title: Why aren't there any arrays of visible light telescope?

text: There have been many radio telescope arrays which are capable of resolving stars significantly fainter than can be resolved with a single "small" radio telescope. Why don't they do the same with light telescopes?


title: Pion production in proton-proton collision

text: Why is $\pi^0$ created in the high-energy collision $p+p\to p+p+\pi^0$?


title: Interpretation of dispersion relation

text: In my research, I found that my system has the following dissipation relation: $$\omega^2=k^2+k_0^2\ , $$ where $k_0^{-1}$ is an intrinsic lengthscale of the system and the units are chosen so that the wave speed is unity. This is what it's looks like (blue curve): ![enter image description here](http://i.stack.imgur.com/ktK1V.png) So for short wavelengths (large $k$) we have standard linear dispersion, and for long wavelengths we have **vanishing** group velocity and **diverging** phase velocity. My question is kind of soft: I can't quite get an intuition about what this does. Do any of you know of a similar situations? Can you describe qualitatively how things behave?


title: Mass Shell in Light Cone Coordinates

text: I'm reading Zweibach's introduction to string theory, and don't understand one of his claims. He defined the mass shell to be the set of points in momentum space s.t. $p^2+m^2 = 0$. Then the physical mass shell is the subset of points where $E=p^0>0$. He claims that in light cone coordinates this may be parameterised by the transverse momenta $\vec{p}_T$ and the light cone momenta $p^+$ for which $p^+>0$. Why the condition $p^+>0$? Surely $p^0>0$ doesn't immediately give us this? Shouldn't there be some $p^1$ dependence in the mix somewhere? Many thanks in advance!


title: How does the inner core relieve stress as the Earth's rotation slows?

text: One of the surprises for me in working out the answer to this question: Why is the Earth so fat? , is that the core is more elliptical than the surface, the extra ellipticity builds up gradually to about 10% (this is false, I miscalculated the ellipticity, it is actually less elliptical by a factor of 1.47, so 47 percent less ellipticity. This doesn't change the question, except the imagined effects become smaller). As the Earth slows down, the interior has to relax to the new shape, and the inner core is solid. This means that the solid core is the wrong shape for a slower rotating Earth, and it must relieve the gravitational stress by a "core-quake" to move material to the poles from the equator. Unlike the crust, I don't see how it can do this by slow flows, because it isn't floating on anything, it's solid. I was wondering if anything is known about these core-stresses caused by rotation slowing. Is the core ellipticity wrong for the current rotation of the Earth? By how much? How does the Earth's core relax to the new stable shape when the Earth slows down? What's the time scale? Does this mechanism have any effect on the Earth's magnetic field? If all of this is unknown, or uncertain, this is a fine answer too.


title: how does accelerating charge produce Electromagnetic radiation?

text: Suppose an electron is accelerating along $x-$axis. How does it produce electromagnetic radiation? Which of Maxwell's equation comes in play and how do I derive the wave equation from it? For oscillating charge the emerging EM wave is explained in this video. What kind of EM wave emerge out in this case (not oscillating but only accelerating in one direction)?   ![enter image description here](http://i.stack.imgur.com/Lc86d.jpg)


title: Meaning of $d\Omega$ in basic scattering theory?

text: In basic scattering theory, $d\Omega$ is supposed to be an element of solid angle in the direction $\Omega$. Therefore, I assume that $\Omega$ is an angle, but what is this angle measured with respect to? None of the textbooks I am referring to give a clear indication of what this $\Omega$ is. The only relevant figure I could find is given below. ![enter image description here](http://i.stack.imgur.com/R0NIA.jpg)


title: How to calculate work done by variable kinetic friction force?

text: A heavy chain with a mass per unit length $\rho$ is pulled by the constant force $F$ along a horizontal surface consisting of a smooth section and a rough section. The chain is initially at rest on the rough surface with $x=0$. If the coefficient of kinetic friction between the chain and rough surface is $\mu$, determine the velocity of the chain when $x=L$. I am applying work energy theorem. Work done by constant Force will be Force × displacement of centre of mass i.e $FL$ but not able to find work done by friction. The friction force at an instant when chain length $x$ lies on the rough surface should be $\mu\rho x g$. This force is continuously decreasing. I feel calculus is involved here but I am unable to apply it. Please help me.


title: Centrifugal force on tilted object

text: The centrifugal force acting on a revolving particle with negligible size is $\frac{mv^2}{r}$. What if the size is not negligible? Say we are talking about a large homogeneous circular disc, so its radius is not negligible when compared to the radius of its revolution. For the sake of simplicity, assume the disc is perpendicular to the plane of revolution. For each point on the disc, the centrifugal force acting on it is the same, namely $\frac{mv^2}{r}$. So, if I am correct, we have to integrate these small contributions of each small point on the disc over the total disc. I have ignored the tangential velocity, since by symmetry the centrifugal force acting on a point is equal to that acting diametrically opposite to it, and they cancel each other out. **(Do they? that's what I think)**. I will calculate the centrifugal acceleration to get rid of the $m$ term in the integration. After the result is obtained, I shall multiply it by the total mass later and get the centrifugal force. To do this, it suffices to simply calculate the following double integral: $$ \int_{0}^{r} \int_{0}^{2\pi} \frac{v^2}{r} d \theta dR $$ My question is: **how do we solve the scenario when the plane of the disc is not perpendicular to the plane of revolution?** Say it makes an angle $\theta$ with the plane of revolution (to those who haven't read the above text, we are not talking about a particle, we are integrating over the whole circular disc). Then, the contributions of the tangential velocities will not cancel out. That is freaking me out. I have also drawn a picture, which basically takes a small shell of radius $m$ and takes an angle $X$, then tries to find the angle of the tangent to the point $(m, X)$ (in polar coordinates), but I cannot go further because it gets really complicated. Any help will be appreciated.


title: Quantum Gravity and the Holographic Mass?

text: So on the net (one forum) I stumbled upon this, and article by Nassim Haramein. Now, I researched this guy a bit, and I couldn't find any peer reviewed article (other than this in 'Physical Review & Research International', which tbh I've never heard of before). What he's saying is: > We find an exact quantized expression of the Schwarzschild solution to > Einstein’s field equations utilizing spherical Planck units in a generalized > holographic approach. I went a bit through the 'article', and the whole 'derivation' is kinda... lacking? All he did was make an assumption (replaced surface area Planck unit with his 'spherical Planck unit'), and made series of 'derivations' comparing to the actual data (he used Cygnus X-1 as a reference, but I saw no uncertainties in his data, which was a bit odd). So is this another 'crackpot' who 'invented' (or better yet simplified) a pretty complex existing theory? I am currently studying the correspondence principle (Kerr/CFT to be precise), and this is rather complicated area with some complicated math behind it (topology, symmetries, etc.), so when I stumbled on this, my inner crackpot meter went kinda on, since I've seen these kind of 'discoveries' before (usually ppl who found a working perpetuum mobile :D). I'm asking, because I know there are physicists here who are experts in the field of general relativity and the holographic principles, so they are more qualified to say if this is nonsense or not. I think it kinda is...


title: Finding the number of particles scattered by a certain angle

text: I'm trying to do the problem below, but it seems like there is incomplete information. PROBLEM STATEMENT: In a scattering experiment, $10^6$ $\alpha$ particles are scattered at an angle of $4^{\circ}$. Find the number of $\alpha$ particles scattered at an angle of 6$^{\circ}$. The reason it seems incomplete is because the number of particles scattered at an angle of $6^{\circ}$ would be dependent on the "intensity profile" of the incident beam, right? By intensity profile, I mean the following (see figure for reference): Imagine that there are no particles other than those that are coming in at distance $s$. In such a case, $\it all$ particles would be deflected by a certain amount, say $\Theta$, and no particles would be deflected by any other amount. Therefore, it seems like the number of particles deflected by any given angle is a direct function of the profile of incident beam, which is not given in the problem statement. To put things another way, the problem statement gives me the information that $10^6$ particles were located at distance $s$, assuming that $\Theta = 4^{\circ}$. It does not tell me how many particles were located at any distance other than $s$. I am assuming a classical picture, which is therefore completely deterministic. ![enter image description here](http://i.stack.imgur.com/Q0Vc9.jpg)


title: Should a polyatomic crystal behave similarly to the bulk of each/either of its constituent elements?

text: Generally, metals are usually fairly conductive, but their oxides aren't. I know conductivity is just one attribute, but in general, should you expect a, say, diatomic bulk crystal's properties to be anything like the bulk properties of each element it's composed of? Or do all those properties get thrown out the window and overwhelmed by the chemistry of the new diatomic crystal?


title: What happens after the collapse of a wavefunction?

text: If I have a quantum system which I prepare in a certain state, this state then evolves unitarily via a Hamiltonian. Suppose an observer provokes a collapse of the wave function by a certain measurement, this means that it must be in an eigenstate of the measurement.   1. What happens subsequent to that?    2. Will it remain in the same state?    3. Will it evolve unitarily according to the same Hamiltonian?   4. If I make the same measurement will I get exactly the same value with certainty?


title: Free fall question: Bill shoots his gun

text: Bill borrows his dad's gun and when he gets outside he fires it straight up into the air. If the bullet left the gun at 400 m/s: How long does it take the bullet to reach its highest point. I know that I have to use the acceleration of gravity which is 9.81 m/s2. Also, I suspect this question will use quadratic equations. This is what i tried.


If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons? The probability of a photon having just the right amount of energy for an atomic transition is $0$.


title: Why is there spectral lines at all?

text: My somewhat basic understanding of the concept comes from lectures I've attended about the Bohr-model, which explains the phenomena as arising from the fact that certain configurations of an atom can only absorb certain wavelengths of light and other configuration can emit the same wavelength and change into the first configuration. Now what I cannot understand is why these effects do not cancel out, and why in some instances absorption wins out and we observe absorption lines, and in other instances it is the other way around. Also, if I haven't misunderstood there are also some instances where we observe both absorption and emission at once. So my question boils down to this: Why?


title: Why do pressure and chemical potential depend on temperature, instead of having symmetric definitions?

text: I'm following an introduction to statistical mechanics and have seen the following definitions for fundamental temperature, pressure and chemical potential respectively: $$\frac{1}{\tau} := \left( \frac{\delta \sigma}{\delta U} \right)_{V,N}$$ $$p := \tau \left( \frac{\delta \sigma}{\delta V} \right)_{U,N}$$ $$\mu := -\tau \left( \frac{\delta \sigma}{\delta N} \right)_{U,V}$$ where $\sigma$ is entropy $U$ energy, $V$ volume and $N$ the number of particles. First, I suppose the inverse in the temperature definition is there because we expect lower temperatures to draw energy. But I can't explain the factor $\tau$ in the definitions of pressure and chemical potential, nor the minus sign in the latter. This is the introduction I read: Consider two systems A and B with entropies $\sigma_A$ and $\sigma_B$ and volumes $V_A$ and $V_B$. They are put into contact so that they can exchange volume, but not energy or particles. The maximal entropy will then be obtained at: $$ 0 = \frac{d\sigma_{AB}}{dV_A} = \frac{d\sigma_A}{dV_A} - \frac{d\sigma_B}{dV_B} \Leftrightarrow \frac{d\sigma_A}{dV_A} = \frac{d\sigma_B}{dV_B} $$ We call this equilibrium quantity $p/\tau$. But why not just $p$?


title: Two coffee beans in a cup of water + vibrations = gravity?

text: If you float two coffee beans in a cup of water that is being vibrated by your subwoofer (go to a sin wave generator online), the two beans will either be attracted to the sides of the cup or if positioned right will be attracted to each other in an accelerating manner. What phenomenon is this, and could it be related to gravity in space?


title: VdW Gas Entropy/Enthalpy/Gibbs Free Energy of Mixing in 2 Chamber Experiment

text: **What are the equations for $\Delta S_{mix}$, $\Delta G_{mix}$, and $\Delta H_{mix}$ for a real gas?** * * * Explanation: In one of the most well known experiments in thermodynamics, two chambers are placed beside each other with a membrane in between. The thought experiment is used to teach thermodynamic principles by calculating thermodynamic property changes after the membrane ruptures. Much like this: ![gases](http://i.stack.imgur.com/JUDut.png) However, this is mainly done for ideal gases and where typically the temperature , number of moles, and pressure are provided for each side of the chamber (such as 1 bar, 298K and 1 mol). Therefore, the thermodynamic properties after rupture can be solved easily with conventional well documented equations such as: $\Delta S_{mix}^{Ideal Gas} = n_A R \ln(\frac{V_{total}}{V_A}) + n_B R \ln(\frac{V_{total}}{V_B})$ $\Delta H_{mix}^{Ideal Gas} = 0$ $\Delta G_{mix}^{Ideal Gas} = \Delta H_{mix}^{Ideal Gas} - T \Delta S_{mix}^{Ideal Gas}$ These are quite easy to solve when given the inital information. However, if the gas behaves like a _real_ gas (for instance a Van der Waals gas), how does this change? Using the Van der Waals Equation of State for example, we know we will need the $a$ and $b$ values for the VdW Equation: $P = \frac{nRT}{V-nb}-\frac{n^2a}{V^2}$ $a=\frac{27}{64}\frac{R^2T_c^2}{P_c}$ $b=\frac{R}{8}\frac{T_c}{P_c}$ These $a$ and $b$ constants can be applied to a pure gas in the two initial states to solve for instance $V$ if $P$, $T$, and $n$ are given for each side. However, once the two gases mix, the $a$ and $b$ will now be different since the molecules will likely interact differently with each other than they do with themselves. So, we need tabulated values for $a_{mix}$ and $b_{mix}$ in order to solve the VdW EOS after mixing. However, even if we do all of this, I have not found hte thermodynamic property equation for mix a real gas. Have these been figured out or is everything for these real gases experimental extrapolation? $\Delta S_{mix}^{Real Gas}=?$ $\Delta G_{mix}^{Real Gas}=?$ $\Delta H_{mix}^{Real Gas}=?$


title: Why does electromagnetic waves travel slower in well isolated conductor?

text: Wikipedia writes, that > Propagation speed is affected by insulation, so that in an unshielded copper > conductor ranges 95 to 97% that of the speed of light, while in a typical > coaxial cable it is about 66% of the speed of light Why does insulation affect this speed?


title: Are the solutions in radicals of cubic and quartic of any use in physics?

text: We all know that there are analytic formulae to solve quadratic, cubic and quartic polynomial equations. But it seems to me that the only solution that widely used is physics is the solution of quadratic we all learnt at school. Is it true that when physicist faces quartic or even cubic equation -- he turns to numerical methods to solve them? Have anyone seen the analytic analysis of some real problems in physics, where these formulae were used?


title: Deformation of light-cone

text: In the paper _The geometry of free fall and light propagation_ by Ehlers and his colleagues ( _Gen. Relativ. Gravit._ **44** no. 6, pp. 1587–1609 (2012)), when the authors introduce the differentiable structure on page 70, they claim: > It should be realized that the representation of light in special relativity > by means of ordinary cones rather than by hypersurfaces of hour-glass shape > depends partly on a particular choice of differential structure. The question is: What do they mean by saying **particular choice of differential structure**? In what condition may the light cone be deformed and become like hour-glass as shown in this figure? Thank you in advance for any help. ![enter image description here](http://i.stack.imgur.com/XoQWY.jpg)


title: What are differences of different telecommunication wavebands?

text: I'm just wondering what are the differences (advantage and disadvantage) of different telecommunication bands ? For example:   * Why does satellite TV use Ku band?    * Is it true the rule is that greater band frequencies (10 ghz vs 1 ghz vs 800 mhz) can transport more data?   * Why mobile phone bands use (for example) 800 MHz or 1800 MHz?    * Is there any other "rules" related to band type and distance covered ? Yes, i know, i'm a little confused. I just would like to understand the differences between "radio frequencies", particularly their advantages and disadvantages. Are there references that explain those types of arguments?


title: Ampere's Law and Circulation?

text: ![enter image description here](http://i.stack.imgur.com/V2GdM.png) The net circulation should be zero if the net current is zero. However, I don't see how the circulation in the Amperian loop above can be zero. All the lines interact the loop only once and all their circulation contributions are positive or negative depending on the assumed direction of integration. Could someone explain how the net circulation would be zero? Thanks!


title: Electrode potential

text: If I connect a zinc half cell (Left hand side) and a copper half cell (right hand side), I get an E cell value of 1.1V taken from the voltmeter. If I replace the voltmeter with a light bulb, I will get light and heat energy of the bulb. My question: Will the voltage across the cell remain the same? I mean, the potential difference arises due to the difference in the amount of charge build up on the electrodes... so an electron flows from the zinc electrode to the copper electrode, will the voltage across the bulb decrease?


title: How to explain the existence of heavier elements in Population I stars and in Population II stars contain lighter one

text: Recently I read Astrophysics Notes where I found a statement that young stars are classified as Population I stars and relatively older one as Population II stars. Population I stars contain heavier elements or "Metals" - that means elements other than helium and hydrogen. While Population II contain older stars and they contain Hydrogen and Helium - lighter elements more in abundance. My doubt is that, stars begin their journey from Hydrogen in nebula. In course of time due to nuclear reactions more and more heavier nuclei are created,and hence Population I stars which should contain lighter elements in much abundance and the older Population II stars should contain heavier elements. Whether the explanation of the Notes is wrong? or any other plausible explanation? Please clarify.


title: Interpretation of $\langle p \rangle (t)=0$

text: If for a quantum mechanical particle $\langle p \rangle(t)=0$ at all time t, in any state $|\psi(t)\rangle$, can I interpret this as the center of mass of the system remains stationary? EDIT: Is $\langle p \rangle(t)$ somehow related to the group velocity of the particle? If the probability current density $J=0$, for some state $|\psi(t)\rangle$ then is it also true that $\langle p \rangle(t)=0$ in the same state?


title: How do we get a wave pulse and wave packet/train?

text: Ok, > _If a disturbance is localized to a small part of the space for a certain > time we get a wave pulse and if the source is active for time greater than > to complete a single pulse we get a wave packet._ > > H.C.Verma, Concept of physics, Part I. However I don't understand what the author means by source, I mean what kind of mechanism induces a wave pulse? Also if I consider the example of holding a string attached to a rigid support I can only visualize of making a sine or k*sine wave but not something like where there is nothing along negative $x$-axis which looks to me more like $|\sin x|$: ![A simple Wave Train/Packet](http://i.stack.imgur.com/2WG5q.jpg) To sum it up, I know what a wave pulse is, but I did like how could I produce one practically? (Could I say ideally?)


I have the following questions.   1. Why can't matter pass the speed of the light?   2. What happens to an object when it comes close to the speed of the light?   3. What makes the object unable to surpass this speed limit? And finally, I need to know whether this speed limit has been experimentally proven?


title: Why do you get electric field of a light wave?

text: Why do you get electric field of a light wave in following form: $E(x,t)=A cos(kx-\omega t- \theta)$?( look at: https://public.me.com/ricktrebino -> OpticsI-02-Waves-Fields.ppt, p. 18)


title: Why is the Schwarzschild radius the radius of an event horizon?

text: I've been searching the web and many references without much success. My question is how do we know that, in the Schwarzschild black hole solution, the surface with coordinate $r=2M$ (in the geometric unit system) defines an event horizon, in the sense that every timelike or null curve that crosses that surface - to the interior - will end up in the singularity at $r=0$?


title: Whats the anti-torque mechanism in horizontal take-off aircraft?

text: In most helicopters there is the anti-torque tail rotor to prevent the body from spinning in the opposite direction to the main rotor. What's the equivalent mechanism in horizontal takeoff single engine propeller, and jet aircrafts, where the air or the jet coming out back from the turbine or propeller is spinning and will cause such aircraft to roll?


title: what gives the vermiculite it's insultative properties

text: i know that vermiculite is used in insulation applications. i found this notion of the R-value of vermiculite, that i don't know if its true. basically i want to know if the attribute of the vermiculite, of expanding in a temperature of 870 degrees Celsius, is what gives it this high R-value? i Guess not, because other wise you couldn't use it in non heated applications (like dwelling walls).


title: An equivalent for the Bernoulli equation for viscous liquids

text: I was wondering whether there is any equation for viscous liquids (probably derived from energy and mass conservation principles) relating the pressure, rate of volume flow, area of cross section and height of the liquid (or any other parameters if required). NOTE : I am aware of Poiseuille's law, but that is not what I am looking for as it relates the pressure _gradient_ to the rate of flow.


During my QFT study I faced a problem of calculating amplitude of 3 to 3 scattering in massless $\phi^4$ theory in zero momenta limit at tree level. One of topologically distinct diagrams corresponding to this process gives a contribution of $\sim \frac{1}{(p_1+p_2+p_3)^2}$ (up to symmetry coefficients and coupling constant), where $p_1,p_2,p_3$ are momenta of incident particles. I have no idea how to take a limit $p_i \rightarrow 0$. Can anyone help?


title: What is the Philosophy Behind Relational Quantum Mechanics?

text: I watched this video on Relational Quantum Mechanics yesterday and my brain has been trying to comprehend it since. The interpretation I currently have is this: If an observer O measures the state S of a system, in doing so they themselves become entangled with that system. To another observer O', the state of both S and O are still completely probabilistic until he measures them himself. However the state of S to O is now deterministic as they have become perfectly correlated with one another (through the measurement/entaglement). This is why to observer O it seems the wavefunction of S has collapsed as there is no longer any randomness in S relative to O (but this is not to say there is no randomness in the system (S+O) to an outside observer). Further if I were not measuring a system (my friend let's say) they could be in one of a very large number of states with each having a certain probability. If I were to now look at them and 'measure' them, in effect one of these states is being sampled and I have become entangled/perfectly correlated with it. My question is, have I completely missed the point or is this the general idea behind "Relational Quantum Mechanics"?


title: Has the mass of longitudinal and perpendicular spin 1 mesons been measured separately?

text: This might be a silly question. When the mass of a spin 1 meson is measured, is there a way to check whether it is the same for all polarizations? Is such a meson mass the same for longitudinal and for transverse polarizations?


title: How could one measure the necessary CP violation needed to account in the SM?

text: The Standard Model contains at least three sources of CP violation. The first of these, involving the Cabibbo–Kobayashi–Maskawa matrix in the quark sector, has been observed experimentally and can only account for a small portion of the CP violation required to explain the matter-antimatter asymmetry. The strong interaction should also violate CP, in principle, but turns out that it doesn't, CP violation in the strong sector is also too small to account for the necessary CP violation in the early universe. Same for PMS matrix in the Neutrino sector. But, how do I measure the CP necessary?


title: Why are there 4 Dimensions and 4 Fundamental Forces?

text: Is it a coincidence that there are four fundamental forces and four spacetime dimensions ? Does a universe with three spacetime dimension contain four fundamental forces? Can magnetism be realized in three dimensional spacetime? Edit 1: Thanks alot for the answer. I'm a first year undergrad student so this may seem naive. If there is a symmetry that mixes spacetime symmetries and internal symmetries of the theory (e.g. gauge symmetry) then there might be ways that spacetime geometry have effects on the particle spectrum and interactions of the theory so you can describe things in geometrical manner . The mechanisms that lead to the structure of spacetime may explain why there are four forces.


title: Are there more bosons or fermions in the universe?

text: The question is in the title: are there more bosons or fermions in the universe? Or is there the same number of bosons and fermions? I think there is the same number but I don't know why exactly.


title: geometry inside the event horizon

text: I'm trying to understand intuitively the geometry as it would look to an observer entering the event horizon of a schwarszchild black hole. I would appreciate any insights or corrections to the above. inmediately after your enter the event horizon, if you look back and try to reach again for the horizon, it will seem to be expanding away quicker than the speed of light. Near this region, the apparent shape of the horizon is a sphere expanding away, and we are inside the sphere Near the singularity, we really don't know what happens. I've heard that spaghettification is not a necessarily occurrence, since the metric field diagonal components are shrinking as the curvature grows, so it could very well be the case that a infinite length hyper-cylinder $S^3 \times R^+$ of constant _physical_ radius is being conformally mapped to the $S^3 - \\{0\\}$ region around the singularity, or that in general a region around the singularity can be mapped to anything in the other end, which is basically because the degrees of freedom of curvature and stress-energy in our end of the spacetime cannot really predict what sort of topology endpoint will connect to the matter in the other end. Since the metric components are tending to zero at the singularity, this argument sounds pretty interesting, since it would seem to imply that observers will "shrink" relative to kruskal coordinates, because the local physics would always be that physical observers will stay fixed relative to their local metric, since the metric is covariantly constant!. However, i'm not expert on how to describe the asymptotic physics in the neighbourhood of the schwarszchild singularity. (which is why i'm asking on this site, after all!). **Question:** _does this argument hold any water?_


title: Can cosmic inflation be explained by matter antimatter reactions?

text: The big bang theory proposes that equal amounts of matter and antimatter were created in the beginning. Shortly afterwards most of it annihilated. Could that have produced enough energy to drive cosmic inflation?


title: What does a non-perturbative theory mean?

text: I'm a science writer and I'm having difficulty understanding what a non- perturbative approach means. I thought I understood what perturbative meant, but in looking for explanations of non-perturbative, I'm just confused about both concepts. Please explain as simply as possible.


title: Electric Field on Surface of Capacitor

text: If I have a dielectric (a piezoelectric, to be exact) sandwiched between two platinum plates (electrodes), and connect one end to positive potential of a battery and the other to ground (I don't even know why one has to connect the top to ground), and also connect the negative potential of a battery to ground, what is the electric field on the surface of the grounded plate? Where do the field lines coming from the bottom plate terminate? I ask because I'm doing an experiment where I'm trying to put particles on top of an electrode on a piezoelectric plate to stretch them. The particle is field-sensitive (sensitive to electric fields) so I thought if I just ground the plate the particles are on, everything would be fine. However, just because the plate is at zero potential (grounded), does that mean the field on its surface is zero?


title: How FAR would a 100mph wind blow a 71kg, 160cm woman? Is there a formula?

text: How **far** would a 100mph wind blow a 71kg, 160cm woman? Is there a formula?


title: Waveguides and Maxwell's Equations

text: **Background** In many textbooks on electromagnetism, the sequence in which topics are introduced are generally as follows -- electrostatics, magnetostatics, electrodynamics, wave propagation in free space, and wave propagation in confined space, in that order. As an example, consider Griffiths' 3rd edition of Introduction to Electrodynamics. Similarly, consider Orfanidis' Electromagnetic Waves and Antennas. By using the discussion on wave propagation in free space as a launchpad, the discussion on wave propagation in a confined space usually introduces some additional boundary conditions that the solutions to Maxwell's equations for wave propagation in free space did not have. If a proposed solution can be plugged into Maxwell's equations and not produce any contradictions, then they are valid. The goal is then to maintain the monochromatic wave solutions that worked for free space wave propagation with some "patches" to account for the fact that the propagating EM energy will be confined by the hollow waveguide. The reason monochromatic (one-wavelength) wave solutions are desirable is that, by superposition, any signal can be expressed as a sum of one or more monochromatic waves, and so any signal's behavior in a hollow waveguide can be understood. One of these "patches" is the boundary condition that $E_{\parallel}=0$. This is because the net electric field in an ideal conductor, such as the material that makes up the confining hollow waveguide, must be $0$ because any externally applied electric field will influence electrons to rush to counter the externally applied electric field. If there is no net electric field (meaning $\vec{E}=\vec{0}$), then there is no net electric field in the tangential direction ($E_{\parallel}=0$) along and inside the metal. If there is no net electric field along the metal, then, by Faraday's law, there must be no net changing magnetic field $\frac{\partial \vec{H}}{\partial t}$. This means that each of the components $\frac{\partial H_x}{\partial t}$, $\frac{\partial H_y}{\partial t}$, and $\frac{\partial H_z}{\partial t}$ must all be $0$ too. If there is no initial magnetic field (meaning $\vec{H}=\vec{0}$, then there must be no magnetic field at any later point. Therefore $\vec{H}=\vec{0}$ and $H_{\perp}=0$. So these are the two additional boundary conditions that must be considered. An implicit assumption is that the material on the interior of the waveguide is isotropic, homogeneous, and linear. This means that $\vec{B}=\mu\vec{H}$ and therefore $\vec{B}=\vec{0}$ and $B_{\perp}=0$ at the boundary of the metal + hollow interior interface as well. **Problem** Frequently, the monochromatic wave solution to Maxwell's equations given the boundary conditions of a hollow waveguide are presented as $$ \vec{F}\left(x,y,z,t\right)=\left[\text{spatial component}\right]\left[\text{temporal component}\right] $$ For example from Orfanidis, $$ \vec{E}\left(x,y,z,t\right)=\vec{E}\left(x,y\right)e^{j\omega t - jkz} $$ and from Griffiths, $$ \vec{E}\left(x,y,z,t\right)=\widetilde{\vec{E}}_0\left(x,y\right)e^{i\left(kz - \omega t\right)} $$ Further, $\vec{E}$ is a 3-dimensional vector with components $E_x\left(x,y\right)$, $E_y\left(x,y\right)$, and $E_z\left(x,y\right)$. **Bottom line** : Why is the spatial component only a function of $x$ and $y$? Further, why does spatial component have $x$, $y$, $z$ components [e.g. $E_x$, $E_y$, and $E_z$] (where $E_x$, $E_y$, and $E_z$ are each functions of only $x$ and $y$)?


title: Quantization surface in QFT

text: ![enter image description here](http://i.stack.imgur.com/RKL4O.png) What does the Quantization Surface mean here? Reference: H. Latal W. Schweiger (Eds.) - Methods of Quantization


title: Please explain me how the Higgs boson gives mass to other particles, more detail?

text: As we know, the Higgs boson gives mass to other particles. But here is onething which is not clear for me. I mean, I do not understand how the Higgs boson gives mass to other particles? Does anyone could explain me more explicitly how procedure goes that the Higgs boson gives mass to other particles.


title: Coefficients of the vectors in a tensor product

text: The postulate says that if we want to build the compound state of two sub- systems, we just take the tensor product $\otimes$ of the respective state vectors. This means that if one of the vectors has an overall phase $e^{i \phi}$, that can be interpreted either as the phase of any of the two vectors in the subspaces, or of the compound one, and this can be easily seen "in the formulas" when using the bracket notation $e^{i\phi}(|\psi\rangle\otimes|\zeta\rangle)=|\psi\rangle\otimes(e^{i\phi}|\zeta\rangle)=(e^{i\phi}|\psi\rangle)\otimes|\zeta\rangle$, or even more directly if we use the matrix representation. This seems a technicality, as usually we just elide the overall phase because it's not measurable. But, I came across this quantum computation problem. Consider the "phase estimation" algorithm presented in _Quantum Computation and Quantum Information_ , Nielsen & Chuang, II edition, page 221 (also Wikipedia). Consider only a part of the circuit described: a qubit register $|t\rangle$ controls (i.e., activates or inhibits) the application of an operator $U$ to a second qubit register, which is initially in the state $|u\rangle$. This $|u\rangle$ happens to be an eigenvector of $U$, so $U|u\rangle=e^{i\phi}|u\rangle$. Now, the algorithm starts by setting $|t\rangle = 0$ and then applying an Hadamard transform, $|0\rangle \rightarrow H|0\rangle = \frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$, and then let it do the job on the second register. The output is $|tu\rangle_{final}=\frac{1}{\sqrt{2}}(|0\rangle+e^{i\phi}|1\rangle)|u\rangle$, for the aforementioned tensor product rule. At the end, we do some operations on $|t\rangle$ and we measure it _getting some information on the phase $e^{i\phi}$_ , completely ignoring the state of $|u\rangle$ (which N&C regard as unchanged, since the phase somehow "passed" to the register $|t\rangle$). I can't fit together these two facts: $|t\rangle$ is supposed to be "controlling" the transform on $|u\rangle$, so it should not change at all; yet, thanks to the tensor product and its "permeability" to numeric factors, I can just shuttle around the $e^{i\phi}$ phase, and decide to measure it (somehow) on the first register, instead of the second, where my intuition would tell me that it resides. Most importantly, as I said initially, putting the phase here and there seems natural, possible in the formulas and completely arbitrary, so I don't see why I shouldn't let the phase stay "attached" to $|u\rangle$ and then get... basically nothing useful for my quantum algorithm. How can I get out of this apparent contradiction? Is this a clever trick set into the very core rules of quantum mechanics, to encode the fact that in two interacting systems there can't really be one spectator (or controller) and one affected (controlled)?


title: How to understand Feynman's reasoning about perpetual motion?

text: I'm studying Feynman's Lectures on Physics, and I'm not really understanding his reasoning here: _Consider weight-lifting machines $\overline{}$ machines which have the property that they lift one weight by lowering another. Let us also make a hypothesis: that there is no such thing as perpetual motion with these weight- lifting machines ... If, when we have lifted and lowered a lot of weights and restores the machine to the original condition, we find that the net result is to have lifted a weight, then we have a perpetual motion machine because we can use that lifted weight to run something else._ Now, I simply can't understand this. If we lift and lower $n$ weights with this machine, obviously the result is that $n$ weights have been lifted and $n$ weights have been lowered. I think then: "well, so everything that was lifted was lowered", but we can start the process with one weight already lifted. Then when we return it to the original state, there'll be a lifted weight in total. I don't know how to reason with this, I think I'm not really getting the point there about perpetual motion. Can someone give some help on how to understand this properly and develop some intuition?


title: Neutrino mass difference and mixing angles

text: What are the most recent values of the mixing angles associated with the 3 neutrinos flavors and what are their mass differences? Have they been measured in the first place?


title: References requested on departments with recitation sessions

text: What physics departments offer recitation sessions for their physics courses on the undergraduate level? If there is a site which has such info it will be greatly appreciated.


title: Is the uncertainty principle axiomatic or derived?

text: To take an example, > Feynman Lectures Vol 3 13-1 > > Let's think of an electron which ban be in either one of two positions [...] > There are two possible states of definite energy for the electron. Each > state can be described by the amplitude for the electron to be in each of > the two basic positions. In either of the definite-energy states, the > magnitudes of these two amplitudes are constant in time, and the phases vary > in time with the same frequency. On the other hand, if we start the electron > in one position, it will later have moved to the other, and still later will > swing back to the first position. (Feynman derives this behaviour from first principles in chapter 8-6 by solving equations for the state of an ammonia molecule, but that's a nice summary). This sounds like the uncertainty principle - that you can know energy or position but not both. Is it possible to derive the uncertainty principle from such an analysis? Or is the uncertainty principle somehow axiomatic in the way this behaviour is derived?


title: View from a helicopter rotor: why is the horizon distorted?

text: This video ("rotor panorama") was captured by a camera attached to the rotor head of a radio-controlled helicopter, with the frame rate set to the rotor's frequency. During a long segment of the video, the horizon looks distorted: ![enter image description here](http://i.stack.imgur.com/Bl6c0.jpg) What causes this distortion?


title: Lagrangian with vanishing conjugate momentum, independent variables

text: Given a Lagrangian density $\mathcal L(\phi_r,\partial_\mu\phi_r,\phi_n,\partial_\mu\phi_n)$, for which we find out that for some $\phi_n$ **its conjugate momentum vanishes** : $$\pi_n=\frac{\partial\mathcal L}{\partial(\partial_0\phi_n)}=0.$$   1. What does this imply?    2. And if you will say that this implies that $\phi_n$ is a field depending on other fields, what does this mean?    3. Does this mean that we can construct another Lagrangian density $\hat{\mathcal L}(\phi_r,\partial_\mu\phi_r)$, which has no $\phi_n$ as its argument, so that all the fields involved are independent, but still gives a Euler-Lagrange equation having the same solution as that of ${\mathcal L}(\phi_r,\partial_\mu\phi_r,\phi_n,\partial_\mu\phi_n)$?   4. Another question, **is it true that the Hamiltonian density** $\mathcal H(\phi_r,\nabla\phi_r,\pi_r,\nabla\pi_r,\phi_n,\nabla\phi_n,\pi_n,\nabla\pi_n)$ constructed using $\mathcal L(\phi_r,\partial_\mu\phi_r,\phi_n,\partial_\mu\phi_n)$ **doesn't contain variables $\phi_n$ and $\pi_n$?**   5. Yet another question, suppose $\mathcal H(\phi_r,\nabla\phi_r,\pi_r,\nabla\pi_r,\phi_n,\nabla\phi_n,\pi_n,\nabla\pi_n)$ does contain $\phi_n$ and $\pi_n$, but under the solution of equation of motion, $\mathcal H(\phi_r,\nabla\phi_r,\pi_r,\nabla\pi_r,\phi_n,\nabla\phi_n,\pi_n,\nabla\pi_n)=\hat{\mathcal H}(\phi_r,\nabla\phi_r,\pi_r,\nabla\pi_r)$, which $\hat{\mathcal H}$ being seen as another Hamiltonian density depents only on independent variables $\phi_r$ and $\pi_r$. Now if we derive the equation of motion of $\phi_r$ and $\pi_r$ from $\hat{\mathcal H}$, **will it be consistent with the original one** derived from $\mathcal L$, looking only at the variables $\phi_r$? The motivation for me to consider these questions is that **only algebraic manipulations that preserve the equations of motion should make sense** , so that the symmetry examinations of $\mathcal L$ will indeed profit us finally.


title: Physical Interpretation of the Bloch vector

text: In the expression of the density matrix of a (Electron-Spin) Qubit $$ \rho=\frac{1}{2}(I + x \sigma_x + y \sigma_y + z \sigma_z) $$ where $\tau=(x,y,z)$ is unit vector in the Bloch sphere, which is the physical Interpretation of $\tau$? Can it be interpreted as the direction of spin axis of the electron?


title: States of Matter and Equilibrium

text: Can I say that, matter generally when cooled decreases in volume because, when it is cooled,i.e., we lower the temperature of the surroundings, then the avg. energy of our sample will be higher than the surroundings and hence, the molecules coming out will be more, therefore, the volume decreases...And when equilibrium is reached the molecules coming out and going in will be same and that's when they are at the same temperature.


title: Could we see a lower dimension within our universe?

text: My question refers to the fact, that, say if our universe were to be sitting on a 4 (spatial) dimensional plane, that we cannot see, then within our universe could there be a point mass in which 1 or 2 (spatial) dimensions could exist. We may not be able to see them, this could be a result of our world only consisting of 3 Dimensions. Although the computer screen, for example, is 2Dimensional, it sits on a 3 Dimensional object. Could a 2Dimensional object or world, exist in our 3D plane without having a 3D object that it is displayed upon, I have illustrated it below to build a clearer picture... ![Point Mass](http://i.stack.imgur.com/BBoqs.png) I hope this makes sense!


title: Evidence of atoms from Dulong–Petit law?

text: All materials have same molar specific heat, cf. the Dulong–Petit law. Is it an evidence of atoms? What other examples are there for atomic theory?


title: When I move my arm forward in vacuum, will my body move backward?

text: Let's say I stay at point $x=0$ in vacuum. When I move my arm forward such that it will have a positive $x$ position (say $x=5$) will the rest of my body move backward such that it will have a negative $x$ position (like $x=-1$)?


title: Small sphere rolling off the top of a large sphere

text: > A heavy sphere of radius r = 1.00 meter is fixed with respect to the ground. > A small uniform solid sphere is placed at the top of the larger sphere. > After a slight disturbance, the smaller sphere begins to roll downward > without slipping. How high h is the small sphere above the ground at the > instant it loses contact with the large sphere ![enter image description here](http://i.stack.imgur.com/mdoEU.png) My atempt of solution: I think, that at the moment when it loses contact, speed of the small sphere is higher than the one in $\Sigma F=mg\cos\theta=mv^2/r$. $\theta r$ is an arc traveled on the sphere. Also since it falls without slipping, $v=\omega r$, where $\omega$ is the angular velocity of the small sphere. The speed at a height h can be found from $$mg(2r)=1/2mv^2+mgh.$$ From foce equation I would get $$v=\sqrt{rg\cos\theta}$$ And from energy conservation: $$h=\frac{4g-v^2}{2g}$$ substituting the expretion for velocity $$h=\frac{4-r\cos\theta}{2}$$ I am not sure if this is correct or no. And I can't express $\theta$ in some other way. Could anyone help?


title: What about the neutron stars with CMB temperature as dark matter?

text: Inspired by How do we know that dark matter is dark? and What is the temperature of the surface and core of a neutron star formed 12 billion years ago now equal to?


title: Does perturbation theory break down for quantum gravity?

text: Perturbation theory presumes we have a valid family of models over some continuous (infinitely differentiable, in fact) range for some parameters, i.e. coupling constants. We have some special values for the coupling constants characterizing the unperturbed model, which presumably, is relatively easy to solve. We also assume the family of models transform smoothly under the coupling constants. Then, we perform a Taylor series analysis. But what if the landscape of valid quantum gravity models is discrete? Even though superstring theory admits a dilaton modulus over 10 uncompactified dimensions, what about the landscape of models we get after compactifying 6 spatial dimensions with nonzero fluxes and some branes, and maybe some orbifolding? We still have moduli when supersymmetry remains unbroken, but what about the metastable states where SUSY is broken? What is the Taylor series of a Dirac delta function? What about perturbation theory from the perspective of path integrals? With path integrals, the Wheeler-DeWitt constraint shows up in a different guise as a projection operator. We start off with some wavefunctionals, and then take the functional integral over some finite time interval T. In the limit as T goes to infinity, we are left with a projection operator singling out WDW solutions. But what happens when we interchange the order in which we take the limit of the coupling constant going to zero, and T going to infinity? If the spectrum of the Hamiltonian constraint is discrete, and varies with the coupling constant, such an interchange won't be valid! This is a fancy way of saying for most choices of coupling constants, the projection operator is zero.


title: Do traversable wormholes exist as solutions to string theory?

text: There has been some heated debate as to whether the laws of physics allow for traversable wormholes. Some physicists claim we require exotic matter to construct wormholes, but then others counter the Casimir effect with ordinary matter is sufficient. But these same physicists seldom come up with an explicit solution or state of ordinary matter keeping the throat of a wormhole open via the Casimir effect. Yet others claim with extra dimensions, a Gauss- Bonnet interaction is sufficient to keep the wormhole throat open, but opposing physicists claim such a term can't arise from string theory. So, my question is, do traversable wormholes exist as solutions to string theory?


title: What are the main algorithms the LHC particle detectors use to reconstruct decay pathways?

text: I am just starting to look into how we understand the data from particle collisions. My question is, what are the algorithms or ways that these detectors interpret the data? Are there standard approaches? Or if not, what are some good papers or places to look to get started in learning more about the implementation and/or details of how this works? So far I haven't dug into any textbooks, but many articles on the web and this was somewhat helpful in pointing to where to look: http://arstechnica.com/science/2010/03/all-about-particle-smashers-part-ii/ So from my understanding so far, there are a few different LCH "experiments", which are physical structures that are optimized to focus on specific aspects of data from a collision event. The detector measures all kinds of particle emissions and changes in electrical fields, and then seems to try to backtrack and figure out all the emission/decay events that might have taken place in that split second. From my understanding so far, basically the computer programs used to compute these possible "decay pathways" must be using some standard algorithms or something, and must have built into them all possible particle emission pathways (like all possible Feynman diagrams if there is such a thing). Are there any good resources or standard algorithms/approaches to understanding how particle detectors analyze their data?


title: The entropic cost of tying knots in polymers

text: Imagine I take a polymer like polyethylene, of length $L$ with some number of Kuhn lengths $N$, and I tie into into a trefoil knot. What is the difference in entropy between this knotted polymer and a circular polyethylene unknot? Is there an approximate way of calculating this for knots of a given crossing number (or other topological invariant such as a Jones polynomial)?


title: Basic geometric optics question - how come we don't have to have exact focus to capture objects clearly?

text: The top frame of the image below shows an image formed on the screen (at right) of an object (pencil on the left) located at some distance $D$ from the lens. The lens focuses all the light rays hitting it from the top of the pencil onto the corresponding point on the screen. The bottom frame shows the same setup, except with the top of the pencil missing. The point on the screen which previously had **only** light rays from the top of the pencil impinging on it, now has rays from other points to the left of the pencil (for instance, the triangle,square,circle, etc.) hitting it. Those points are all completely different light sources (different frequency, phase, etc.), their combination at the screen will not be coherent or of any single frequency. This means that a lens focused on an object a distance $D$ from it (to photograph the bottom half of the pencil), should show make a screen image with the bottom half of the pencil sharp, but anything behind its (missing) top half completely blurry. But then how come in reality, when we take regular photographs, even though we set the focus to capture an object some specific distance away, the objects (not too far) behind it still come out mostly properly (correct colors) and sharply? In other words, how come it is almost never the case that when we focus a camera or our eyes on some object, everything else in front or behind it is blurry? ![enter image description here](http://i.stack.imgur.com/wPrzh.png)


title: What could cause an asymmetric orbit in a symmetric potential?

text: My question can be summarized as: **Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry?** Below is the full motivation for this question. A while back I came across an intriguing orbit (or rather class of orbits) that is not symmetric with respect to the $z=0$ plane in a potential with axial symmetry (axis along $z$) as well as symmetry with respect to reflection along the $z=0$ plane. Naively I would expect the symmetry of the potential to be reflected in the symmetry of the orbits, and this is the case in every textbook example I've seen, though admittedly I haven't done an exhaustive search through all classical mechanics texts. The effective potential is: $$\Phi_{eff} = \frac{1}{2}v_0^2\ln\left(R^2+\frac{z^2}{q^2}\right)+\frac{L^2}{2R^2}$$ It is drawn from Galactic Dynamics 2ed eq. 3.70 (see also fig. 3.3), and is a crude model of the potential of an oblate spheroidal galaxy with constant circular speed $v_0$. The parameter $q$ controls the axis ratio, basically how "squished" the spheroid is. For the examples I show below it's fixed to $q=0.7$. The azimuthal motion of the particle is essentially ignored - since a test particle in this potential just goes around the $z$ axis with constant angular momentum, this is easy to do. The effective potential still accounts for the angular momentum due to this motion, of course. By "following the particle" in the azimuthal direction, the motion can be described as a trajectory in the $R-z$ plane. In general, the motion of a bound particle (i.e. negative total energy) is expected to be confined to some region in this plane, the shape of which depends on the $L_z$ and $E$ of the orbit. Typical regions look like the top two panels here: ![A selection of orbits in the potential of interest.](http://i.stack.imgur.com/9gDvI.png) The lower right panel is also a typical orbit, but it fills in its "box" very slowly, so it looks a bit peculiar here. The bottom left panel is the strange orbit I'm interested in. Notice that it fills in a well-defined region that is not symmetric about $z=0$. **What's going on here? Why isn't the region symmetric about $z=0$ as my intuition suggests it should be?** The orbital parameters $(E,L_z)$ are given above the plot. An equivalent way of expressing the orbital parameters is in terms of initial conditions. Example initial conditions that give an orbit qualitatively similar to the one in the plot: $$R_0 = 0.3; z_0=0.1; \dot{R}_0 = 0; \dot{z}_0 = 0$$ _Footnote regarding the numerics:_ Orbits were computed using the RK4 algorithm with a timestep of $0.002$. I've played around with the parameters (timestep, initial conditions, different integrators, etc.) to be reasonably confident that this is not a numerics issue. Furthermore, one of my colleagues has independently computed the same type of orbit, the only thing I provided was the expression for the potential and the ICs. Of course we may both be doing something wrong, but the probability for that is much lower than for just me having screwed up...


title: What is the difference between a low vs. high entropy plasma just after and before a singularity occurs?

text: Although it appears that the universe is not closed (since it is accelerating) I have been reading different websites on how the universe would look like if it was closed and the big crunch did occur. I believe that I understand that from a big bang singularity, the universe expanded into a low entropy plasma (leptons, quarks, …) and from here, the entropy increased as structures form. When a closed universe starts collapsing and is headed back towards a singularity, the entropy of the universe must be increasing so the particle plasma just before the big crunch would be a high entropy plasma now. **Question:** if I could make some measurement on the plasma just before the big crunch occurs (at least one Planck time ($t_P$) before it occurs and I assume the second law of thermodynamics whould still be valid), how would I distinguish between the low entropy plasma of the big bang vs. the high entropy plasma just before the big crunch?


title: Do photons make the universe expand?

text: I have a problem understanding the ideas behind a basic assumption of cosmology. The Friedmann equations follow from Newtonian mechanics and conservation of Energy-momentum $(E_{kin}+E_{pot}=E_{tot})$ or equally from Einsteins field equation with a Friedmann-Lemaitre-Robertson-Walker metric. In a radiation dominated, flat universe, standard cosmology uses the result from electrodynamics for radiation pressure $P_{rad}=\frac{1}{3}\rho_{rad}$, where $\rho_{rad}$ is the energy density of radiation in the universe and $P_{rad}$ is the associated pressure. It then puts the second Friedmann equation into the first to derive the standard result $\rho_{rad} \propto a^{-4}$, where $a$ is the scale factor on the metric. Putting this result into the first Friedmann equation yields $$a\propto\sqrt{t}$$ where $t$ is the proper time. Therefore we used the standard radiation pressure of classical electrodynamics to derive an expression for the expansion of the universe. My problem is in understanding why this is justified. Is the picture that photons crash into the walls of the universe to drive the expansion really valid? Certainly not (what would the walls of the universe be, and what are they made of ;)?), but at least this is how the radiation equation of state is derived. Is there any further justification for this? Be aware of that I'm talking here about a radiation dominated universe, so matter and dark energy can be neglected. Therefore, can we not derive a certain rate of expansion for the universe without anything mysterious like Dark Energy?


title: Gravity change as a function of time only

text: Is it possible to find how gravity changes with time? That is, height is not part of the equation. For example, $g$ can be expressed as a function of height that does not involve time with this relation: $g_i=g_0 (r /(r+h))^2$ where $g_i$ is $g$ at any height and $g_0$ is on the Earth's surface. I also found through the above relation that $g_i = g_{i-1} ((r+h_{i-1})/(r+h_i))^2$ By the same token, there should be a relation between $g_0, g_i, t$ that does not involve distances. An object in free fall will be going through changes in $g$ as time progresses. Is it possible to create such an expression?


title: Why can interference from two independent sources be observed?

text: Having read this question and answers to it, I've learned that somehow two light beams from independent sources can actually produce interference pattern, if the properties of their sources are good enough. Now, this conflicts with my understanding of quantum particles. I suppose that interference of independent beams means interference between pairs of particles from each beam. Consider a pair of non-relativistic non-interacting bosons such that it can be described by Schrödinger equation. Its state function, up to normalization, would be $$\Psi(\vec r_1,\vec r_2,t)=\psi_1(\vec r_1,t)\psi_2(\vec r_2,t)+\psi_2(\vec r_1,t)\psi_1(\vec r_2,t).$$ Let now $\psi_1(\vec r,t)$ be a 2D gaussian wave packet going along $y=x$ axis, and $\psi_2(\vec r,t)$ be a similar wave packet going in direction of $y=-x$. Obviously there exists an area where they "intersect". Let this point be around $(x,y)=(0,0).$ At this point we might place a detector, along $y=0$, which would show us the intensity of the particle beam, which would be governed by the following formula: $$D(x)=\int_{-\infty}^\infty |\Psi((x,0),(x_2,0),t)|^2\;dx_2.\tag1$$ Now I wasn't able to find this integral analytically, but numeric calculations show that there's no interference pattern on the screen, the intensities of both beams just add up. **This is what I get** for particle density in $(x,y)$ space — evaluated as in $(1)$: ![enter image description here](http://i.stack.imgur.com/OlY7H.gif) And **this is what I'd expect based on the answers** to the question mentioned above (this was generated as a probability density for single particle in two- packets state): ![enter image description here](http://i.stack.imgur.com/IkvXV.gif) So **the question** : what's so special about photons that they do exhibit interference pattern, while usual non-relativistic bosons obeying Schrödinger equation don't? I suppose the core reasons might be some of:   1. Non-relativistsness of Schrödinger equation, which my analysis was based on   2. Different form of equations governing evolution of light, i.e. Maxwell's equations vs Schrödinger's one.   3. Something related to QED, which is not taken into account in QM   4. My mistake   5. Something other What are the real reasons for this discrepancy?


title: Solids: is energy expended in some fashion by, say, a table to keep the top from sinking down against gravity?

text: A friend and I were discussing this, and couldn't decide. Since it takes energy to physically raise something up above the planet's surface, does it continue to require energy in order to _keep_ it above the surface? While gravity is extremely weak relative to atomic/molecular bonding forces, we were split on whether or not some tiny amount of energy needed to be _expended_ \- perhaps like radioactive decay? - to keep that bond from being eventually broken apart by gravity (ie, the table breaking and eventually flattening to an even thickness in being pulled to ground level by gravity). UPDATE I: if no energy is being spent to keep the table from sinking down to ground level, how does this differ from, say, a ball of something magnetic being suspended in the air over an electromagnet? Energy is required to keep it up - if you cut power the the electromagnet, the ball falls. UPDATE II: This question is a direct result of trying to learn more about it on my own :) I'll be taking intro physics as an MD program pre-req in Sept, and have started exploring snippets in a hit or miss way governed by what is of interest to me. So my knowledge of physics is _extremely_ patchy right now :)


title: How to measure distances to stars by means of spectroscopic parallaxes?

text: How to measure distances to stars by means of spectroscopic parallaxes on practice? What is the accuracy of measuring distances using this method compared with distances based on HIPPARCOS trigonometric parallaxes?


title: How is energy transferred from one incompressible fluid to another?

text: When you apply pressure to an incompressible fluid the pressure is transferred. If you stop applying the pressure there is no motion. Volume and density are integral parts of calculating how much energy is required to achieve certain useful motion like lift a truck or press a part. Why don't certain fluids compress and others do? If you start with a large pressure on one end of a fluid tube and you have an even larger pressure on the other end of the tube will the fluid move the moment you increase the pressure to a slightly higher level? What is the reason water doesn't compress or move like air?


title: Why do we consider the electric field of an infinite plane?

text: I never understood why one would calculate the electric field surrounding an infinite plane, if such thing does not exist. Is there physical motivation for using this model? Are the results applicable to real-world systems? Is it because of the mathematical simplicity?


title: Equation for Photon and Electron Propagation

text: What equation accurately describes the movement of a photon? Does this equation also apply to the movement of an electron?


title: Is electrons ability to produce mechanical motion considered the only reason for it to be material particle?

text: "Cathode rays (streams of electrons) produce mechanical motion of a small paddle wheel placed in their path indicating that they are material particles."$_1$ Isn't this statement wrong? Assuming electrons to be material particles, "if we use light to observe the position of electron, photons can transfer momentum to the electron at the time of collision"$_2$. Isn't here photon causing mechanical motion of electron? Then we can also consider photon to be material particle based on the above reasoning of considering electron to be material particle. Isn't it? I don't think photon is considered to be a material particle. Is it a material particle? So, is the first quote correct that electron can be considered as a material particle only because of its ability to produce mechanical motion? * * * Reference: $_1$Principles of Physcial Chemistry-Puri, Sharma, Pathania-Page No.21. $_2$ Modern's abc of Chemistry-Dr.S.P.Jauhar-Page No.169. _Data is subjected to modification without the loss of meaning up to my knowledge and page no's may change depending on editions._


title: Idempotent Operators

text: If $P$ is an idempotent operator, $P^2 = P$ and we have a vector $|\psi\rangle$, $P\neq1$, and the relation $$PL |\psi\rangle = L|\psi\rangle,$$ what conclusions can we draw about $L$, which is a Linear Operator?   1. $L = P$. Are there anything else? If not how does one prove this?


title: Why don't bubble lights explode?

text: As a child, I loved to watch the bubble lights at Christmas time. The colorful bubbling was hypnotic. However, there was always something about them that bothered me. With all of that boiling happening within the glass vial, why didn't the entire thing explode? I knew how explosive steam boiling could be, why was the bubble light able to withstand the constant boiling, and pressure changes that were going on inside it? Also, how was the fluid able to boil within an enclosed space (where the volume could not change?)


title: Why is the electric field of an infinite insulated plane of charge perpendicular to the plane?

text: I'm studying Gauss' Law, and I came across a section where we're supposed to find the electric field of various shapes (like an infinite line of charges, etc), and for an infinite plane with a uniform positive charge per area, it says here in my notes: Planar symmetry => Charge distribution doesn't change if we slide it in any direction parallel to the sheet => At each point, the field is _perpendicular to the sheet_ , and it must have _the same magnitude_ at any given distance on either side of the sheet. It's not clear to me why having a charge distribution that doesn't change will result in a field perpendicular to the sheet. Can anyone help me clarify?


title: What is the status of applying numerical analysis to QM/QFT problems

text: This is something I don't ever seem to hear about, except regarding QCD ("lattice QCD"). What about QED? Is numerical integration always inferior to hand-calculating Feynman diagrams in perturbation theory? What about numerical simulation of the full time-evolution of a quantum field (rather than just calculating correlation functions)? Here are some specific questions: 1) Numerical solutions to the Schrodinger equation. Has the time evolution of a complex quantum system ever been numerically simulated in order to shed light on the measurement problem? 2) Has the time evolution of a quantum field ever been numerically simulated? What about QED? If not, how much more computing power is needed? Could it be useful? 3) Ignoring lattice QCD, is numerical integration ever useful for calculating physical quantities in the SM? For example analytic computation of the terms in perturbation theory yields a value of the anomalous magnetic moment of the electron to something like 10 decimal places. How many decimal places would straight-up brute-force numerical integration get you? 4) What is the current state of the field? Are there any numerical-analysis- aided-achievements in theoretical particle physics outside lattice QCD worth noting?


title: Geodesics and trajectories

text: I'm a mathematician studying Arnold's Mathematical Methods of Classical Mechanics. On p. 83 the following definition is given. > Let $M$ be a differentiable manifold, $TM$ its tangent bundle, and $L:TM \to > \mathbf{R}$ a differentiable function. A map $\gamma: \mathbf{R} \to M$ is > called a motion in the lagrangian system with configuration manifold $M$ and > lagrangian function $L$ if $\gamma$ is an extremal of the functional > $\Phi(\gamma)=\int_{t_0}^{t_1}L(\gamma')dt$, where $\gamma'$ is the velocity > vector $\gamma'(t) \in TM_{\gamma(t)}$. (1) Is it correct then that geodesics in $M$ (if $M$ is Riemannian) are just a special case of this construction? (2) Homogeneous spaces, i.e. manifolds of the form $G/K$, where $G$ is a Lie group and $K$ a closed subgroup, provide interesting examples of manifolds. What would a physical system look like which has $G/K$ as a configuration space? I remember hearing something along the lines "global $G$-invariance, local $K$-invariance" but I'm not sure. And what interpretation do the geodesics then have in this model?


title: Is there an upper bound on the gauge group rank in F-theory compactifications on CY 4-folds?

text: It is known that in F-theory compactifications on CY 4-folds one can get gauge groups with very large ranks. The largest single factor* gauge group for compact CY 4-folds I found in the literature is the mind-blowing SO(7232) in this paper: http://arxiv.org/abs/hep-th/9706226 . One can imagine that there exist 4D compactifications of F-theory, which don't have Heterotic duals, with gauge groups that are even bigger in rank. Now, my question is whether there exists an upper bound on the ranks of single factors* in product gauge groups in either F-theory compactifications on CY 4-folds or in G2 holonomy compactifications of M-theory? An order of magnitude answer, if known, would be good enough :) . (*) Thanks to @Luboš Motl for correcting my question!


title: Aside from carbon, what materials change structure under intense pressure?

text: I was thinking the other day about what sort of exotic materials one would find in the depths of a planet. I have heard theories about how an enormous diamond might be found in the centre of gas giants. Current theories have a ball of iron at Earth's core - would that be like the iron up here on the surface or does the pressure change its structure? So here's the question: Aside from a carbon becoming diamond, what materials change structure under intense pressure?


title: Is (rest) mass quantized?

text: I learned today in class that photons and light are quantized. I also remember that electric charge is quantized as well. I was thinking about these implications, and I was wondering if (rest) mass was similarly quantized. That is, if we describe certain finite irreducible masses $x$, $y$, $z$, etc., then all masses are integer multiples of these irreducible masses. Or do masses exist along a continuum, as charge and light were thought to exist on before the discovery of photons and electrons? (I'm only referring to invariant/rest mass.)


title: How does one measure the mass of a galaxy? And other such large quantities

text: Trained as a pure mathematician, I see claims about the mass of a galaxy and other such huge measurements that are arrived at experimentally, and I just have to scratch my head. I know this is a bit of a vague question--but does anyone have a good resource for something like "measurement in astrophysics" or an introductory history of how astrophysicists figured out how to make measurements of this kind?


title: Why is GNUplot so pervasive in Physics when there are much more modern tools?

text: First, I want to say upfront that this question need not dissolve into arguments and discussion. This question can and should have a correct answer, please don't respond with your opinions. GNUplot is very pervasive in Physics research. Many of the plots appearing in things like PRL and JPB are made in GNUplot. Why is this the case. There are much more modern tools for doing these types of graphs, and from my uninformed position, it appears that this would be easier. One obvious and relevant first point to make is that GNUplot is free and opensource. I respect this, but do not expect that this is the primary reason. I am hoping for answers that specify what GNUplot can do that can be achieved in other programs efficiently, say Mathematica. If there are none of these, and the reason is simply tradition/resistance to change, that is also fine, but I expect there must be some specific tasks one wishes to perform. Thanks!


title: If the LHC doesn't find the Higgs Boson, what would be the implications for the Standard Model?

text: What would be the implications to the Standard Model if the Higgs Boson hadn't been found with the LHC? Also, if the Higgs Boson had not been found with the LHC, would it have been successfully proven as non-existent? Or would we just wait for an experiment with higher energy ranges?


title: Entropy of Reeh-Schlieder correlations

text: Any state analytic in energy (which includes most physical states since they have bounded energy) contains non-local correlations described by the Reeh- Schlieder theorem in AQFT. It is further shown that decreasing the distance between wedges will increase the entanglement as measured by a Bell-type inequality, until it reaches a maximum for tangent wedges. In this situation all analytic states are maximally entangled. Does maximal entanglement translate into infinite entropy of entanglement? My intuition is based on the fact that the vacuum state (which is analytic hence subject to RS correlations) follows a UV-divergent area law or a UV- divergent log law for entanglement entropy, depending on the dimension, criticality or the bosonic/fermionic character of the field, but anyway, entropy diverges. Vacuum being maximally entangled, it means that all maximally entangled states have the same entropy of entanglement i.e. infinite entropy. Another point that backs my intuition is the result that the reduced state has norm dense components i.e. is highly mixed. But I can't find or formulate a rigorous statement on the entropy of the RS correlations.


title: Diffraction in Electromagnetic Waves

text: Diffraction can be observed in physical waves very easily, however when it comes to the diffraction of electromagnetic waves in things like the single slit experiment, I become a little confused. In things like water, it seems like there is something "holding together" the wave, although I'm not sure what it is. In the case of electromagnetic waves, why does diffraction occur? I know it works out when viewed via Huygens' principle, but what is the mechanism behind electromagnetic diffraction?


title: Am I properly identifying the resistor terminal voltage?

text: > The frequency applied to a circuit of voltage 120 V with a **real** coil and > a resistor has a value of 50 Hz. The resistance of the resistor is 10 > $\Omega$. The voltage at the resistor terminals $u_1=60V$. The voltage at > the coil's terminals is $u_2=90V$. $$\nu=50\text{ Hz}$$   $$R=10\ {\Omega }$$ $$U=120\text{ V}$$   $$u_1=60\text{ V - resistor terminal voltage}$$   $$u_2=90\text{ V - coil terminal voltage}$$ > Find: > >   * the intensity of the current $I$. >   * the parameters of the coil. > I think by "parameters of the coil", it is meant the resistance and the impedance of the coil. $$I=?$$   $$L=?$$   $$R_L=?$$ I've been trying a bit, but I am quite poor at physics. This problem is suggested in a book, I want to prepare for a testpaper. What I've been thinking of is to calculate $$\cos\phi=\frac{U_r }{U}=\frac{60}{120}=\frac{1}{2}$$ $$\implies \phi=\pi/3$$ But I am not sure if the resistor terminal voltage is the same thing with $U_r$. Is this right?


title: The Observance of Electromagnetic Phenomena

text: As far as I've seen, E&M waves are sinusoidal. Our eyes observe these patterns and give us colors, but in a situation like such: Why do electrons emit radiation? There is still a wave, or at least a pulse, but it's not necessarily sinusoidal, and I'm not sure what 'wavelength' would be used. Nonetheless, radiation produced in this way does have a wavelength-it is used in synchrotrons. So what am I missing?


title: The Double Slit Experiement

text: The equation for the double slit experiment requires an approximation in naming the two angles used to both be theta, correct? I feel like the majority of equations are exact relations, and it just seems strange that the equation for calculating the maxima an minima doesn't have an exact form. Is the solution of d*sin(theta)=m*lambda really just an approximation. I know that it _is_ a very accurate one, given the size of wavelengths, however it just seems so strange to be using an approximation, and to never see the _real_ solution.


title: Electrons in a box

text: According to the Pauli principle, there can be no more than two electrons in a given state. If there are a number N of electrons in this box in the lowest states possible, show that the energy of the "top" electron - the "Fermi energy" $E_F$ is $E_F$ = $(2$$\pi$$\hslash$$N)$$/$$2mA$ , where $A$ $=$ $L^2$ and $L$ is the length of the square box the electrons are in. Now what I am thinking of using is ($E_{n_x n_y}$)$=(n_x^2+n_y^2)($$\pi^2$$\hslash$$)/$($2mL^2)$. Any hints on proceeding to next steps?


title: If fields die off proportional to R^2, why does light keep going?

text: Why does light continue on forever if it was created from some source whose radiation dwindles at a rate of the inverse square of distance. Clearly light can be viewed as an interdependent phenomena, the E field pulling the B field along with it, but if all light must come from a source, and that source creates a field dependent on distance, why doesn't the light die off?


title: On Cohomological Gauge theory Calculation

text: I am in trouble with calculation details of Witten's Two dimensional Gauge Theories Revisited. My questions is about (3.21) and (3.27). From section 3, we have $$\delta A_i=i\epsilon \psi_i\\\ \delta \psi_i=-\epsilon D_i\phi \\\ \delta \phi=0\\\ \delta \lambda=i\epsilon\eta\\\ \delta\eta=\epsilon[\phi,\lambda]\\\ \delta \chi=\epsilon H\\\ \delta H=i\epsilon [\phi,\chi]\\\ V= \frac{1}{h^2}\int_\Sigma d\mu {\rm{Tr}} (\frac{1}{2}\chi(H-2\star F)+g^{ij}D_i\lambda\psi_j) $$ Then the (3.21) is given by $$ L=-i\\{Q,V \\}\\\= \frac{1}{h^2}\int_\Sigma d\mu {\rm{Tr}}(\frac{1}{2}(H-f)^2-\frac{1}{2}f^2 -i\chi\star D\psi+iD_i\eta\psi^i +D_i\lambda D^i\phi +\frac{i}{2}\chi[\chi,\phi]+i[\psi_i,\lambda]\psi^i ) $$ My questions are followings: 1) What is the relations between $\delta \bullet$ and $\\{Q,\bullet\\}$? Is there a minus sign when Q-operator crossing $\lambda$ or $\chi$ ? I always found different signs in terms $ -i\chi\star D\psi$ and $ D_i\lambda D^i\phi$ when I use relation $\delta\bullet=-i\epsilon\\{Q,\bullet \\}$. 2) Why the two terms $ -i\chi\star D\psi$ and $ D_i\lambda D^i\phi$ have different signs in (3.21) and (3.27)? Anything wrong with it? ======================================================================== ===== Based on discussion with Trimok, (Thanks to Trimok but this does not mean Trimok agrees with my views) I think I understand part of the problem. First, the relations is $\delta\bullet=-i\epsilon\\{Q,\bullet \\}$. $\delta$ pass $\chi$ and $\eta$ will give a minus sign. So in the formula (3.17), some of terms should be $ i\chi\star D\psi-D_i\lambda D^i\phi$ and (3.27) is correct. While I have a new question now about (3.28). From (3.27) to (3.28), the procedures are the followings: First, perform variation of H, and then integrate out H. Second, perform variation of f, and then integrate out $\lambda$. Second, perform variation of $\eta$, and then integrate out $\chi$. After these calculation, the last term in (3.28), i.e. $\frac{1}{t^2} \frac{1}{2} (-D_kD^k+i[\psi_k,\psi^k])^2 $ does not appear. It seems from variation of $f$ from first part of (3.28). How to produce such a term in integrating out fields?


title: Serious advice/ plan for getting into Physics/Math Grad schools of choice

text: I am currently studying a Bachelor of Technology in the subject "Food Technology". I have completed 2 years just now.Yes, I have been exposed to Mathematics in my first year of college studying Differential and Integral Calculus,Ordinary Differential Equations,Linear Algebra, Complex Numbers, Vector Calculus,Probability. As for Physics, I have been exposed to courses like Oscillations and Waves, Wave Nature of Light, Special Theory of Relativity, Wave Mechanics, Atomic Physics(typically in the first year). The courses were not so rigorous( I am into an average university). In the 2nd year, we had different physics subjects like Fluid Mechanics, Thermodynamics, Heat and Mass Transfer. I am now going to be exposed to more Food Subjects from the 3rd Year like Food Engineering and Meats,Poultry etc . This was only to inform you of my current status. However, I am not really keen on pursuing Food Science in my Post Grad career. I cannot change my course of choice right now,unfortunately. However,for the Post Grad, I have majorly three to four options in mind, comprising of Maths, Physics, Mechanical Engineering or Computer Science. I know, not a clear goal yet. Out of these, I have been strongly inclining towards Maths/Physics at the moment. Doing Food Technology had never been my goal. Due to a lack of clear focus, I ended up getting bad grades and choosing a course, perhaps not so suitable for me. I always had an intensely logical approach to everything. Whenever I study Mathematics, I want to delve down into the details of how a particular proof was created. I just lose interest in solving problems when I don't know all the details that went into creating it.I absolutely love the idea of constructing new mathematical models or creating new science, something never known before, not for the sake of getting 'famous', but for the sake for the unlimited intellectual stimulation and satisfaction it would provide me with. Since my college courses weren't so rigorous, I nearly memorized a lot of things very unwillingly and had very good marks in some of the maths/physics subjects, and not so good in some other such subjects. I am truly fascinated by the idea of Astrophysics. Any physics or maths, that helps me understand how the world works, and especially would help me innovate or write a new model after having a thorough read of the earlier established work in "intricate" detail is the best for me. I think of "why's" to every possible maths or physics statement for a very long time. Yet as of today, due to no clear structure, I have not been able to have a firm grasp on the Physics or Maths Fundamentals. I reside in India, and it is not so research driven as countries like U.S.A. with the exception of some premier institutes(which unfortunately I didn't get into, because I was very unsure of what I wanted to do in my life). I have decided I will finally work to the best of my abilities and get strong in the basics. I am not a genius, but I am smart. I believe I can do it. I have been looking at some of the top graduate schools for these programs like MIT,Princeton,Cal tech (you get the idea), but the lack of a proper structure and plan have always lead me in confusion. I know I will love very very intellectually stimulating places, looking at every piece of math or science work , and thinking what lead to this in extreme detail. Also, I would love a place where cutting edge research is done, creating the potential of developing several new innovations that change the future of math or science. I have also considered the option of integrating food science and physics/maths/mechanical engineering in research to create something challenging and deeply meaningful. Also,I have always been very very interested in the theoretical maths/physics rather than the applied(attending labs) parts. The lab courses just cannot hold my interest for long. Now, I know, that on a scale of 1-10, I want to go to 10, and I am currently at 0-1. Would would you suggest I do? How should I prepare? How can I get into such top schools? How can I start at this particular moment? I am open to all useful suggestions. Especially, from people who have experience in such fields. If I don't do this, I will regret not having done this for my whole life. I clearly need help, because I realize that if I don't have a great plan, I won't be able to achieve this. What are the 'essentials' I really need and after then,what next? Please take this into consideration. I have about 2 years of college left, what can I do?


title: What is the energy of interaction between a point charge and an infinite cylinder?

text: I don't remember enough from my electromagnetism course and I can't find any simple, full example on this subject. I know, that I can consider the cylinder as a wire with the same charge density (when outside of the cylinder), so I consider the wire case with the same charge density, $\lambda$. I set the $y$ direction to pass through the wire, and the $x$ direction to pass through the point charge and perpendicular to the wire. Everything is in the $z=0$ plane. Hence, the particle is at $x=r$ position. From Gauss law, I learn that the field at a point at distance $r$ from the wire I have a field which scales like $\lambda/r$. To find the potential, I need to solve the integral $V = -\int_b^r E dl = - k \int_b^r \lambda/x dx$ Where $k$ holds the constants and $b$ being a point where the potential is 0. The solution of this integral is $V = - k \lambda \log (1/r) + C$ When $b=1$ the potential is 0 so the potential is $V = k \lambda \log (1/r)$ and the energy is $U = k q \lambda \log (1/r)$ Here are my questions:   1. Is any of this true?   2. I tried to derive this by starting with coulomb law and calculating the energy for a segment of the wire, I get an answer which scales like $1/r$, can you derive the answer for this?


title: Is watt unit depended on turbine speed

text: I'm new to electronics. I have a doubt. That is... Is watt unit depended on speed of turbine ? **In my mind** When turbine rotates fast the power in increase. Is it right ? Please help me. Thanks for your response...


title: Is it possible to derive Lorentz transformation equation without Einstein's postulates?

text: # Overview Einstein's proof for the Lorentz transformation is given here: From $O$'s view point, $x^2+y^2+z^2 = (ct)^2$. Form $O'$'s view point, $x'^2+y'^2+z'^2 = (ct')^2$. We find that Einstein has imparted the information that the velocity of light observed by $O$ and $O'$ is constant (Einstein's first postulate). # Problem statement All this has made me wonder why should a postulate derive his result? Could his results be derived by the existing laws of physics? Every textbook that I have referred says that his postulates are a direct application of Michelson- Morley experiment's results. But what actually causes this time dilation and length contraction? # Update I haven't asked about why we define postulates. I understand that at one point we must have postulates. But to elaborate, my question is about: is it possible to **derive** Einstein's postulates form works of Maxwell? Note: I know that a postulate does not have a derivation, but how do you think this postulate works? To show you that Maxwell's laws have something to do with Einstein's postulates: Consider 2 point charges moving with the same velocity parallel to each other. We observe that force acts on both the particles due to magnetic field. But, the observer moving along with the charge must observe no force at all! Don't you think Einstein's postulates can be derived from Maxwell's work?


title: How exactly does static discharge work?

text: Assume I have built up a pretty high charge by rubbing the floor or something. I want to understand these situations:   1. I almost always get shocked when I touch a metal doorknob with my bare hand.   2. I occasionally get shocked if I touch the wooden door first, then touch the metal doorknob.   3. I almost never get shocked if I'm holding a metal key, and use that key to touch the doorknob. Sometimes I can even see sparks between the key and the doorknob.   4. This just happened, and I feel is really weird: I'm holding a metal travel mug (water bottle) full of water. I start pouring the water down to a metal sink. I get shocked exactly when the water hits the sinks.


title: Changing effective mass to lower frequency

text: I'm trying to scale a physical object up in size, either double or quadruple. It's a circular acrylic plate, with multiple weights attached around it's edge, to lower the resonant frequency to a specific frequency, 32hz. The plate is 16” in diameter, the weights around it's edge add up to 1.05 kg. It needs to be scaled to 32” or 64”. It will scale in diameter but not thickness, which will remain 1/8” for all diameters. If the size is doubled to 32”, along with doubling the weights around the edge to 2.1 kg, will the resonant frequency be lowered to the same frequency as the 16” plate with 1.05 kg weights? If not, how does this scale? How far off approximately will the resonant frequency be from 32hz? Same question for scaling to 64” with 4.2 kg weights around the edge.


title: Phased array radar equations

text: Suppose we have several antennae to transmit and receive radio waves. What should one transmit, and what kind of equations are used to compute $reflectivity(\vec{x})$ for points in space from a given discretized signal over several antennae?


title: How exact is the analogy between statistical mechanics and quantum field theory?

text: Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a few questions about the relation between the two objects.   1. Loop diagrams in quantum field theory have a nice interpretation in terms of virtual particles. What is the interpretation of loops in statistical mechanics?   2. Does the relation between the two objects imply that for every quantum mechanical phenomenon there's a corresponding statistical mechanics phenomenon and vice versa? If not, where does the analogy fail?    3. If so, what would be the phenomena analogous to the Aharonov-Bohm (AB) effect? It's hard for me to see the analog for any quantum effect that depends on phase interference like the AB effect.


title: Frame of reference for moving charge in relation to a magnetic field?

text: We know that a moving charge produces a magnetic field. But which frame of reference it must move to produce magnetic field? And also if a charged particle moves in a magnetic field, magnetic force acts on it. In which frame of reference it must move to feel a force?


title: Is this formula for change in angular momentum of a combination of bodies correct?

text: In my dynamics notes I have written the following: $$\frac{d\vec{p}_A}{dt}= \sum\vec{AC_i}\times m\vec{a_{ci}} + \sum \frac{dR_i}{dt}\left\\{{I^{(i)}_{ci}}{\omega}^{(i)}_{ci}\right\\}+\sum R\left\\{{I^{(i)}_{ci}}\frac{d{\omega}^{(i)}_{ci}}{dt}\right\\}$$ where $A$ is a random point, $C_i$ the center of mass of object $i$, $\left\\{{I^{(i)}_{ci}}{\omega}^{(i)}_{ci}\right\\}$ (an admittedly strange notation for) the resulting vector from $I_{i}\vec{\omega_{ci}}$ if $I_{i}$ is a diagonal matrix and $R_i$ a matrix that projects object $i$ to its principal axes of inertia. I am, however, incapable of finding my derivation of this formula. Is this formula always correct? And also, -if correct- could $\frac{dR_i}{dt}$ be replace with $\vec{\omega_i}\times R_i$?


title: General way to model baths? Harmonic Oscillators valid?

text: I am trying to model an open system interaction without making strong assumptions on coupling strength or temperature. In general i understand that open systems are modeled by a Lindbladian, but as far as i know the Lindbladian approximation holds only if we have Marcov, Born and Circular Wave approximation. Since I want to cover a broad range of temperatures and coupling strengths how should i model the bath? Any suggestions on how to proceed? More specificly a colleague suggested using the coupled harmonic oscillator formalism has the advantage of not making any assumptions apart from being modelable by harmonic oscillators and being analytical solvable! Anyone has recommendations where i can read up how this is done or an opinion if this approach is valid?


title: Advantages/Disadvantages of "hanging off" a motorcycle when leaning

text: The closest question I could find with regards to this subject was this one:   Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ways to lean when turning a motorcycle:   1. Upper body remains upright while the bike leans.   2. Whole body remains aligned with bike.   3. Most of the body "hangs off" the side leaning in. I'm trying not to make any assumptions to allow for detailed and proper answers addressing issues I may not have considered; hopefully, without being too generic. So to summarize, I would like to know whether the first 2 items are sufficient for all conditions or whether the 3rd has some physical properties necessary in certain conditions.


title: The criteria for potential flow theory

text: I am learning aerodynamics. In this course a potential flow is denoted that a flow in which the rotation is zero everywhere. But the book told me that we can add vortex into a flow field, and we can also use potential theory to analysis it. I get confused about this. If a vortex is added in a flow field, I don't think there exist any potential. The rotation of a vortex is infinite! Could anyone explain to me, why potential flow theory can be used while there are some vortexes in the flow field?


title: How did neodymium magnets get their name?

text: Like in the question. Why neodymium magnets (Nd2Fe14B) are called "neodymium magnets"? Why not boron magnets? Or iron magnets?


title: Is the electrical signal delivered to a load by a receiving antenna always $\propto \frac {\partial}{\partial t}$ of the $\vec{E}$ or $\vec{B}$ field?

text: A time-varying $B(t)$ field through a loop antenna induces a voltage proportional to $\dot{B}(t)$. A Hertzian dipole along a time-varying $E(t)$ field also induces a voltage across a load--while I haven't seen a rigorous derivation of what it is, since we have a zero output when $\dot{E}(t) = 0$, it seems likely to me that the output is proportional to $\dot{E}(t)$. So I was wondering if this is true of _any_ antenna? Since in radiation, at any point in the far field, the magnitudes $E(t) = cB(t)$, is it true the voltage across any resistive load at the receiver is proportional to $\dot{E}(t)$? **If so** , since in the far field $E(t) \propto \dot{I}(t_r)$, does this mean that the voltage across the load in the receiver is proportional to $\ddot{I}(t_r)$? And since this would mean that the power transferred to the load would depend on $\ddot{I}(t_r)$ as well, and we know that the Poynting vector depends on $\dot{I}(t_r)$, what happens to the difference?


title: Image contrast as function of exposure for a CCD detector

text: In a laser interferometry experiment, we project a pattern of interference fringes onto a CCD sensor. For best results, we want good contrast between the bright and dark fringes, and we carefully compensate for various sources of noise - for example, by taking camera images with no fringes present, and with the laser turned off, and subtracting these images in the proper sequence. We'd expect therefore that the remaining signal should be highly linear, with the CCD signal at each pixel in direct proportion to the number of photons reaching it during the shutter time. What we actually find is that, as we vary the laser intensity and shutter time such that the average intensity across the image remains constant, with no pixels saturated, there is a definite "sweet spot" where the fringes are much more well-defined than at other settings. Either increasing or decreasing the laser intensity away from this point (with corresponding decreases or increases in shutter time) causes the fringe definition to deteriorate. I can't think of any reason why this should be. I know that in cases where the process generating the pattern has a time-constant (for example, using laser speckle interferometry to measure Brownian motion), there is an optimum exposure setting, but that shouldn't be the case in our system which is entirely static. So, what am I missing? I assume it's some property of the CCD sensor that I've overlooked.


title: UCM unidentified force

text: > _A train rounds a curve of radius 235 m (turning right). The train track is > flat, and the train is traveling at a constant speed. A lamp in the train > makes an angle to the vertical of 17.5 degrees. How do you calculate the > speed of the train?_ The first thing I need is to draw a free-body diagram of the lamp.![free-body diagram of lamp](http://i.stack.imgur.com/SQTWH.png) Sorry about the bad drawing. What confuses me is what force drives the lamp to the left. It seems to have something to do with inertia, I think it is probably equal to the centripetal force that the train exerts on anything in it. Can someone identify this force and explain the problem?


title: good and reasonably cheap way of connecting glass and metal in a vacuum setup

text: Sorry for this very technical question, but we suffer from this problem at work and I do not know any other place to ask. Its about a good and cheap way of connecting a glass tube with a metal tube in a vacuum setup. There are some solutions with gradually changing glass- materials in order to minimize the tension caused by the different heating- extensions of metal and glass. However they are rather expensive and we would prefer a cheap solution. We found a promising image of possible connection, however there was no manufacturer and no name of the flange given. ![enter image description here](http://b1online.de/public/vacuum.jpg) So does anyone of you recognize this type of flange? Or does anyone know where to ask such a question? What would you suggest as a connection between metal and glass in a vacuum setup?