the whole way, pretty much). I've also heard that it allows a somewhat smooth transition into quantum mechanics. We did work out a way to get Schrödinger's equation doing stuff with the action. But still something's not clicking. My questions are the following: Why do people use the Hamiltonian formalism? Is it better for theoretical work? Are there problems that are more easily solved using Hamilton's mechanics instead of Lagrange's? What are some examples of that?


title: Recommendation request for a book explaining string theory to a common idiot (me)

text: I find the idea of string theory fascinating, but I'm not a student of physics, mathematics or science in general. Are there any books which effectively break down the concepts in a way that laymen like me can understand without being overly simple but also overly technical?


title: How to positively charge an object with a power source?

text: How do you positively charge something consistently? By what mechanism could this be achieved?


title: Are all static solutions of Einstein's equations spherically symmetric?

text: Is it true that all static solutions in GR are also spherically symmetric? Is there a proof of this? Similarly, are all stationary solutions axisymmetric?


title: phase difference between incident plane wave incident on a dipole and radiation fields from dipole

text: i have an incident plane wave and a dipole, consider that plane wave incident on dipole. at this moment what happen for dipole ? we know that after incident of plane wave on dipole, the radiation have occurred, and i want derive the **phase difference between radiation field and incident plane wave field** ? please introduce me a reference


title: Heat production of magnifying glass

text: Why Magnifying glass(convex lens) produces heat when placed in front of sun?


title: Density distribution of gas in a centrifugal field

text: The problem asks me to find the density of gas in a cylinder of radius $R$ and length $l$ rotating about its axis with angular velocity $ω$, there being a total of $N$ molecules in the cylinder. What I have done is shown as following: I choose to look this scenario in a static frame with the cylinder, which is rotating at an unchanging angular speed $ω$. Then we can consider the field is a centrifugal field. Thus the energy of a particle can be written as $$E = E_0 - \frac{1}{2}m\omega^2 r^2\tag{1}$$ I haven't determined $E_0$ yet as I'm not sure about the thermal energy of the particle and the energy caused by the centrifugal field differs with the choosing of zero potential point. After that, I wrote the probability as $$\mathrm{d}P = \frac{\rho \mathrm{d}V}{N} = \frac{\rho \cdot 2\pi r\mathrm{d}r\cdot l}{N}\tag{2}$$ where $\rho \mathrm{d}V$ is what I want to find. My goal is to convert all $r$ and $\mathrm{d}r$ into $E$ and $\mathrm{d}E$ and finally compare it with Boltzmann distribution $$P(E)=C\cdot e^{-E/kT}\tag{3}$$ where $C$ is a constant. However, I have met with some problems doing this. From (1), it can be derived $$dE=-m\omega^2 r dr\tag{4}$$ After I plug this into (2), I find $P(E)$ in $\mathrm{d}P=P(E)\mathrm{d}E$ is always negative. Thus is cannot be compared with the Boltzmann distribution. How can I fix this?


title: Will changing the color of the light source change the apparent brightness on a traffic light?

text: Let's say you have a traffic light with the well known red, yellow, and green tinted glasses.   * Setup 1: Each glass has a white light bulb behind it.   * Setup 2: Each glass has a colored bulb behind it which matches the tint on the glass. So there is a red light behind the red glass, a yellow light behind the yellow glass, and a green light behind the green glass. Assuming all the light bulbs -white and colored- have the same power specs, which setup would appear to be brighter to the human eye?


title: How does Landauer's Principle apply in quantum (and generally reversible) computing

text: I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time. However, I have been thinking about what happens when a reversible computer _initializes_. Consider the state of the physical system that the memory is built from just before power up and initialization. By dint of the reversibility of underlying microscopic physical laws, this state stay encoded in the overall system's state when it is effectively "wiped out" as the computer initialized and replaces it with a state representing the initialized memory (set to, say, all noughts). So it seems to me that if $M$ bits is the maximum memory a reversible algorithm will need to call on throughout its working, by the reasoning of Landauer's principle, ultimately we shall need do work $M\, k\,T\,\log 2$ to "throw the excess entropy out of the initialized system". _**Question 1: Is my reasoning so far right? If not, please say why._** Now, specializing to quantum computers, this seems to imply some enormous initialization energy figures. Suppose we have a system with $N$ qubits, so the quantum state space has $2^N$ basis states. Suppose further that, for the sake of argument, the physics and engineering of the system is such that the system state throughout the running of the system only assumes "digitized" superpositions, $i.e.$ sums of the form: $$\frac{1}{\sqrt{\cal N}}\sum_{j\in 1\cdots 2^N} x_j \,\left|\left.p_{1,j},p_{2,j},\cdots\right>\right.$$ where $x_j, \;p_{k,j}\in{0,1}$ and ${\cal N}$ the appropriate normalization. To encode the beginning state that is wiped out at power up and initialization, it seems to me that the Landauer-principle-behested work needed is $2^N \,k\,T\,\log 2$. This figure reaches 6 000kg of energy (about humanity's yearly energy consumption) at around 140 qubits, assuming we build our computer in deep space to take advantage of, say, 10K system working temperature. _**Question 2: Given that we could build a quantum computer with 140 qubits in "digital" superpositons as above, do we indeed need such initialization energies?_** One can see where arguments like this might go. For example, Paul Davies thinks that similar complexity calculations limit the lower size of future quantum computers because their complexity (information content) will have to respect the Bekestein Bound. P.C.W. Davies, "The implications of a holographic universe for quantum information science and the nature of physical law", _Fluctuation and Noise Lett_ **7** , no. 04, 2007 (see also http://arxiv.org/abs/quantph/0703041) Davies points out that it is the Kolmogorov complexity that will be relevant, and so takes this as an indication that only certain "small" subspaces of the full quantum space spanned by a high number of qubits will be accessible by real quantum computers. Likewise, in my example, I assumed this kind of limitation to be the "digitization" of the superposition weights, but I assumed that all of the qubits could be superposed independently. Maybe there would be needfully be correlations between the superpositions co-efficients in real quantum computers. I think we would hit the Landauer constraint as I reason likewise, but at a considerably lower number of qubits. **Last Question: Am I applying Landauer's principle to the quantum computer in the right way? Why do my arguments fail if they do?***


title: Is it possible for a material to shift the frequency of all light reflected off of it by a specific and constant value

text: Without reducing the energy more than necessary due to the frequency decrease? And if this happens/works, is there an index of such materials and their optic properties?


title: Is the uncertainty principle valid?

text: The uncertainty principle says that the product of the uncertainties in position and momentum can be no smaller than a simple fraction of Planck's constant $h$. Several articles lately suggest this is not true. Today in Physicsworld.com > Looking at the position and momentum of spin-polarized neutrons, they found > that, as Ozawa predicted, error and disturbance still involve a trade-off > but with a product that can be smaller than Heisenberg's limit. and earlier work in Toronto, Canada > Aephraim Steinberg and colleagues at the University of Toronto conducted an > optical test of Ozawa's relationship, which also seemed to confirm his > prediction. Ozawa has since collaborated with researchers at Tohoku > University in another optical study, with the same result. Can we safely throw out the Heisenberg uncertainty principle and start to view physics with more certainty?


title: What is the Laughlin argument?

text: The fundamental question is > Why is Hall conductance quantized? Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the x-direction, then the y-direction develops a voltage $V_H$. The Hall conductance is $\sigma_H = I/V_H$ ![Hall bar \(http://members.home.nl/skoric/quantum/setup.gif\)](http://i.stack.imgur.com/0bhnE.gif) > To make Laughlin's charge pump, how should we wrap the Hall bar? Identify > the left and right, or top and bottom sides? Based on my understanding, we should paste top and bottom side together. (correct? Figure 1. left of the Paper maybe a little confusing.) Laughlin assumes the Fermi level is in the middle of the gap, so that the ring is an insulator. But the changing flux will induce an current by taking "adiabatic derivative" of total energy w/r flux $$I = c\frac{\partial U}{\partial \Phi}$$ which flows in y-direction and where $c$ is speed of light. Following Laughlin's calculations, as one threads one flux quantum, there will be $p$ (number of filled Landau levels) electrons transported. Then $$U=peV$$ where $V$ is the potential difference of two edges. From the current formula, we find the quantized Hall conductance. The heart of the problem is > What is an adiabatic derivative? Why is ${\bf j} = \partial {\cal > H}/\partial {\bf A}$ valid?


title: Fermi's Golden Rule and Density of States

text: I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition matrix elements. I'm struggling to do a derivation based on the density of states. I know that under certain circumstances it's a good approximation to replace $\sum_f$ with $\int_F \rho(E_f) \textrm{d}E_f$ to calculate the transition probability, for some energy range $F$. Doing this calculation I obtain $$\Gamma_{fi} ~=~ \int \rho(E_f) \frac{2\pi}{\hbar}\delta (E_f - E_i) |M_{fi}|^2\textrm{d}E_f.$$ Now assuming that the $M_{fi}$ are constant in the energy range under the integral we get $$\Gamma_{fi} ~=~ \rho(E_i) \frac{2\pi}{\hbar} |M_{fi}|^2.$$ Now this is **absolutely not** what is written anywhere else. Other sources pull the $\rho(E_f)$ out of the integral to obtain Fermi's Golden Rule of the form $$\Gamma_{fi} ~=~ \rho(E_f) \frac{2\pi}{\hbar} |M_{fi}|^2$$ for any $f$ with $E_f$ in $F$ which makes much more physical sense. But why is what I've done wrong? If anything it should be more precise, because I have actually done the integral! Where have I missed something?


title: Noise spectrum of two systems and interacting Hamiltonian

text: I've been discovering recently the concept of noise spectrum, defined as: $$S_{xx}[\omega] = \int dt<x(t)x(0)>\text{e}^{-i\omega t}$$ Roughly the Fourrier transform of the two-point function. Apparently it represents, the probability that the system has to absorb (or emit) energy for positive (negative) $\omega$. I am not familiar with this new object to me, but let's say that I look at composite system, for example an oscillator in a bath. The Hamiltonian pictures says that the exchange of energy between both are caused by the existence of an interacting Hamiltonian: $$H_{int} = g\;\hat{F}.\hat{x}$$ quantum in this example. From what I said about the noise spectrum, I would say that the exchanges of energy would be motivated by an overlap of the two noise spectrum functions $S_{xx}$ and $S_{FF}$. However, I don't see yet how to conciliate these two points?


title: If we charge a capacitor can we discharge it into a battery?

text: I have read that we can charge a capacitor using a battery, but can the vice versa happen? My project needs to show a battery being charged through a fully charged capacitor.


title: How does the X-Y mode of an oscilloscope work?

text: I recently used an oscilloscope in X-Y mode to draw the phase ellipsis of two voltages. I then used the formula phi = arcsin(2y/B) where y is the value of the ellipsis at x = 0 and B is the total distance from the highest point of the ellipsis to the lowest. Now I really want to know why this works, thank you.


title: Will earth rotation be slowed down?

text: > **Possible Duplicate:**   >  Are tidal power plants slowing down Earth's rotation? Since we have various energy acquiring facilities that harvest energy from earth rotation. (e.g. wind, tidal power planet) Will our earth rotation be slower down? Is there any form of force to accelerate earth rotation speed?


title: When will the moon fall down?

text: > **Possible Duplicate:**   >  Are tidal power plants slowing down Earth's rotation? I've heard that there are turbines converting energy from tidal waves. Tidal waves are created by the moon's gravity, so I assume the energy gained by the turbines is taken from the moon's potential energy. My question is; How many watt hours can we harvest from tidal waves before the moon falls down on top of our heads.


title: The further the focal length, would more or less be projected in the image?

text: When the focal length of a camera gets further, the object projected on the image gets larger. But would more or less of the object be projected on the image? I know the answer is that less of the object would get projected on the image because just try it on a camera and I could see the effect. But I don't understand how is this so. I drew a quick diagram below to illustrate my thoughts: ![enter image description here](http://i.stack.imgur.com/9MFT1.png) The $f_1$, $f_2$ and $f_3$ are 3 different lengths of focal length from the the camera lens denoted by the small circle in the centre. The projected object on the image are the arrows. So it looks like the further the focal length, the larger the projected image gets. But this doesn't put on any restriction as to how much of the projected object on the image could be shown. In other words, it appears like whatever the lens could see of the object could be enlarged into the image if the focal length is increased without having the projected object being truncated on the image. What have I missed out? I am assuming that the lens is a normal camera lens.


title: What's a better phrase than "speed of light" for the universal spacetime speed constant?

text: The phrase "speed of light" is commonly used for the constant c =3E8 m/s, a feature that's "hardcoded" into the structure of spacetime. All massless waves and particles move at this speed, and it's a key concept in all fundamental theories in physics. Light, in vacuum, is one fine example. But light in air or glass, or microwaves in a waveguide, move slower than c. The speed of actual light isn't the "speed of light". And of course there are plenty of other things besides electromagnetic quanta whose behavior is described by equations involving c. The letter "c" alone isn't good for general writing and conversation, especially with non-scientists. It is fine as a mathematical symbol in equations, but isn't catchy or self-descriptive (albeit misleading) as "the speed of light". EDIT: I have an impression I'm not asking this question in quite the right way. It's not at all about light, or phase or group velocities of light, but about our spacetime geometry having a fundamental constant speed "built in" - what to call it? Historically it was discovered in connection with light, but c isn't specific to electromagnetism. It's important in all the fundamental forces, and in all situations with high energy particles flying about. "Universal spacetime speed constant" would be an answer, but for that it's long and clumsy to repeat often in writings about physics. I'm looking for some name or phrase shorter and easier than that, but not so brief as just "c" which is okay in equations and tables of physical contants.


title: Noether First and Second Theorem

text: I have this question related to the the Noether's Theorems. I want to know a rigorous enough enunciation of this theorem, the context is Classical Field Theory without fancy geometrical structures but the usual stuff you need to know to do QFT and the use of Lie Groups(without being too abstract, I need a sensible connection with particle physics). For what I read around in standard classical mechanics texts, Peskin, Brading and Brown and the thesis of one those authors,it is not really clear to me what a symmetry transformation and Noether's theorems are if viewed with a group theoretic perspective and the knowledge constraints mentioned above. For what I read in other posts on the site, the group that acts on the Lagrangian and gives the conservation of currents(conservation law) and Noether's theorems is the group of transformations on the space of fields $ \mathfrak{F(\mathcal{M})}$ that is $\mathcal{G} = \\{ \Lambda: \mathcal{M} \rightarrow G \\} $ where $\mathcal{M}$ is a manifold(for now let just say Minkowski space or Euclidean ), $\Lambda(x)$ is the transformation and $G$ is a group usually compact as $SU(N)$ or Poincare/Galileo. But the problem is that there is a big distance in understanding between this fact and what I have read about Noether's theorems using the literature mentioned above . Following what they do in the paper, lets define the total variation of the action as $\hat{\delta}S\equiv S(\phi'(x'), \partial_{\mu},\phi(x'),x') -S(\phi(x),\partial_{\mu}\phi(x),x) $. They also define a generic transformation of the action as $\Delta S \equiv \tilde{S}(\phi'(x'), \partial_{\mu},\phi(x'),x') -S(\phi(x),\partial_{\mu}\phi(x),x) $. The transformations that give both variations are "infinitesimal"(what are they more rigorously?). **Question a)** Are these elements of $\mathcal{G}$? I think they are. In the thesis they define a symmetry as the transformations (I suppose elements of $\mathcal{G}$) that give $\hat{\delta} S = 0$. Here I think they are again talking about the action of some infinitesimal transformations of $\mathcal{G}$. Then they proceed to derive the so called Noether relations without imposing the Lagrange Euler conditions. Those are: \begin{equation} \sum_{i=1}^{N} \left( \partial_{\mu}\frac{\partial \mathcal{L}}{\partial(\partial_{\mu}\phi_i)} - \frac{\partial \mathcal{L}}{\partial \phi_i} \right)\delta \phi_i= \sum_{i=1}^N \partial_{\mu}\left( \frac{\partial \mathcal{L}}{\partial (\partial_{\mu}\phi_i)}\delta \phi_i + \mathcal{L}\delta x^{\mu} \right) \end{equation} Then they do following. To enunciate Noether's First Theorem they restrict to "finite dimensional continuous group of transformations depending smoothly on $\rho$ independent parameters $\omega_{i}, (i= 1, \cdots, \rho)$ " that give $\hat{\delta}S = 0$. Then they proceed to expand $\delta \phi$ around the parameters and impose Lagrange Euler equations and get the conservation theorem. For what I understand is that they restrict to the "infinitesimal group action" of some group of transformations that depends on finite parameters. **Q b)** This is not a Lie group, right? What is the relation with the usual physicist defnition of global symmetries as "the infinitesimal action of a finite dimensional Lie group that leaves $S$ invarant" **Question c)** Are they talking about a subgroup of $\mathcal{G}$ that is finite? how is that if $\mathcal{G}$ is infinite dimensional? Are they talking about $G$? or is that the subgroup of $\mathcal{G}$ is somehow isomorphic to G? They seem to act the same way. In the paper they just refer to transformation that do not act on coordinates ("they defined them as gauge transformations") but in the thesis the same approach is done with one that changes coordinates. For Noether's second theorem they consider the infinite dimensional group of transformations with finite parameters that depend on x (i.e. functions). I really don't understand this. How is that having the parameters depending explicitly on spacetime changes your the dimension of the group of transformations. How this Second Theorem relates to usual local symmetries as defined in textbooks of physics is even muddier at least for me. Thanks in advance.


title: Why is momentum quantized in a 1D box even though the operator doesn't give eigenstates?

text: We don't get eigenstates of momentum when we operate momentum operator in the wave function of particle in a 1D box problem yet we say momentum is quantized in this situation. Why is it so?


title: Linear motion with and without Friction

text: Could we still use Newtonian mechanics in a frictionless world?


title: Can sound be used to purify/filter water?

text: I remember reading about all chicken at a poultry farm being violently sick/dying for apparently no reason. It turned out the culprit was machinery at a nearby factory that emitted sound at a frequency equivalent to the resonant frequency for brain cavity of the chicken.   * Could the story be true?   * Could sound be used to purify water of bacteria/viruses (preferably filter, else cull)?


title: Period of Double Slit Experiment

text: What is the period of the pattern from the double slit experiment? It varies along the pattern right? Namely I'm confused because when considering two point sources (See: Period of Interference Pattern on a Substrate) this should be like the double slit, at least along the x-axis. That being said, it gives the period as $\frac{\lambda}{2 \sin(\theta)}$ at the origin. I don't know how to calculate the period in the double slit experiment though, so I don't know if this agrees.


title: Why does the moon drift away from earth?

text: I once saw on TV that the moon is slowly drifting away from the earth, something like an inch a year. In relation to that the day on earth what also increase in time. I wonder why is that?


title: Would the Moon drift away from the Earth due to extraction of tidal energy?

text: > **Possible Duplicate:**   >  Why does the moon drift away from earth? It seems to me that, due to conservation of energy, the moon would drift away from the Earth if humans began extracting large amounts of energy from the ocean due to the shift in water levels due to the tides. This would occur to decrease the gravitational energy in the system. Some have said that it would cause the rotation of the moon to slow down, but that doesn't seem right to me. Edit: To make it certain that something must happen, assume that the energy extracted from the tides is 100% radiated outside of the closed system that includes all volume surrounding the moon and the earth. The inside of that system must lose energy somehow. Edit: If your answer involves the rotation of the moon and/or earth, what would happen if neither were rotating?


title: Why there are constant numbers in the universe?

text: Why the ratio of a circle's circumference to its diameter is always the constant $\pi$? Moreover many of you know better than me about _golden ratio_ $\phi$, _Euler's number e,_ and many other constants. How explain this while everything seems to be in chaos? Is there any explanation for this kind of questions in physics?


title: Relation between pressure, velocity and area

text: In a nozzle, the exit velocity increases as per continuity equation $Av=const$ as given by Bernoulli equation (incompressible fluid). Pressure is inversely proportional to velocity, so we have lower pressure at the exit of the nozzle. But as per definition of pressure, $P=F/A$, i.e., pressure is inversely proportional to the area which contradicts the above explanation on basis of continuity and Bernoulli equation. Which is true? What relation is true for compressible flow?


title: Does Uchimizu (watering streets in summer) help reduce temperature in an area?

text: It appears that in Japan, there is an old custom called Uchimizu. The name is a combination of words "road" and "water". The essence of it is moisturizing small parts of populated areas like sidewalks, streets, parks, gardens. A very nice diagram explaining how Uchimizu is performed can be found on this site. Apart from being a traditional and cultural thing, various sources (Wikipedia) claim that it helps reduce the heat in the surrounding area, but don't say by how much exactly. They also say that it prevents dust particles from spreading, but this is a more obvious part of Uchimizu, as watering sandy ground should prevent the wet sand particles from flying around. I'm more interested in the cooling effect of Uchimizu here. Let's say we have enough people watering everything in a small city, enough to make 1/2 of all the outside surfaces wet at all times. Potential harm to structures aside, by how much degrees Celcius will the average temperature in that city decrease? Let 30°C be the average summer temperature during the day. What about watering only the area in immediate proximity? For example, everything around your house. Will that help reduce the summer heat?


title: Is this a photograph of an electron-positron annihilation?

text: With degrees in Mechanical and Electrical engineering but no advanced education in physics, I submit a query based on ellipsometric macro photography of TEMS supplied by FDA/NIH. In one TEM a triangle of RNA/DNA indicates ionic activity.   PHOTO 1. ![100nm RNA/DNA Traingle](http://i.stack.imgur.com/mMdGD.jpg) This piqued my curiosity, so I photographed the 100nm size triangle with a macro lens in order to enlarge the 35-42,000x TEM further and obtained unexpected images upon which the question is based. I angled the macro lens camera to the light source hoping to enhance the images within the photographic gel. The black-gray shades in TEMS are not ink but silver atoms crystallized in the original film negative by electron beams then projected into a silver-halide photographic gel. Electrons convert silver halide over 10,000 times more efficiently than photons. The biological samples, dark stained with nano-gold, provide a plethora of particle targets and possibly emit surface plasmon resonances that generate latent photon induced images hidden due to the shortened photographic development time required to form primary images with electron precipitated silver atoms. Collisions between electrons and particles must have occurred as can be seen in the spiraling burst emanating from a point above the bottom angle of the triangle that impressed me as having ionic interactions. The triangle legs are about 2nm wide with 100nm between vertices. Microvilli sized ion channels appear to be in the picometer range and may be waves generated from electron collisions. PHOTO 2. ![Electron-particle collision erupts above lower angle](http://i.stack.imgur.com/djUBK.jpg) An invisible clear cloud seemed to lie between the left two vertices and I took hundreds of photos in an attempt to illuminate it. ![A spiraling cloud illuminated](http://i.stack.imgur.com/RFgEb.jpg) PHOTO 3 is the result of those efforts. I assume the cloud to be one of those hypothetical latent images of energy associated with electron-particle collision. Unfortunately the color forces in QED do not relate to colors. PHOTO 4 was taken in the same area as PHOTO 3 with a different lens-light configuration. ![Annihilation?](http://i.stack.imgur.com/2407g.jpg) Might the simultaneous Lycurgus Cup-like red/green~emission/absorption seen in PHOTO 4 correspond to an electron travelling back in time (positron) colliding with an electron beamed or displaced in the TEM vacuum and depict an annihilation?


title: Comparison of 1D and 3D wave functions

text: When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy to the corresponding 1-dimensional case. This is because the Laplace operator in spherical coordinates can be written in the form $$L = \frac{1}{r}\,\frac{d^2}{dr^2}r.$$ Hence my making the substitution $\psi\to r\psi$, the 3D radial wave function $r\psi(r)$ satisfies exactly the same Schroedinger equation as the wave function $\psi(x)$ in the 1D case. So far so good. However, at this stage some authors point out that this substitution is merely feasible, as long as the condition $r\psi\to0$ in the limit $r \to0$ is met. If not, then the wave function diverges at the origin, and this is unacceptable on physical grounds. [One may counter this argument, by pointing out that in the calculation of expectation values the square of the absolute value of the wave function is always multiplied by the spherical shell $4\pi r^2\,dr$. The factor $r^2$ neutralizes the above mentioned divergence.] Indeed there appears to be a slight difference between the 3D and 1D case, when one observes the elementary case of a particle in a box. In both cases, outside of the box the wave function is exponentially decreasing. Inside, where the particle is "free", the solution is oscillatory. In the 1D case, the wave function can be written as $$\psi(x) = A\sin(kx) + B\cos(kx).$$ In the 3D case, the wave function is given by the zeroth order Bessel function $$\psi(r) = C\sin(kr)/r.$$ [Apparently the term $D\cos(kr)/r$ is omitted since it is considered unphysical, see previous paragraph.] Now if the wave function inside the box has only one free parameter $C$, all one can really do is determine its value by demanding continuity of the wave function on the boundary of the box. On the other hand, QM textbooks claim that one should always seek a solution in which not only the wave function itself, but also its first derivative is continuous on a boundary! All in all I find the omission of the $D\cos(kr)/r$ term on physical grounds confusing. First of all it creates a difference between the 3D and 1D case. This seems odd to me since the corresponding wave functions satisfy essentially the same Schroedinger equation. Secondly, by omitting this term one loses an adjustable parameter $D$, which plays an important role in meeting the full set of boundary conditions.


title: What could explain the measurements that the Methuselah star is older than the universe?

text: So there has been talk in the news of a star named Methuselah that is "older than the universe". Moreover, this star happens to belong to our very own Milky Way. The article mentions that Methuselah is consistent with universe age estimates if we consider the margin of error, but this would seem to imply (statistically-speaking) that this method of age estimation is biased towards overestimation. The article also mentions that other studies have put Methuselah's birth at pre-Big-Bang. This seems to indicate that many methods are overestimating its age. To me this seems to indicate a fundamental theoretical misunderstanding or some consistent problem in the measurement phase of the estimation. I must admit that I only have a modicum of familiarity with stellar evolution, and so these incredible headlines have left me strapped with questions:   1. How reliable is this research?   2. What method do they use to measure the age of such a star as Methuselah?   3. Which is more likely to be wrong, the age of Methuselah or the current estimate of the age of the universe?   4. Could relativistic effects account for some of the age?


title: Is this picture correct from the point of view of physics?

text: ![enter image description here](http://i.stack.imgur.com/Hgytn.jpg) This picture violates some laws of physics. Am I right?


title: Increased likelihood of photon emission due to "nearby" absorber?

text: Is an excited atom more likely to emit a photon if there is a similar atom in the ground state nearby ready to absorb it? When I say "nearby" I guess I mean that the absorber has an approximately zero **spacetime** separation from the excited atom. I suppose there are a vast number of ground state atoms with zero spacetime separation from any given excited atom out in the Universe so that adding some more wouldn't significantly change the probability that the excited atom will emit a photon.


title: How do we know for sure a theory is non-renormalizable?

text: In quantum field theory, we are looking for a Lagrangian that is, amongst other, renormalizable. But how do we determine whether or not a theory is renormalizable? Is this purely done by power counting due to Weinberg? **This question is already answered in the aprevious question.** My question result from the fact that the Yang-Mills Lagrangian was considered to be non-renormalizable, and thus non-physical, for a decade until Veltman and 't Hooft found a method to regularize the theory. Keeping this in mind, **is it possible that there are theories that we today consider to be non- renormalizable, and thus non-physical, which actually _are_ renormalizable but we haven't (yet) discovered a way to do this?** I apologize in advance if my question is vague and if I'm using the wrong terminology, but I'm very new to the idea of renormalizability.