title: Readings of the detectors at Japan and Izu-Bonin-Mariana Trenches

text: Given the relevance of this subduction system, I would expect that a wide range of detectors (temperature, vibration, seismometers, whatever) are deployed in the depth of these trenches. What would be the canonical source at which one could access the readings of these detectors?


title: Goldstone mode in O(N) (non-linear $\sigma$ model)

text: The question is does the Non-linear $\sigma$ model have a Goldstone mode? Consider a $O(N)$ mode for which the Hamiltonian is $H=J\sum_{i,j}\vec{n}_i \cdot \vec{n}_j$, where $\vec{n}=(\vec{\pi},\sigma)$ is a N component unit rotor with fixed length, say $\vec{n}^2=1$. If we consider the low energy excitation above symmetry breaking ground state $\vec{n}=(0,0,0,\sigma)$, writting $\sigma=\sqrt{1-\vec{\pi}^2}$, one can have the non-linear $\sigma$ model for small $\vec{\pi}$, $H=\int d^dx[\frac{J}{2}(\nabla\vec{\pi})^2+\frac{J}{2}(\vec{\pi}\cdot\nabla\vec{\pi})^2-\frac{\rho}{2}\vec{\pi}^2]$, where the continuous limit is assumed and $\rho=N/V$. The first term in the bracket looks like a spin wave excitation in a $XY$ model, say a Goldstone mode. However, the second term seems reflect the interaction of those excitation which may open a gap, and the the third term seems a mass term. Does this mean there is no Goldstone mode in a $O(N)$ rotor mode whose ordered states do break continuous symmetry?


title: virtual boxes mirror reflection

text: The problem statement > Find the lightpath with a given starting and ending points via one or more > mirrors. In those kind of problems you try image someone pointing a laser with a very narrow beam at a certain direction to the mirror, so it will reach point `B`. For example: You are seeing a square mirror room (with mirrored walls `a`, `b`, `c`, `d`) where you point from point `A` via the mirrors `c`, `b`, `d` and `a` to point `B`. A sketch can be made easily made: ![\[IMG\]http://i.imgur.com/QkWF4e6.png?2\[/IMG\]](http://i.imgur.com/RiIayEw.png) In order to find a more accurate solution, we flip the base cell with the points `A` and `B` a few times as shown in the image. After the mirroring is done, the line connecting `A` is drawn towards the mirror image `B'`. > Question: Construct the path in the original square. Complete the drawing. ![http://i.imgur.com/LkjW29I.png](http://i.stack.imgur.com/pbW7r.png) **My confusion** Why do I need to do with those virtual squares? I don't see an logical way to draw the reflections easily. And why is the line drawn from `A` to `B'` through all those other virtual rooms?


title: Properties of material affecting magnetic refrigeration

text: I am reading about magnetic refrigeration at the moment - I see that two factors affecting the applicability of the material for use in magnetic refrigeration is that they must react strongly (i.e the magnetic moments) with temperature at the operational temperature of the refrigerator and that to maximize cooling, necessarily a small specific heat. My book says there are other properties that could be advantageous for this application, but I am not sure what they could be. Any ideas? Many thanks.


title: Semiclassical Approximation

text: In many books I read about semiclassical approximation applied to the field of Bose-Einstein condensation. But I don't understand what it really means. For example I read that an expression like this $f_\textbf p (\textbf r) \frac{d^3\textbf rd^3\textbf p}{(2\pi \hbar)^3}$ for the state density. Have anybody a good explanation applied to this case? Or a general definition of semiclassical approximation?


title: 2D Ising model simulations: Wolff algorithm acceptance probability with an external magnetic field

text: I have implemented the Wolff algorithm to simulate a 2D ferromagnet. It works by building a cluster of like spins and flipping them all at once to move quickly through phase space. In the case of no external field and in interaction Hamiltonian which depends only on nearest neighbor interactions, the acceptance probability for adding a spin to the cluster is particularly simple. It works like a charm, but I would like to generalize it to include the contributions from an external magnetic field. All the resources I can find only take into account nearest neighbor interactions. If I add an external field to the mix, is there still a nice form for the acceptance probability?


title: Entropy of a polymer contained in a sphere with infinitely thin chords

text: Imagine that I have a polymer (approximated as a freely diffusing, freely jointed chain with some number of subunits 'N'), and I place this polymer into a sphere of some volume 'V'. Next, I proceed to add a series of infinitely thin, immobile chords of length 'L' to the inner walls of the sphere. Because these chords are infinitely thin, they will not change the inside volume of the sphere, but should nevertheless place certain topological and geometric constraints on the behavior of the diffusing polymer. Can we quantify the change in entropy caused by the addition of these infinitely thin chords? For this calculation, what changes if we replaced the polymer with a monoatomic gas?


title: Can (or How) Anthropic Principle be Made into a Scientific Theory?

text: Anthropic Principle says > physical Universe must be compatible with the conscious life that observes > it. I thought it is just philosophy mumbo-jumbo and it's not physics. But I could be wrong; I wonder whether is it possible to formulate it into a specific scientific theory that is falsifiable, at least in principle? The argument that "the theory is true because we are here; our existence proves the theory and if we are not here, the theory is disproved" is extremely unsatisfying, mainly because it can be formulated to support any kind of philosophical mumbo-jumbo.


title: Direction of current in concentric cylinders

text: Example 7.2 in David Griffiths E & M book (3rd edition) has a side view of 2 concentric cylinders, with smaller radius $a$ and larger radius $b$. The region in between $a$ and $b$ has conductivity $\sigma$. "If they are maintained at a potential difference $\textit{V}$, what current flows from one cylinder to the other for a given length $L$?" The E field is pointing radially outward along $\textit{s}$. My question is: what direction is the current? Do electrons flow in the opposite direction of an E field? If so, does that mean the current is flowing radially inward, along $\textit{-s}$, from $b$ to $a$?


title: origin of cusps in simulated dark matter halos

text: I keep reading that cusps are one of the most "robust" predictions of N-body simulations of dark matter halos. But any paper I've found on the topic makes it sound like these simulations are complicated and slow and that the cusps are just an observed result of the simulations rather than that the cusps have some understandable physical origin. But my immediate reaction was that the cusps' origin is trivial -- just the result of phase-space considerations -- and that interaction-less dark matter simulations should be one of the easiest things in the world. I remember writing a program to simulate non-interacting particles orbiting each-other with an inverse square law on an old PC over a decade ago, and I recall being able to get a pretty good picture of the density profile by tracing the paths of just a few particles. This only took a minute or two on a very slow PC. Indeed I remember something of a cusp being obvious, simply because the orbits of each particle tended to intersect near the CM, an effect that overrode the countervailing fact that individually each spent less time near the CM. In fact, even without doing a simulation, I would assume this would be the case because Keplerian motion clearly indicates that the time spent near the CM drops close to linear in R while volume goes as R^3. Anyways, I'm just wondering if these observations are basically correct, or if the origin of the cusps is somehow more obscure/complicated.


title: Does anything exist in the intergalactic space?

text: I am a part time physics enthusiast and I seldom wonder about the intergalactic space. First, it is my perception that all(almost all) the objects in the universe are organized in the forms of galaxies; or in other words, the universe is a collection of billions and billions of galaxies which are spaced far apart. Does anything actually exist in the empty space between galaxies? If yes, how did it reach there?


title: How would a laser gun actually work?

text: So, let's assume that the "laser gun / phaser / beam weapon" from all sorts of Sci Fi were an actual thing. You know - a weapon that uses a laser to kill somebody. I'm trying to imagine the physics of such a device, and two issues make me think that the real world physics of the thing make it an impossibility, even if you could get a laser to be that small in reality.   1. The beam should keep travelling too far to be safe, right? So, if you fire a normal gun, and miss your target, the bullet continues to travel for a bit. While there is disagreement as to how far, there is still a pretty good reason why you build a firing range against a hill - a stray bullet can still kill at considerable distance. With light, however, I don't see anything that would stop the beam. If gravity were to affect said beam (and one question I have is, would it?), it would seem that the speed of light, unlike a Star Wars special effect, would mean that the 'bullet' should be able to travel around the entire earth more than 7 times in less than a second. While a bullet is clearly going to hit the ground due to gravity within a space of less than a mile, I wonder, how long would it take a laser beam to dissipate? Since light has a speed that exceeds escape velocity, I can't see that gravity actually pulls the beam to the ground. My question is, does the beam continue in a straight line, eventually leaving the atmosphere, and going off into space, or would the curvature of the earth keep the beam orbitting the earth for some time? And, how far would such a beam go? At a certain distance, I would assume that orbitting spacecraft would eventually be hit by the beam, or if it closely followed the earth, it seems like the beam would eventually cause a swath of destruction as far as it went. So, how long would it take for the beam to be dissipated in the air just as a matter of course?   2. The pulse should be way too long to be tactical, right?  I remember Admiral Grace Hopper showing an 11" bit of wire, and saying that is how far light would travel in a nanosecond. Her objective, of course, was to show how fast a nanosecond really is. Applying that to a laser, however, I'm imagining that no computer could actually be fast enough to actually start and stop a laser beam in a nanosecond. Applying that to a laser gun - and let's assume that it was affected by gravity - means that a normal person triggering a pulse could actually start and stop in 1/8th of a second. Again, at the speed of light, that would mean the pulse should theortically be a long as the circumference of the entire earth at that point, making it tactically impossible to guide in any fashion. I'm curious what a rational limit would be for a microprocessor would be in terms of time, and then how big of a bolt that would produce. So, given just these two considerations - length of the bolt in relation to turn on/off times and distance that it would travel, how would a real-world "laser gun" actually work in practice?


title: How would one test the hypothesis of human free will?

text: In this context, I define free will to mean that a human's **high-level actions** (not the quantum states of his particles) are _not_ determined, in the same sense that some quantum effects are not determined. The simplest (hypothetical) experiment to verify the existence of free will would be to observe the actions of a human for a period of time, then "go back in time" to the beginning of the experiment and observe them again, watching for actions that differ from the first run. Obviously, we can't do that. Is there any conceivable experimental setup that might bring us closer to confirming that we have free will?


title: The Higgs vacuum

text: Srednicki's "Quantum Field Theory", an electronic copy of which is freely available here, seems to state on p 205 that the states eq. (32.3) which differ by a phase factor that can range through [0,2$\pi$) are mutually orthogonal. But if the underlying Hilbert space is separable this does not seem possible. Who can enlighten me?


title: Material resistency to lasers beam

text: Keeping the average power constant, why some materials are more eager to be damaged by pulsed laser with respect of C.W. lasers, or viceversa? When i talk about pulsed lasers i think for examples of duty cycles in the order of $10^5$. For example optical elements (such as a vortex phase plate for donut-shaping the beam) have different tolleration regimes regarding the incident power not simple dependent on the average power but also on the peak power for pulsed beam.


title: How do neutron stars burn? Is it decay or fusion or something else?

text: * What makes a neutron star burn, and what kind of fusion/decay is happening there?   * What is supposed to happen with a neutron star in the long run? What if it cools, then what do the degenerated matter looks like after it cools? Will the gravitational equilibrium be ruined after some burn time? How does it explode if it can explode at all?


title: The implication of anti-commutation relations in quantum mechanics

text: All the textbooks I saw are very clear about the implications of commutating operators in quantum mechanics. However, much less is said about anti- commutation relations. Does it have a general implication if two operators anti-commutate?


title: Which collision energy at LHC is better for hunting 125 GeV Higgs, 7 TeV, 8 TeV or 14 TeV?

text: Increasing collision energy in hadron collders doesn't always improve the abiilty to hunt down the Higgs. I know that if the Higgs mass is just above LEP exclusion, then even 7 TeV is too high to be optimum. However, I don't know the situation for a ~125 GeV Higgs. If the Higgs mass is really around 125 GeV as recent data suggest, does it make sense for the LHC to increase the energy next year to 8 TeV, and does it make sense for the LHC to shutdown at the end of next year to prepare for 14 TeV run? Of course, increasing the collision energy generally benefits BSM searches, but I'm asking the question assuming only the Higgs is taken into consideration.


title: Why does physics not attempt to explain observations in addition to describing them?

text: Physics are there to describe observations of things' behaviours to recreate them or basically use nature for your goals. Which is not enough. Why do physicists not try to explain, why things are the way they are? In other words: > Why does it work? instead of > How does it work?


title: Is it safe to study from MIT and Berkeley course series, or they contain wrong information?

text: After surveying most of the universities introductory physics courses, I found none is using Berkeley physics books or MIT physics books as textbooks. All are using Halliday, or Serway and the like. What is the reason behind not using these books anymore (once they were the standard textbooks, may be before halliday I suppose) ? Do they contain old/outdated/wrong information or something? Did Berkeley and MIT develop a new set of books to substitute those books?


title: Energy required to kick a planet orbiting the Sun from an elliptical to a parabolic path

text: I am trying to solve the following problem from Goldstein's Classical Mechanics: A planet of mass $M$ is in orbit of eccentricity $e=1-\alpha$ where $\alpha<<1$, about the Sun. Assume that the motion of the Sun can be neglected and only gravitational forces act. When the planet is at its greatest distance from the Sun, it is struck by a comet of mass $m$, where $m<<M$, traveling in a tangential direction. Assuming the collision is completely inelastic, find the minimum kinetic energy the comet must have to change the new orbit to a parabola. My reasoning: Using the conservation of energy equation, we can find the energy of the planet in its elliptical orbit. Since the motion is purely tangential at this point, we have $$ E = \frac{1}{2}M(r\dot\theta)^2 - \frac{k}{r}$$ Because it is an ellipse, we have $E<0$. Therefore, the energy the comet should have is $-E$ (since for a parabola, $E=0$), $$E_{comet}=\frac{k}{r}-\frac{1}{2}m(r\dot\theta)^2$$ All that now remains is to simplify the expression for $E_{comet}$ in accordance with the given data. Am I correct in my general reasoning?


title: Air simulation environment

text: I will preface this with the fact that I am not a physicist...I am an engineer by trade. I am working on a research problem that will involve flight of an organism with varying shapes, and I am interested in finding an open-source environment that successfully models the varying forces and whatnot found in the atmosphere. Basically, I want to create a 3D representation of my flyer and put it into an environment and be able to have natural forces act upon it (to see how it reacts). Does such a beast exist?


title: Can we describe the classical laws of physics in a frame-of-reference-independent way?

text: First of all, I am not a physicist, so I cannot guarantee things I say will make sense. I will try my best, though. In classical mechanics we have the notion of inertial frame of reference. If my understanding is correct, such frames are exactly those for which Newton's laws of motion have the usual form. I believe I have also heard, that they are the frames that are "moving at a constant speed" with respect to some distinguished point in space. So we have to be careful whether our frame is accelerated or not. Which makes me wonder: > Does there exist a set of physical laws (of same descriptive power Newton's > laws have, but perhaps expressing relations in some other set of physical > quantities) such that the laws from this set look the same, no matter how > the frame of reference moves? > > Does such a set of physical laws exist if we restrict to polynomially moving > frames of reference? (By this I mean that the motion of the frame is > described by a polynomial in $t$, where $t$ is time.) I imagine this could simplify some calculations.


title: Special Relativity - Reconciling 3 different frames

text: A Space Station S has two ships parked at it: P - PuttPutt and Q - Quick. S, P and Q synchronize their clocks. At noon P and Q take off in the same direction. P quickly accelerates to $c/4$ and Q quickly accelerates to $c/2$. Both P and Q are given a time to turn around and return to S. This time is calculated such that both P and Q will arrive at S concurrently. On the way out, once P and Q arrive at their cruising velocity, S observes their clocks. It notes that Q's clock is moving slower than their own. $$\gamma_q=\sqrt{\frac{1}{1-\frac{(c/2)^2}{c}}}=\sqrt{\frac{4}{3}}\approx1.1547$$ S measures each second on Q being $1.1547s$. The same analysis for P shows each second measuring $\sqrt{\frac{16}{15}}\approx1.0328s$. In Q's reference frame (once cruising velocity is achieved):   * Q1: How fast are S and P moving?   * Q2: Does Q see S's clocks as moving slower or faster?   * Q3: Does Q see P's clocks as moving at $\gamma_p$ or at $\gamma_q/\gamma_p$? In P's reference frame:   * Q4: How fast are S and Q moving?   * Q5: Does P see a difference in S and Q's clocks? Once S, P and Q are reunited. What is the order of the clocks? Which one is earliest, which one is latest and which one is in between?


title: Empirical meaning of relativity in the context of QM

text: In special relativity an event E is mapped to coordinates (x,t) in one inertial frame, and to coordinates (x',t') in another, and SR provides the relation between (x,t) and (x',t'). What is the empirical content of this theory (e.g. how would you operationally test it)? Since there are two frames, two observations are required - one that measures the (x,t) of E in one frame, and another that measures (x',t') of E in the other frame. Classically this presents no problem, since we can assume an ideal measurement exists that would not disturb whatever is being measured (the event E), and so two of these measurements can be made in rapid succession, one in each frame. But in QM, the result of measurement is intrinsically tied to the measurement apparatus and also the very act of measurement affects what is being measured. So when you observe an event E (say, particle position x at time t) in the first frame, using the apparatus in that frame, you can no longer observe that same event E in the second frame. Your second observation will at most be measuring the position of the particle after it has been observed in the first frame. So, in effect, a single event E does not have well defined (empirically/operationally) coordinates in all frames of reference at once. How then can we even talk about a relation between (x,t) and (x',t'), when these are not well defined?


title: Rolling bowling ball with slipping

text: If a bowling ball is moving with some initial velocity while slipping, how far will it move before it begins to roll once it experiences static friction? $\ddot{x} = \mu_{kf}g$ And there is also a torque from the kinetic friction on the ball (R = radius of the ball) $$mg\mu_{kf}R = \frac{2mR^2}{5} \ddot{ \theta} \implies \ddot{ \theta} = \frac{5g\mu_{kf}}{2R}$$ The condition for rolling without slipping is $v = R \omega$ and from the time the ball makes contact with the ground, transversal velocity decreases while angular velocity increases to a point where they are equal. I am not sure what I should do at this point, because everything I try doesn't seem to work. $$\ddot{x} = v \frac{dv}{dx} = \mu_{kf}g \implies v^2 = (2\mu_{kf}g)x + v_o^2 $$ I don't quite know what to do with this Differential equation that won't involve $\theta$ so that I can use it in the linear equation of motion. I have tried using time, but I don't know how that would help, And the actual angle itself is useless. $$\ddot{ \theta} = \frac{5g\mu_{kf}}{2R}$$ I can't say $x = R \theta$ because of the slipping


title: Determine the flow and amplitude equation for thermal energy (with Del operator)

text: It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ) . Within this room, the heat obey a certain equation ( for e.g. $T = 25 + 5z$ ) .We know that heat flows from higher temperature regions to lower temperature regions. With this information in mind > How could I be able to determine the amplitude and the direction of travel > of the thermal energy with the Del operator? I'm not looking for a definitive response, but an equation that could give me potentially the result for the amplitude and the direction. I also want to know if thermal energy follows a loop pattern within my room (and be able to explain it mathematically by using the del operator once again of course)? You can find the lecture source here. From those, we are able to get the Amplitude: For one dimensional heat flow, we have $q= k \dfrac{T_2-T_1}{L}$ , where $T_1$ and $T_2$ are terminal temperatures and $L$ is the length of the material. Switching to $3$-D spaces, we need to look at the fourier system of the heat transfer before proceeding further. $\dfrac{q_x}{A}= - K \dfrac{dT}{dx}$. So integrating we obtain $$\dfrac{q_x}{A}\large \int_{0}^{L} \ dx= -k \int_{T_1}^{T_2} \ dT.$$ So given that the heat flow ( rate of conduction ) in the $3$-D space $(x,y,z)$ is given by the following equation $$ q= - k \nabla T = - k \bigg( \hat{i} \dfrac{\partial T}{\partial x}+\hat{j} \dfrac{\partial T}{\partial y}+\hat{k} \dfrac{\partial T}{\partial y}\bigg).$$The negative sign, there indicates the transfer of heat from one place to another. So we can simply substitute the heat equation in the place of $T$ and compute the partial derivatives to get the rate of flow of heat. What about the direction?


title: Can colliders detect B violation?

text: I think there is some theoretical uncertainty whether high-energy collisions can violate B. It is known that at high temperature (higher than the Higgs scale) you violate B by SU(2) instantons. But in a situation where you have a very energetic 2-particle collision at arbitrarily high energy, I am not sure if there is a non-negligible probability of producing a Baryon violating configuration. I don't know of any calculation of B violation expected in accelerators, although there might be an argument that it should be very close to zero, because of the non-thermalizing nature of 2-particle collisions. Can you detect standard model B violation in colliders? Does LHC look for rare B violating events, or would such rare events be indistinguishable from a proton or neutron escaping undetected?


title: Can quantum field theory be seen as an epistemic restriction on (quantum) causal structure

text: Suppose we take Vicary's quantum harmonic oscilator as a kind of "toy quantum field theory". Next, take the category of internal comonoids to _not_ represent the background causal structure. We normally take the comonoids to be something like the cobordisms in TQFT. Instead, we take the internal comonoids to represent classical causal structure (where ordering is taken from the string diagrams in the category of internal comonoids). This classical causal structure can be understood as the ordering of events in your laboratory (turning knobs, flashing lights etc.). The background, or underlying causal structure, is taken as the string diagrams in the base monoidal category. The idea being that the underlying causal structure is quantum and the interface to it is via the string diagrams in the classical surface which we see as the category of internal comonids. Thus, looked at this way, a quantum field theory might be seen as an epistemic restriction on (quantum) causal structure. We map diagrams in the background, quantum causal structure into the classical interface and this is the concept of an epistemic restriction. I guess the question is, can we interpret quantum field theory as an epistemic restriction on causal structure?


title: Solid objects inside the event horizon - can they remain "solid"?

text: So, once something is inside a black hole's event horizon, it can only move towards the center. This is fine for a point-object. But 3D solid objects rely on molecular forces to stay in one piece. These forces act in all directions inside the solid. But there could not be any interaction between atoms at different distances from the singularity, right? So, what happens to a solid (let's assume a crystalline lattice, for simplicity) hypothetically placed inside the event horizon? Does it get cleaved in ultra-thin concentric layers, centered on the singularity?


title: SDE for particle, PDE for the density

text: Given a particle on the plane we can assume that it follows 2D Brownian motion. On the other hand if there is a lot of such a Brownian particles one can be interested in the evolution of the density of such particles. How is the PDE for the density derived? I guess it should be similar to the heat equation and there should be connection with a gas dynamics. Could you refer me to the literature?


title: Does a photon see a 0-D universe?

text: For a massless particle the spacetime interval between its point of emission and point of absorption is zero: the two points coincide. From the vantage point of such a particle space-time has reduced to a single point. In the Standard Model, _all_ particles start with zero mass, so does this suggest that our familiar 4-D spacetime is a consequence of the Higgs field or some similar mechanism by which mass is acquired? Note: if you believe the large-scale 4D structure of spacetime is a pre- existing given, this question makes little sense. In a relational view, where spacetime emerges out of event relationships, then the question suggests that a universe comprised solely of massless particles would have a fundamentally different event-structure.


title: Functional Derivative of Convolution

text: How to carry out the following functional derivative? $$\frac{\delta F}{\delta n(r)}$$ where $$F=\int dr n(r) \int C(|r-r'|) n(r') dr'$$ is it simply: $$2 \int dr' C(|r-r'|) n(r')$$?


title: Is there a different behavior between proton and antiproton beams at the Tevatron?

text: This question has its origin to the reference on the Aegis experiment at CERN where they aim to produce super cooled antihydrogen and detect whether its reaction to gravity is negative. It set me thinking that the beams in the Tevatron circulate for more than a second and everything falls about 4.9 meters in a second, so the bunches must be falling too. This of course will be compensated by the fields that keep the bunches in track among all the other corrections necessary. If though the antiprotons have a different behavior under gravity, this difference would appear in the orbits of protons and antiprotons. The question has two points: a) since the beams are travelling equal and opposite paths through the magnetic circuit, a negative gravity effect on antiprotons would disperse the antiproton beam up with respect to the path of the proton one. Could one get a limit on the magnitude of the gravitational effect difference between protons and antiprotons from this? I found one reference where the antiproton beam has a different behavior in chromaticity than the proton one, and it is explained away. Now I am completely vague about beam dynamics which I have filed under "art" rather than "physics" but b) am wondering whether this observed difference could be interpreted as a gravitational field difference in a dedicated experiment. Maybe there are beam engineers reading this list. My feeling is that if antiparticles had negative gravity interactions , beam engineers would have detected it since the first e+e- machine, but feelings can be wrong.


title: Why do car keys have longer range when held next to your head?

text: I first saw this on Top Gear, and assumed it was a load of rubbish, but today I tried it out and it actually works, if you walk away from the car continuously unlocking/locking it until it stops, and go a bit further away so that the car will not un/lock. Then out the car keys next to your head and point them directly at the car it will un/lock. How does your head/brain/etc increase the range of the keys? And why does it only work next to your head if you point the keys directly at the car, when you do not have to point towards the car when in normal range?


title: The effect of dark lines in the Sun's spectrum on reflected paint/ color

text: Its well known that the Sun's spectrum is not continuous, and that there are dark bands within the suns spectrum. Is it possible to produce a color of paint that is bright in, say, indoor lighting and dark in the sunlight?


title: Why is a critical quantum system described by a conformal theory in one higher dimension of space?

text: These questions are linked, so I've asked them in a single post: Why is a critical one-dimensional many-body system a two-dimensional conformal field theory?- Why the switch from 1D to 2D? What does 2+1 dimensional mean? Two dimensions of space and one of time? Or is it a strange way of saying three dimensional? Can a critical many-body system in thermal equilibrium be a 2+1 dimensional system? - Assuming the "+1" is time, considering a Wick's rotation, does the +1 become a measure of temperature?


title: Number of blades in a helicopter rotor

text: I was wondering how it is possible to determine what is the optimal number of blades in a helicopter rotor. I think that the length of the blade is involved as a longer blades would have to spin slower in order to avoid the extremes to overcome the speed of sound, and so one should be able to add more blades avoiding turbulences. Are there any other parameters? Is there a way to combine them together or we just rely on trials and empirical experience? * * * Looking around a bit I've found this question Wind generators - why so few blades? The physics case is just opposite, however that situation has a pretty different answer. It seems to me that there is a correlation with the weight of the helicopter, for instance the CH-53 has 7 blades while the famous bell 206 just has two. Still comparing it to the case of wind generators, I cannot get an overview of what's going on. ![CH-53](http://i.stack.imgur.com/50LNQ.jpg) ![bell 206](http://i.stack.imgur.com/2XSaG.jpg)


title: Does coffee with cream cool slower than black coffee?

text: At Modernist Cuisine, Nathan Myhrvold states that "Coffee with cream cools about 20% slower than black coffee". He then gives three reasons, two of them related to radiation and the third one to the influence of viscosity on the evaporation rate. My question is twofold:   1. **Is his conclusion correct?**   2. **Are those reasons relevant?** The question is somewhat open-ended, because "20% slower" could refer to the instantaneous cooling rate at $t=0$ or to the time needed to reach some lower temperature. It would be great to consider both parameters in the answer (will they behave the same?)


title: Commutator of parity and Hamiltonian operators under even potential function

text: I need to show what is $[H,P]$ where $H$ is the Hamiltonian and $P$ the parity operator. $V(\underset{\sim}x) = V(-\underset{\sim}x)$ in this case. I start off with $$ \langle \underset{\sim}x|HP|\psi\rangle = \langle \underset{\sim}x|(\frac{p^2}{2m}+V)P|\psi\rangle = \langle \underset{\sim}x|(\frac{p^2}{2m}+V)P|\psi\rangle = \langle \underset{\sim}x|\frac{p^2}{2m}P|\psi\rangle+\langle \underset{\sim}x|VP|\psi\rangle $$ and since $\langle \underset{\sim}x|V = V(\underset{\sim}x)\langle \underset{\sim}x|$ (is this step valid?) and $ \langle \underset{\sim}x|P = \langle -\underset{\sim}x|$, the above equation becomes $$ \langle \underset{\sim}x|HP|\psi\rangle = \langle \underset{\sim}x|\frac{p^2}{2m}P|\psi\rangle + V(\underset{\sim}x)\psi(-\underset{\sim}x) $$ Similarly I have $$ \langle \underset{\sim}x|PH|\psi\rangle = \langle \underset{\sim}x|P\frac{p^2}{2m}|\psi\rangle + V(-\underset{\sim}x)\psi(-\underset{\sim}x) = \langle \underset{\sim}x|P\frac{p^2}{2m}|\psi\rangle + V(\underset{\sim}x)\psi(-\underset{\sim}x) $$ Taking the difference of the two, I find that $$ \langle \underset{\sim}x|HP-PH|\psi\rangle = \langle \underset{\sim}x|\frac{p^2}{2m}P-P\frac{p^2}{2m}|\psi\rangle = -\langle \underset{\sim} x|\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x_i^2}P|\psi \rangle +\langle -\underset{\sim} x|\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x_i^2}|\psi\rangle $$ which I had trouble evaluating. Any hints?


title: How do fermion and scalar masses run with energy? Is the difference in their running the core of the hierarchy problem?

text: Do fermion and scalar running masses run in the same way? Specifically, what are the qualitative differences in the mass beta functions for, say, scalar $\lambda\phi^4$ field theory and the fermion masses in QED? Next, is there some obvious intuition for whether the masses should get bigger or smaller in the UV? Since particle masses become more and more irrelevant in scattering processes at higher energies I'd think that the running masses would get smaller in the UV, but this might not be the correct intuition. Finally, can one see that scalar masses are unnatural solely from their mass beta functions? Do they just run very quickly so that they are sensitive to their values in the UV?


title: Rayleigh scattering in three dimensions

text: How does the Rayleigh scattering intensity depend on the polarization angle of the incident, linearly polarized light, and the observation angle in three dimensions?


title: How is external pressure transmitted when a fluid is not enclosed?

text: Pascal's principle states that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid. How is the pressure transmitted in the case where the fluid is not enclosed? For instance, pushing a block of wood to a beaker with water such that the area of the bottom of the block of wood is does not enclose the mouth of the beaker. How do we solve for the force on the walls of the beaker?


title: Regarding binary systems

text: Are binary systems (in case of stars and other celestial bodies) more favorable than independent existence? I've been going through an article regarding pulsars, where it was stated that 'many pulsars are found in binary systems.The companion of pulsars have been found to be normal stars,planets,white dwarf stars,neutron stars and even another pulsar.'So what are the criteria to form a binary systems ? i know that their sizes should be comparable that leads to the equilibrium of the gravitational attraction between the bodies,etc. As it is a known fact that neutron stars and pulsars are quite heavy and dense,how are they able to co-exist as binary systems with other stars,planets,etc.? Search this @ http://outreach.atnf.csiro.au/education/everyone/pulsars/


title: Can a super-positioned human be used to differentiate between the Copenhagen interpretation and many-worlds?

text: I'm pretty new to quantum physics, so there's a good chance that I have this all backwards. However, by my understanding of the Copenhagen interpretation, the wave function 'collapses' upon observation. In the many worlds interpretation, the observer becomes decohered and collapse never occurs. I understand that it's fairly difficult to super-position big things. However, if many-worlds holds correct, then it should be really easy to super-position a human. For example, they observe the result of an experiment. Upon seeing result `A` they take a step back. Upon seeing result `B` they take a step forward. Bam, we have a massive super-positioned object. So the question is, is it possible to super-position a human such that they can interfere with themselves in some way? Or at least such that we can measure whether or not they are super-positioned? For example, perhaps the super-positioned person carries a "photon gun", and shoots it at where his super-positioned self would be. He may not see anything special, but could it be set up such that an outside observer (unaware of where the super-positioned human is standing) could measure the interference between the photons shot by the photon gun? If so, then it seems that there _is_ an experiment which can differentiate between the Copenhagen interpretation and many-worlds. I've been told that this is not the case, so I'm wondering where my logic failed.


title: How important are constrained Hamiltonian dynamics and BRST transformation as a formalism?

text: I am to study BRST transformations, for which I'm currently trying to understand constrained Hamiltonian dynamics to treat systems with singular Lagrangians. The crude recipe followed is Lagrangian -> Hamiltonian -> Dirac brackets and their quantization. I have been told that these techniques are used in QFT, string theory/high energy , etc. My question is are these formalisms indeed good and useful to learn? I'm confused because there are other formalisms and recipes (for example directly working with the Lagrangian). From a modern perspective, are these relevant? And does there exist any other formalism that I should not ignore? I will be starting my graduation soon; is it late to be studying constrained H formalism/BRST? Thanks in advance


title: Was Sun a part of a binary system?

text: I've read that many stars and other celestial bodies are found to constitute binary systems where the two bodies spin around each other. But our Sun is one of the exceptions. Could it be possible that the Sun was also a part of a binary system long ago ?


title: Can exergy and exergy destruction be understood through thermodynamical and/or statistical-mechanical principles?

text: My textbook _Fundamentals of engineering thermodynamics, Moran and Shapiro_ states: > The exergy is the maximum theoretical work obtainable for an _overall_ > system consisting of a system and the environment as the system comes into > equilibrium with the environment (passes to the dead state). The exergy of a system (which I'll call $\chi$), at a specified state is given by the expression: $$ \chi = (U-U_o)+p_o(V-V_o)-T_o(S-S_o) +KE +PE$$ Where $S_o, U_o$ etc. denote the dead states of a system. An Exergy change is : $$\chi_2 - \chi_1 = (U_2-U_1)+p_o(V_2-V_1)-T_o(S_2-S_1) +(K.E._2-K.E._1) +(P.E._2-P.E._1)-^?T_o\sigma_o$$ Where $\sigma_o$ is the "entropy production" and I'm not sure if it belongs there or not. The equation is clearly related to the Gibbs free energy, but the gibbs free energy is for an isothermal and isobaric process _(natural variables are T and P)_. It seems obvious to me that if a system is passing to the dead state it's temperature and pressure could change, for example: as a cup of coffee comes into equilibrium with the environment it's temperature will eventually be the same as the temperature of the "reservoir".(Note that these equations can also be expressed as rates) I haven't really been satisfied with the depth of the physics in my textbook and have had trouble finding good conceptual and mathematical explanations of exergy and exergy destruction. Can someone present a thermodynamic or statistical-mechanical description of exergy and exergy destruction? The intuitive mechanical engineer explanation I've come across is that it is about the economics of energy use ( _for example: heating your house with a radiator would be a poor use of exergy_ ), but I'd like something more mathematically rigorous if possible. Online references or a generalized example would be great too.


title: Force on a submerged triangular plate

text: > _A triangular plate ABC is submerged in water with its plane vertical. The > side AB is 4m long and is 6m below the water surface while the vertex C is > 2m below the surface. Find the force exerted by the water on one side of the > plate (density of water is 1000 kg m^3)._ I'm looking at it and all I can think is that the answer is 0? Maybe I'm misinterpreting it?


title: What is the area in Faraday's law if we have only a piece of metal moving in a magnetic field?

text: If a piece of metal of length $l$ is moving with a speed $v$ in a region where there is a uniform magnetic field $B$ perpendicular to it, there will be a potential difference across its terminals equal to $lvB$ which is known as motional EMF. This can be shown and understood in terms of magnetic and electric forces on the free charges in the metal. How can one calculate such EMF from Faraday's law, $\displaystyle\mathcal{E} = \left|\frac{d\Phi_B}{dt}\right|$? (where $\Phi_B$ is the magnetic flux $\int \bf{B}\cdot d\bf{a}$) (If $B$ is not changing, then the change in the magnetic flux must be due to change in an area, but the area of what? What are the boundaries of this area?)


title: Double gyroscope: Can a spinning pencil tumble on only one axis?

text: Picture an object such as item 7 on this page .. http://en.wikipedia.org/wiki/List_of_moment_of_inertia_tensors Call that the x axis and z is in to the distance. See diagram below. We are in deep space. The object is 10 meters long, a couple inches diameter and weighs 100kg. OK, we make it spin on it's own length. Let's say at about 2 hz. ![x y and z up](http://i.stack.imgur.com/3ZCmy.jpg) So it's spinning on it's own long axis, our x axis. Now for clarity, we will refer to "All the points along the center of the rod" as ATPATCOTR. So far it's only spinning on the x-axis. Looked at from any anywhere, it is of course obviously unchanging: Note that every ATPATCOTR is completely stationary, the coordinates x,y,z of every ATPATCOTR never change in any way. Now: we make it also tumble on the z axis. So the left end begins to move slowly down and the right end begins to move slowly up. The whole thing tumbles end-over-end, let's say once every few seconds. To be clear, every ATPATCOTR now descibes a perfect circle in the XY plane, with z always zero. BUT WAIT -- here's the question. Now, if you actually try to do this, typically it will also wobble. What do I mean by wobble? Look at it from overhead, and it will be varying it's angle - note the second diagram. (ie, the angular velocity along the y axis is no longer zero - it goes back and fore a bit.) It is no longer the case that ATPATCOTR make perfect circles (z=0), they are forming all sorts of weird spirals. THE QUESTION -- in fact, quite simply, IS IT POSSIBLE in this universe, to have the object both spin on the x axis, and, tumble on the z axis, CLEANLY with NO rotation or angular velocity in the y axis? In other words grab your pencil and throw it away from you, spinning it along it's length, but also make it tumble end-over-end a little through the air. In fact, can the tumbling motion be perfectly clean in one flat plane? Or is that actually impossible? (ie, you would have to use two glass sheets that forcefully retain the tumbling motion to be in one perfect plane only? In other words, make a platonic pencil spin on it's length and lay it on a platonic frictionless table. Now make it additionally spin like a baton as seen from above. Is that in fact "impossible", i.e. it will be angry that the flat table is holding the baton-spin to one perfect plane and it will force against it? In other words: http://www.youtube.com/watch?v=wfCgCXvw50A   it looks like (A) the board is spinning on it's own length, and, (B) slowly rotating on the z axis (using our diagram). Superficially (C) there's no rotation from overhead, rotation on the y axis. But is that simply wrong - if we observed closely there would be some rotation/wobble on the y axis also? In other words, can you spin a pencil along it's length, and also have it tumble in one perfectly flat plane only? Or will there necessarily be "wobble", essentially some rotation or change of angle in all three axis? In this universe can an object in fact spin in "two axis" only, or is that impossible? You can (I think!) have an object spin cleanly in one axis, but after that do you have to go straight to all-axis rotation? Thanks! ![enter image description here](http://i.stack.imgur.com/7b0fY.jpg)


title: Dimension of vector resulting from tensorial product

text: I'm quoting what I found in a book about quantum computation: > _Individual state spaces of $n$ particles combine quantum mechanically > through the tensor product. If $X$ and $Y$ are vectors, then their tensor > product $X\otimes Y$ is also a vector, but its dimension is $\dim(X) \times > \dim(Y)$, while the vector product $X\times Y$ has dimension > $\dim(X)+\dim(Y)$. For example, if $\dim(X)= \dim(Y)=10$, then the tensor > product of the two vectors has dimension $100$, while the vector product has > dimension $20$._ I don't understand: how can he state that the result of a vector product has dimension $\dim(X) + \dim(Y)$? What does he intend for dim?


title: What is the purpose of iron bars in concrete?

text: What purpose do iron rods in concrete serve? Do these iron rods impart any strength to the concrete apart from defining the framework for the concrete to solidify upon initially?


title: What is the ontological status of Faddeev Popov ghosts?

text: We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they "superficially" interact over finite time periods.   1. So, what is their ontological status?    2. If they don't really exist, can we just formulate a local theory without them?    3. OK, we can using spin foams?    4. So are they not really needed?    5. If they do "exist" out there, then say a state with an electron and no ghosts is "actually" different in "reality" from the state with same electron with the same momentum, but with a ghost added?    6. According to the formalism, they are different states. But observationally, we can never tell the difference. Both states will always give the same observable results for any physical observation. So are they the same state or not?    7. Do we just take the partial trace over the ghost sector?    8. But that's not gauge invariant except asymptotically, is it?


title: Tight binding operators in 2D lattice system

text: I have a very naive problem about lattice system, how to translate common operators defined in the bulk ($\hat{x}$, $\hat{p}$...) into their lattice analogues. In a single- band tight-binding description, the hopping Hamiltonian is taken in the form $$\hat{H}_0=-J(\sum_{m,n} a^{\dagger}_{m+1,n}a_{m,n}+a^{\dagger}_{m,n+1}a_{m,n}+H.c)$$ Then in the limit of lattice constant $a\rightarrow0$, how can we recover the usual kinetic energy term? $$\hat{H}_0=\frac{1}{2m^*}(\hat{p}_x^2+\hat{p_y}^2),$$ with a effective mass $m^*=1/(2Ja^2)$.


title: Alternate method of transmitting wireless electricity?

text: I have currently been researching a lot lately about wireless transmission of power. Currently the only methods i have seen that is viable is magnetic induction, and high voltage discharge(tesla coil and van de graff generators). The 2 methods above are not viable and not as efficient, and they require alot of input voltage(especially for the tesla coil and vdg generators). Are there any other alternatives known? even if it is ineffecient.


title: Quantum Entanglement - an illusion based on a wrong assumption?

text: Almost all resources I've read about Quantum Entanglement speak about how 'amazing' it is that two entangled particles are bound over any distance, and that the state of one particle determines the state of the other. I believe that there is possibly a profoundly wrong assumption here that doesn't get addressed properly. The assumption is that when the state of one particle is observed, it is then, and only then, determined, exiting it's super position state (and thus the state of the other particle also being determined, over any distance, instantly - which is where most of the focus lies when talking about entanglement). But here is my problem - why is the assumption that the state of the first particle is being _determined_ on observation so easily accepted ? It seems to me much more logical and absolutely free of unexplained voodoo that:   1. the particles are entangled (have opposite symmetrical states).   2. The state of the first and second particles is _unknown_ and unknowable until observed, but is predetermined from the moment of the particle's inception.   3. Upon observation, nothing in the particle changes, except that our knowledge of the first particle's state leaves a "super-positioned" state into a specific one.   4. Basic logical consistency dictates that we "instantly" know the state of the second particle, without the need for "spooky action at a distance". So I guess that my basic premise is - it seems much more reasonable that our (my?) understanding of superposition is wrong, rather than that particles exchange state information instantly across any space. Please help me understand where I am wrong ?


title: Angular momentum power plant on Earth

text: If tidal power plants are slowing down Earth's rotation then is it theoretically possible to build a power plant that would drain energy from Earth's angular momentum (thus slowing down it's rotation)? **What would such machine look like?**


title: Why do cars gain lift while going at a high speed?

text: I've been researching the physics involved with spoilers and I've just been turning up the same information about spoilers giving the back wheels of a car more traction by acting as an up side down airfoil. So my question is, what exactly causes the car to apparently gain lift while moving quickly, so as to merit the use of a spoiler, and is this entirely due to the aerodynamics of the vehicle in question? Edit: Clarity of question.


title: Grassmann fields according to Peskin and Schroeder

text: On page 301 in Peskin and Schroeder, they claim that a Grassman field $\psi(x)$ may be decomposed as $$\psi(x) = \sum_i c_i \phi_i(x),$$ where the $c_i$ are Grassmann numbers and the $\phi_i$ are "orthonormal basis functions". I don't understand what is meant by "orthonormal basis function". Surely they would need to define some metric on the space of all fields to do this? I can't think of a natural one. They claim that for the Dirac field the $\phi_i$ are a basis of four component spinors. Presumably they mean spinor fields here. I don't know of a natural basis for these fields. Could someone clear up whether this is an error in the book or whether I'm missing something?


title: Why are Saturn's rings so thin?

text: Take a look at this picture (from APOD http://apod.nasa.gov/apod/ap110308.html): ![Saturn's rings at APOD](http://apod.nasa.gov/apod/image/1103/titansaturn_cassini_900.jpg) I presume that rocks within rings smash each other. Below the picture there is a note which says that Saturn's rings are about 1 km thick.   Is it an explained phenomenon?


title: Is time the property of an object?

text: I don't know if the title makes much sense, but hopefully it will become clear with the text. Temperature is not a property of a point in the three dimensions, but actually of the object occupying that point. Similarly, is time the property of the point in three dimensions or of the object occupying it? If time is the property of an object, take the example of the twin's prardox in relativity. The twins have different ages, but it seems to me that they share the same time after they both stop at earth. EDIT:In case we say that time is an independent dimension, (just like z on a graph is independent of x and y), then the question is how does age relate to time? If time is not the property of an object, then age seems to be one. But then what is age? Can it be compared to distance/displacement?


title: How does the Fourier Transform invert units?

text: I don't really understand how units work under operations like derivation and integration. In particular, I am interested in understanding how the Fourier transform gives inverse units (i.e. time transforms into frequency), and if there are physical interpretations of the transform that involve units other than time.


title: Gravity theories with the equivalence principle but different from GR

text: Einstein's general relativity assumes the equivalence of acceleration and gravitation. Is there a general class of gravity theories that have this property but disagree with general relativity? Will such theories automatically satisfy any of the tests of general relativity such as the precession of mercury or the bending of light?


title: Does white phosphorous burn in ammonia?

text: In tonight's session of a science fiction role-playing game, I used a white phosphorous grenade against a group of ammonia-breathing aliens on their home turf, and I must confess that neither the GM nor I thought to think about whether the stuff is actually effective in that kind of atmosphere. I've heard it does burn in water. So, does it actually burn in ammonia?


title: Lorenz gauge in the Gupta-Bleuler Method

text: Greiner in his book Field Quantization page 180 & 181 wrote: > As shown in (7.24) the Lorenz condition cannot be enforced as an operator > identity. Instead we will use it _as a condition for the state vectors in > Hilbert Space $|\Psi\rangle$_. Only those state vectors are admitted for > which the expectation value of the gauge condition is satisfied:   >  $$\langle\Psi|\partial^\mu\hat{A}_\mu(x)|\Psi\rangle=0\tag{7.48} $$ And finally he constructed a condition to pick out the physical states $|\Psi\rangle$ > $$\partial^\mu\hat{A}^{(+)}_\mu(x)|\Psi\rangle=0$$ from which he achieved (7.48). Below is my question:   Suppose all that we will discuss is in the physical state space $V=\\{|\Psi\rangle\\}$, now **(7.48) would mean** $\partial^\mu\hat{A}_\mu(x)=0$ in this space $V$, **but this is apparently not true** , since even the most trivial condition failed $$\partial^\mu\hat{A}_\mu(x)|0\rangle=\partial^\mu\hat{A}^{(-)}_\mu(x)|0\rangle\neq0$$ since $\hat{A}^{(-)}_\mu(x)$ consists of creation operators.   So **what happened**?


title: Probability of absorption and emission of photons

text: Suppose you have a single electron in a box, and you shoot a single photon at it. How does one calculate the probability that the photon will be absorbed and the particle excited? Or that the photon will stimulate emission?


title: Solving for the phase shift of a neutron due to precession in magnetic field

text: In the famous experiment that was used to prove the sign change of the wave function due to a rotation of 2$\pi$ by Werner et al. It is stated directly that the phase shift of the neutron beam is equal to $2\pi g_{n} \mu_n M \lambda B l / h^2$ Where l is the length of the region within the magnetic field, $g_n$ is the neutron magnetic moment, and $\mu_n$ is the nuclear magneton. I am trying to show this for myself but I am having quite a bit of trouble picking up many of the terms they have. I am starting with the same trick they use to "rotate" their neutrons. We know a stationary neutron in a magnetic field has a hamiltonian = $-\mu B$. The time evolution operator is as follows $U(t,0) = e^{-iHt/\hbar}$ and the rotation operator $D_s(\phi) = e^{-i S_s \phi /\hbar}$. If we actually work out our hamiltonian and plug it into our time evolution operator we get $U(t,0) = e^{-i( 2 g_n \mu_n S_s t B) /\hbar^2 }$ its clear that this is the same as the rotation operator if we pick $\phi$ to be $\frac{2 g_n \mu_n S_s t B}{\hbar}$. From here I am stuck. I'm not sure how to correctly extract a statement on the phase from what I have. And I assume I will pick up some of their terms when I sub in for t in terms of the variables at hand, yet I don't see how I will get their exact solution. Any advice onw here to go from here would be much appreciated, here is a link to the paper, http://www.rpi.edu/dept/phys/courses/PHYS6510/PhysRevLett.35.1053.pdf . Any additional information needed is on the first page. Thanks in advanced.


title: How can space be euclidean when light bends?

text: I have read people arguing that tridimensional space sections of space time continuum (whatever its number of dimensions) appears to be euclidean from empirical evidence. I cannot reconcile it with my understanding that   1. Mass does exist    2. Mass does curve the spacetime continuum and 3D space sections    3. light bending has been explained by spacetime curvature.


title: fermions and quantum gates

text: Say that I have 2 qubits \- 2 spin half fermions. my initial condition is $|00\rangle$ in the spin-wave function and some anti-symmetrical spacial wave function. I'm wondering about what happens when applying a NOT gate. The Fermions total wave function still has to be inverted when swapping the particles. so does it mean that a NOT gate has to effect the spacial wave function? y.a.


title: Vector Derivative Transport Theorem Application

text: I have a position vector in frame A, the derivative of which I want to take relative to an observer in frame B. I apply the Vector Derivative Transport Theorem. The obtained velocity vector is left in frame A coordinates. Now, I need to find the acceleration relative to an observer in frame B. Do I apply the Vector Derivative Transport Theorem again, or can I take a straight derivative of my velocity vector without converting it first to frame B coordinates?


title: Resampling spectral data?

text: I want to use the CIE CMFs (Color Matching Functions) ![CMFs](http://upload.wikimedia.org/wikipedia/commons/thumb/8/8f/CIE_1931_XYZ_Color_Matching_Functions.svg/446px- CIE_1931_XYZ_Color_Matching_Functions.svg.png) provided here: http://www.cvrl.org/cmfs.htm With data from my spectrometer in 10 nm increments. However, the CMFs are only provided at 5 nm increments. What would be the best way to do this? Would it be okay to resample the spectral data with a linear interpolation? Any ideas?


title: What's the Standard Model width of a 125 GeV Higgs?

text: There's a fairly broad mass spread in the new results out of Atlas and CMS. I'm curious how this fits with the expected SM width.


title: TEM mode and currents

text: In a TEM mode, if the electric field is perpendicular to the direction of propagation, i.e. electron drift is perpendicular to direction of propagation, why do we have a current flowing into the load? I'm aware that my reasoning is probably flawed.


title: Maximum curvature in a black hole

text: If the curvature inside the horizon of a black-hole is not infinite in some quantum gravity theories (as in Loop quantum gravity), then what is the expression of the maximum value of the curvature that is reached at the former "singularity"?


title: How can black holes be so dense?

text: It is said that if the Earth were a black hole, it would be the size of a peanut!? How is this density possible, are atoms really that sparse that they can be compressed so tightly? Is there some other physical dimension that the matter gets sucked into?


title: quantum entanglement at microwave frequencies

text: Entanglement of optical photons using non-linear crystals has been around for a long time. Macroscopic entanglement using diamonds recently reported in the literature and receiving considerable attention. Quantum mechanics in biology has been the subject of fascinating research. Has anyone demonstrated entanglement of low frequency (i.e., microwave) photons? I see no theoretical objection, has it ever been demonstrated? Ditto entanglement at xray?


title: Noether Charge For Scalar Fields Under Lorentz Transformations

text: The conserved charge associated with the Lorentz transfomation of a **scalar field** is given by $Q^{\alpha\beta}=\int d^3x\frac{1}{2}(x^\alpha T^{0\beta}-x^\beta T^{0\alpha})$. The quantities $Q^{ij}$ is recognized as the components of orbital angular momentum but what physical quantities does $Q^{0i}$ correspond to for $i=1,2,3$? This cannot be intrinsic angular momentum or spin because we are considering a scalar field. What is the significance of these quantities?


title: How to find the total current supplied to the circuit?

text: Recently, I came across a question based on finding electric current of a circuit. Here's the image... ![](http://i.stack.imgur.com/doMjB.jpg) I know, by using the formula $I=V/R$, we can easily calculate the current as $V$ is given and $R$ can be calculated from the diagram. In the book (from where I got the question), > Solve the $R$ (net) by combining the $6 \Omega$ and $2 \Omega$ resistances > in parallel, and with both, $1.5 \Omega$ in series and whole parallel with > $3 \Omega$. I didn't get the logic they used. First, I thought of keeping 6, 2 and 1.5 ohm resistors in parallel and with all, the 3 ohm in series. But, that didn't work. Can someone please help me?


title: Galilean transformation in relativity

text: Assume flat spacetime in a general relativistic framework (or special relativity for that matter) and two observers $A$ and $B$, with non-vanishing velocity relative to each other. We know that they are both moving in their own (global) inertial frames $I_A,I_B$ and these physical frames are related by a Lorentz transformation, namely a Lorentz boost. This must be so, because for examples, one light ray has the same velocity in both of these frames. Starting from the frame of $I_A$, what is the physical interpretation of the coordinate system we get, if we make a Galileian transformation, i.e. a Galileian boost? We might do this by, say, using the spatial part of the relative velocity $v_{BA}^i$ of $A$ and $B$. Maybe there is a better choice than $v_{BA}^i$ $-$ I'm especially (but not necessarily only) interested in a choice of the transformation parameters, such that the spatial centre of the new coordinate system coincides with the worldline of observer $B$. I assume this is possible, because both transformations transform the world line of $A$ into a straight line. Maybe then the velocity vector will not be normed any longer, but this seems to be just an issue of proper time. Is this a system which doesn't correspond to any free physical observer because the time evolution in this system is unnatural? If so, what might be a cause/force on a physical observer to move through spacetime according to this and how does he experience the world around him (the observers $A$, $B$ and light rays)?


title: When is temperature not a measure of the average kinetic energy of the particles in a substance?

text: I had always thought that temperature of a substance was a measure of the average kinetic energy of the particles in that substance: $E_k = (3/2) k_bT $ where $E_k$ is the average kinetic energy of a molecule, $k_b$ Boltzmann's constant, and $T$ the temperature. (I'm not sure of the 3/2 coefficient.) Then I heard from several folks that this is a simplistic notion, not strictly true, but they didn't explained what they thought was flawed with this idea. I'd like to know what (if anything) is objectionable about this idea? Is it that the system must be macroscopically at rest? Is it that it ignores the quantum mechanically required motion of particles that persists at low temperatures? When is it not valid?


title: The Einstein-Klein-Gordon (EKG) equations

text: I am a little confused about a few papers I read on the Einstein-Klein-Gordon (EKG) equations. From what I understood one takes the energy-stress-tensor of the scalar field: $$T_{\mu\nu } = −\partial_\mu \varphi ∂_\nu \varphi − \frac12 g_{\mu\nu}∂_\alpha\varphi∂_\alpha\varphi − V(φ )$$ $$V(φ) = −\frac12 (mφ)^2 + \fracκ4φ^4$$ Where $κ$ is the usual self-interaction coupling constant . Then this stress-tensor is plugged into Einstein's equation and solved usually with the Schwarzschild or other convenient metrics. Now from what I know about QFT, isn't $φ$ an operator that maps the Hilbert space $H$ of particle states to $H$ itself? Doesn't that make the components of the energy-stress-tensor observables and thus operators as well? If so, then how can one equate the components of the Einstein tensor (which are purely geometric tensor fields) to operators? I once read that people (as of today) usually plug in < $T_{μν} $ > in Einstein's equation, but in the papers I read they directly used the operator itself and not it's expectation value. I also wondered how people plug the Maxwell stress tensor into Einstein's equations in a similar way? I get that the EM and scalar field are real valued fields, but shouldn't we use the expectation values in Einstein's equation? What am I missing? Here is a link to one such paper: http://arxiv.org/abs/0805.3211


title: Hermitian operator and reality of eigenvalues

text: Prove or disprove: The eigenvalues of an operator are all real if and only if the operator is hermitian. I know the proof in one way; that is, I know how to prove that if the operator is hermitian, then the eigenvalues must be real. It's the other direction that I'm not sure.


title: No-cloning theorem with 3 particles

text: I know how to demonstrate that it is not possible to make a unitary operator so that $|a\rangle|0\rangle$ turns into $|a\rangle|a\rangle$ , but is it possible to have $|a\rangle|0\rangle|0\rangle \rightarrow |a\rangle|a\rangle|c(a)\rangle$ which would allow a kind of cloning thanks to a third particle which would be useless except to preserve unitarity ?


title: How is angular momentum conserved when a spinning top finally stops spinning?

text: Where does the top's angular momentum get transferred to? Does it _very slightly_ change the angular momentum of the table, and then the angular momentum of the Earth?


title: Maximal Gravity

text: I found this interesting problem in Introduction to Classical Mechanics with Problems and Solutions by David Morin: > Given a point $P$ in space, and given a piece of malleable material of > constant density, how should you shape and place the material in order to > create the largest possible gravitational field at $P$? Any ideas?


title: What does it mean to be stationary?

text: I'm looking for a simple answer. What do we regard a stationary. Do we mean an object that is not moving noticeable from the viewers perspective because then a parked car would be considered stationary, but (assuming it's on earth) the earth is rotating and those at the circumference where the spin is greatest are traveling 1 038 mph and the earth itself is moving with the Milkyway at 600 000 mph. I have a bunch of other questions but I rather not put them all in one post, but do we really account for theses other speeds or do we ignore them.


title: What's the typical material used as a low-k ILD in semiconductors?

text: Semiconductor companies (namely IBM, Intel, TSMC and etc.) may use different low-k materials as inter-layer dielectric (ILD) in their fabrication process. I'm wondering what is the most typical one. Where can I find their thermo- electro-mechanical material properties? I need these information for FEM simulations.


title: Canonical form of GHZ and W state

text: What is the Schmidt decomposition of the tripartite states$|GHZ\rangle=\frac{1}{\sqrt 2}[|000\rangle+|111\rangle]$ or $|W\rangle=\frac{1}{\sqrt 3}[|001\rangle+|010\rangle+|100\rangle]$? Are these same as that of their canonical forms?


title: If nothing weighs something then doesn't that mean there is mass associated with spacetime?

text: Lawrence M. Krauss says, "If you removed all of the particles, all of the radiation,absolutely everything from space and all that remained was nothing that nothing would weigh something." What weighs something has mass. If you remove everything else then all that is left is spacetime. Meaning, there is mass associated with spacetime. Mass physically occupies three dimensional space. A particle moving through the mass associated with spacetime would displace the mass analogous to the bow wave of a boat. If mass is associated with spacetime then wouldn't it be the mass associated with spacetime which waves in a double slit experiment?


title: Direction of planetary tilt

text: I am building a 3d solar system simulation using WebGL and have come across the problem of establishing the direction of tilt of the various planets. No I know the tilt of the planets in degrees what I don't know is the direction of the tilt. Consider the following, on earth summer solstice (on the northern hemisphere) is on the 21st of June. So on that day the north pole is tilted towards to sun. Good times from this I can figure out which way in the 3d coordinate system to actually tilt the earth those 23.5 degrees. However how and or where do I find out the same information for all the rest of the planets. There is a wikipedia article (for instance) on seasons on Mars that has the dates for the equinoxes for Mars. Any idea where I could find similar information for all the planets, or better yet, an ever better way of determining the direction of the tilt of the planets.


title: Does Hamilton Mechanics give a general phase-space conserving flux?

text: Hamiltonian dynamics fulfil the Liouville's theorem, which means that one can imagine the flux of a phase space volume under a Hamiltionian theory like the flux of an ideal fluid, which doesn't change it's volume. But is it possible to reproduce every phase space conserving flux with an appropriate Hamiltonian? So can I simply imagine the entity of all possible Hamiltonian dynamics as all possible phase space conserving fluxes? Or are Hamiltonian dynamics a special case for phase space conserving fluxes? If they are a special case, what would be an example for a phase space conserving flux for which there is no Hamiltonian that can produce it?


title: Why do tsunami waves begin with the water flowing away from shore?

text: A sign of a tsunami is that the water rushes away from the shore, then comes back to higher levels. It seems that waves should be both + and - polarized and that some tsunamis should go in the opposite direction. That is the first indication of them would be that the water begins rising. However, other than situations very close to the source, it seems that the wave always begins with the water drawing away from the coast. For example, the wikipedia article on tsunamis states that: > In the 2004 Indian Ocean tsunami drawback was not reported on the African > coast or any other eastern coasts it reached. This was because the wave > moved downwards on the eastern side of the fault line and upwards on the > western side. The western pulse hit coastal Africa and other western areas. The above is widely repeated. However, when you search the scientific literature, you find that this is not the case: Proc. IASPEI General Assembly 2009, Cape Town, South Africa., Hermann M. Fritza, Jose C. Borrerob, "Somalia Field Survey after the December 2004 Indian Ocean Tsunami": > The Italian-speaking vice council, Mahad X. Said, standing at the waterfront > outside the mosque upon the arrival of the tsunami (Figure 10a), gave a very > detailed description of the initial wave sequence. At first, a 100-m > drawback was noticed, followed by a first wave flooding the beach. Next, the > water withdrew again by 900 m before the second wave partially flooded the > town. Finally, the water withdrew again by 1,300 m offshore before the third > and most powerful wave washed through the town. These drawbacks correspond > to 0.5-m, 4-m, and 6-m depths. The detailed eyewitness account of the > numerous drawbacks is founded on the locations of the offshore pillars. So is there a physical reason why tsunamis, perhaps over longer distances, tend to be oriented so that the first effect is a withdrawal of the water?


title: Why is it often assumed that particles are found in energy eigenstates?

text: Energy eigenstates provide a convenient basis for solving quantum mechanics problems, but they are by no means the only allowable states. Yet it seems to me that particles/systems are assumed to be in energy eigenstates "in nature". Some examples of what I mean:   * Solving the Schrodinger equation for the Hydrogen atom gives the standard $|n,l,m \rangle$ basis of energy/angular momentum eigenstates. But we speak of "filling up" these orbitals with electrons, or transitions between energy levels. Why should we expect to find the electrons only in such energy eigenstates, as opposed to say, some arbitrary superposition?   * In quantum statistical mechanics we have Bose-Einstein and Fermi Dirac distributions that give the number particles in a state of energy $\epsilon$, but why must a particle be found in a state of definite energy to begin with?


title: Superluminal particles with causality

text: What kind of CLASSICAL theories would allow to true (non-apparent) superluminal particles (beyond speed of light, BSOL) agreeing with causality to exist? I mean, are causal superluminal classical objects forbidden in any theory? Please, note that the "prejudices"/hypothesis for this question are: 1st. Classicality ansatz. A classical theory is defined as a theory containing (likely) SR as (low energy, or some other parameter) limit. I don't restrict it to usual Lorentz invariance. So, perhaps, the term "classical" should be complemented with classical invariance (group). 2nd. Causality hypothesis. Causality in the usual physical sense, i.e., every effect is preceded by some cause. 3rd. Superluminality. BSOL "definition": a superluminal particle is any object who can travel at higher speed than (known) light "in vacuum", i.e. $c$, without violating the previous two hypothesis, namely, "classicality" and "causality". So my question can be also formulated as follows: can we build a "sensible" physical theory where the above 3 postulates do hold? In the context of 3+1 relativity, with c as invariant velocity it is imposible. But is every theory with true superluminality necessarily a causality-violating (CV) theory?


title: The most general entropy

text: What is the most general (likely non-extensive) entropy allowed/realized in Nature and its symmetry group of transformations? We know Shannon-Gibbs-Von Neumann entropy, Tsallis entropy, Sharma-Mittal- Taneja entropy and other similar entropies. What and how could we determine the most general and possible entropy function and its symmetry features? Bonus: Why does it matter/is it important to Physics at the current era?


title: Unitary spacetime translation operator

text: Srednicki writes: We can make this a little fancier by defining the unitary spacetime translation operator $$ T(a) \equiv \exp(-iP^\mu a_\mu/ \hbar) $$ Then we have $$ T(a)^{-1} \phi(x) T(a) = \phi(x-a)$$ How do we get the second equation from the first equation?


title: How Special Relativity causes magnetism

text: So my physics teacher assigned us an article about how special relativity causes magnetism in a wire with a current, even with the low drift velocities of electrons in a current. It seemed that the basis of the article was that magnetism is just relativistic electricity, so I was wondering how a permanent magnet worked? It makes sense to me that a moving charged particle attracts unmoving particles of the opposite charge, but how do the orbits of electrons in a magnet cause it to have a magnetic field?


title: Mechanical similarity in Landau

text: I've read this very short paragraph from Landau & Lifshitz's Mechanics (Chap.2, Par.10) (that you can find here) about Mechanical similarity. I was looking for some more detailed explanations of the matter, at a level like the one in the first chapters of Landau's book. I've been able to find this article but it's a little too much for me. Can you give me some references that do not go into quantum mechanics, i.e. that refer only to classical mechanics and Lagrangian formalism, about the subject? Thank you in advance. **Content of the cited paragraph** As requested in the comments, I will summarize the paragraph's content; I will give my personal understanding of Landau's explanation, so I can be corrected if I'm wrong. Suppose a system of particles is described by a Lagrangian $\cal L(\mathbf{r_1},\mathbf{\dot{r_1}},\mathbf{r_2},\mathbf{\dot{r_2}},...,t)$ and suppose the potential energy is such that $U(\alpha \mathbf{r_1},\alpha \mathbf{r_2},...)=\alpha ^k ·U(\mathbf{r_1},\mathbf{r_2},...)$. Since multiplying the Lagrangian by a constant leaves the equations of motions unaltered, we may multiply $\cal L$ by $\alpha ^k$. In that case, the kinetical energy becomes (let's look at the kinetic energy of a generic particle): $$\alpha ^ k · T = \frac{m}{2} (\alpha ^{k/2}\dfrac{ \text d \mathbf r}{\text d t})^2=\frac{m}{2}(\dfrac{\text d \,\alpha \mathbf{r}}{\text d \, \alpha^{1-k/2}t})^2,$$ so letting $\mathbf{r'}=\alpha \mathbf{r}$ and $t'=\alpha^{1-k/2}t$ we get $$\alpha ^k \cal L (\mathbf{r_1},\mathbf{\dot{r_1}},\mathbf{r_2},\mathbf{\dot{r_2}},...,t)=\cal L (\mathbf{r_1'},\mathbf{\dot{r_1'}},\mathbf{r_2'},\mathbf{\dot{r_2'}},...,t').$$ In conclusion, if lenght and times are scaled respectively by a factor $\alpha$ and $\alpha ^{1-k/2}$, the resulting equations of motion are identical and the paths followed by the system of particles are similar. From this we may infer the ratios of times in similar paths from the ratios of lenghts beetween the two paths. For example: for gravitational potential $k=-1$, so:$$t/t'=(l/l')^{3/2},$$ which is Kepler's Third Law.


title: Energy-momentum tensor of Bosonic Ghost Action in String Theory

text: When quantizing bosonic string theory by means of the path integral, one inverts the Faddeev-Popov determinant by going to Grassmann variables, yielding: $$ S_{\mathrm{ghosts}} = \frac{-i}{2\pi}\int\sqrt{\hat{g}}b_{\alpha\beta}\hat{\nabla^{\alpha}}c^{\beta}d^2\tau, $$ where the $-i/2\pi$ just comes from convention/Wick rotated or not. My first problem is the notion of the 'fudicial' metric $\hat{g}$. I find its role in the path integral procedure a bit confusing. What is its relation to the 'normal' metric $g$? Why is it introduced? Related to this confusion is that fact in my lecture notes it is said that the energy momentum tensor is given by: $$ T_{\alpha\beta} :=\frac{-1}{\sqrt{\hat{g}}}\frac{\delta S_g}{\delta\hat{g}^{\alpha\beta}} = \frac{i}{4\pi}\left( b_{\alpha\gamma}\hat{\nabla}_{\beta}c^{\gamma} + b_{\beta\gamma}\hat{\nabla}_{\alpha}c^{\gamma} - c^{\gamma}\nabla_{\gamma}b_{\alpha\beta} - g_{\alpha\beta}b_{\gamma\delta}\nabla^{\gamma}c^{\delta} \right), $$ I have trouble deriving this. Varying the $\sqrt{\hat{g}}$ in the action yields the last term I would say: $$ \delta\sqrt{\hat{g}} = -\frac{1}{2}\sqrt{\hat{g}}\hat{g}_{\alpha\beta}\delta \hat{g}^{\alpha\beta} $$ However, this term does not have a 'hat' on the covariant derivative, which I find strange. The first and second term follow easily when writing the action with all indices low (except for a factor of 1/2), but I really don't see where the third term comes from and it also misses a hat on the covariant derivative. It looks like there has been done a partial integration, but I don't see why. I guess I am missing the point of the fiducial metric here. Explanation greatly appreciated! EDIT: In the discussion below I mentioned that $b_{\alpha\beta}$ is traceless: $b_{\alpha\beta}g^{\alpha\beta} = 0$, I forgot to place that here. It is a consequence of the path integral procedure.


title: Is the Ground State in QM Always Unique? Why?

text: I've seen a few references that say that in quantum mechanics of finite degrees of freedom, there is always a unique (i.e. nondegenerate) ground state, or in other words, that there is only one state (up to phase) of the Hamiltonian with the minimum eigenvalue. My questions: Q1) Is it true? Q2) Under what condition is it true? Q3) I can easily construct a Hermitian operator, in a finite dimensional space, which has two lowest eigenvectors. For example, if $ \left\\{ {\left| a \right\rangle ,\left| b \right\rangle ,\left| c \right\rangle } \right\\} $ is an orthonormal basis of a 3-dimensional Hilbert space, define a Hamiltonian $H = 1 \cdot \left| a \right\rangle \left\langle a \right| + 1 \cdot \left| b \right\rangle \left\langle b \right| + 2 \cdot \left| c \right\rangle \left\langle c \right|$ . Then $\left| a \right\rangle $ and $\left| b \right\rangle $ are two ground states. How is that consistent with the answer to Q1 (if that answer was positive...)?


title: Do laser beams interfere noticeably with each other?

text: I want to arrange some red lasers along a 90 degree arc of a circle, aimed towards the center of the circle. When their beams hit the opposite side of the circle, will I notice any interference effects? What if I use dozens of lasers? ![Laser arc](http://i.stack.imgur.com/Ok0m9.png) If they do interfere, how do I calculate the interference pattern?


title: Identification of extended quantum objects?

text: In some physics theories like string theory we have notion of spatially extended quantum objects - strings, membranes etc. Assuming that such objects exist, how would they appear in experiments ? More precisely are there any thought experiments for determining whether a quantum thing being observed has spatial extension or not, and if it has spatial extension then what is its dimension, topology etc.


title: How does non-Abelian gauge symmetry imply the quantization of the corresponding charges?

text: I read an unjustified treatment in a book, saying that in QED charge an not quantized by the gauge symmetry principle (which totally clear for me: Q the generator of $U(1)$ can be anything in $\mathbb{R}$) but for non-Abelian gauge symmetries the "charge" are quantized by virtue of this principle. Could someone give a hint (or reference) of the calculation showing that.


title: Why can radio wave travel through walls while imfrared can't?

text: > **Possible Duplicate:**   >  If both radio waves and gamma rays can travel through walls Does it have anything to do with the materials used to build the wall? What determines if a material can absorb an (x) wavelength?


title: Effect variable cylinder radius has on airflow

text: Can someone shed some light on the following problem? I'm unable to get any traction on it as I know nothing about fluid dynamics (I'm a computer engineer). It's a problem I made up over a lunch discussion with a friend. I've illustrated it as folows: ![enter image description here](http://i.stack.imgur.com/sgj3p.jpg)


title: Reynolds number with hyper-viscosity

text: Is it possible to evaluate a Reynolds number when viscosity operator is substituted by hyper-viscosity operator at the power H (Laplacien to the power H) in the incompressible Navier-Stokes equations ?


title: Is it valid to calculate mass of electron using the speed of the wave packet and energy

text: A gaussian wave packet. It's peak is moving at speed v. We know the energy of the packet is E. Can I deduce the mass of the electron using $m=2E/v^2$


title: Mirror image at relativistic speeds

text: Imagine moving parallel to the surface of a very large flat mirror at relativistic speeds. What would be the effect of viewing yourself in the mirror? At non-relativistic speeds your image would be similar to what you would see when stationary. Assume you are moving to your right with respect to the mirror at high speeds. Without doing the math I would expect your image would start moving to your left. Also, your image would start to distort because the path lengths of the photons from various parts of your body would take different times to arrive back at your eye. So what arrives simultanously to your eye would be different regions of yourself at different times in the past. Also, assuming that the light source that is illuminating you is moving with you, the photons would transfer some of their momentum and energy to the mirror, and so the light from the image would be red-shifted. The last part I am not sure about, is reflection a process of absorption and re-emission from the surface atoms of a mirror?


title: Stress-energy tensor. Why this general form?

text: How is the stress energy tensor obtained? In most textbooks, it's simply stated as $$T^\mu{}_\nu=(\rho+P)U^\mu U_\nu-P\delta^\mu{}_\nu$$ I can see why this makes sense for a comoving observer at rest wrt. the perfect fluid. But I don't understand how the general case is arrived at. Would someone kindly explain?


title: Are there any other mechanisms that can make virtual particles 'real' other than Hawking Radiation and Universe Births?

text: As I understand it, if virtual particles do not recombine within the plank time they become 'real'. This is proposed to happen in Hawking Radiation, where one virtual particle crosses the black hole's event horizon and the other does not, where it robs some energy from the black hole. Lawrence Krauss also proposes in his talk 'A Universe from Nothing' that from nothing (meaning the QED Foam) with a net energy of zero, a universe can be born, presumably (if simplistically) 'creating' matter by 'borrowing' energy from the Foam. These are both just proposed, but are there any other proposed (or demonstrated) mechanisms by which virtual particles 'become real'? Say extremely unlikely 'borrowings', or two close simultaneous events that repelled the particles before recombination, or small 'universe birth' events within our universe? If it is indeed possible, to maintain the conservation of energy would there be some sort of 'negative energy' field left in the wake of the two created particles?


title: Potential energy in Special Relativity

text: In Special Relativity, the energy of a free particle is $E^2=p^2c^2+m^2c^4$. But what would be the energy when there is potential energy? If it's something like $E=\sqrt{p^2c^2+m^2c^4}+U$, what does it mean if a particle has zero or less energy? **Addendum 2013/09/26** The potential momentum is used only in gauge theories (like EM). But could it be used in SR+Newton's gravity, without introducing the concept of curvature (GR).


title: Force acting on an object?

text: You have a bar of metal in an environment with no gravity. A force is applied on one end of it. How does it rotate? ![enter image description here](http://i.stack.imgur.com/mXf1t.jpg) There is a non-zero torque on any random point selected on the bar. For example, on point A the torque is $T_A = F*y$, but on point B the torque is $T_B = F*x$. So the torque on any point on the bar except the point where the force is applied, is non-zero. If there is a non-zero torque on one point, the object must rotate around that point. But since there is a non-zero torque on _every_ point, and the object can't rotate around every point, how does it rotate and around what point?


title: Do physicists believe the singularity theorems to be accurate?

text: This question is largely based on the last post by reddit user RobotRollCall who gave some fantastic explanations of phenomena in relativity on a layman's level. About a year ago, she said: > _The short answer is that the "singularity" of which you speak is a > mathematical artifact that only arises under certain conditions, and cannot > meaningfully be said to exist. A black hole consists of an event horizon and > nothing else._ Everything I've read up until now, however, contradicts that. As far as I understand, the Hawking-Penrose singularity theorems give nice (and fairly lax/physical) restrictions on a spacetime under which black holes must form true singularities. Is this the case, or is there something I haven't read up on so far which suggests that the singularity theorems do not apply in general? I'm aware that they're really for classical GR, but does quantum physics invalidate them?


title: Force in tetrahedron edges

text: I am looking for a formula that enables me to calculate the force in a tetrahedron edge such that it relates $F_b$ with $F_z$ through the beam thickness and length. I have the following assumptions:   * The beams are circular and hollow. So the have a radius $r$ and a thickness $t$.    * The static force points in the negative $z$-direction and is active in the c.o.g.    * The contribution of the vertices/joints is neglected.    * The tetrahedron is standing on one vertex as shown in the image below.    * The beam length is $a$. I have drawn the situation in the following image: ![enter image description here](http://i.stack.imgur.com/Trxfl.png) Can someone provide me with a formula or some pointers on how to find the beam force? * * * Edit, using Jaime's hints. As the c.o.g. is alined with he lower vertex the structure is in equilibrium. When looking at the lower vertex the vertical component of the three beam forces equals the gravitational force. $$ F_{b_{y1}}+F_{b_{y2}}+F_{b_{y3}}=F_{g}\\\ F_{b_{y1}} = F_{b_{y2}} = F_{b_{y3}}\\\ F_{b_{y}} = \frac{m \cdot g}{3} $$ From the Encyclopedia Polyhedra written by Robert Gray I found that the half- cone angle is 35$^{o}$. This means that: $$ F_{b} = F_{b_{y}} \cdot cos 35\\\ F_{b} = \frac{m \cdot g}{3} \cdot cos 35 $$


title: What's the difference between the equivalence principle and curvature of spacetime?

text: Calculating using the equivalence principle only accounts for half the deflection of light, whereas the other half is from curvature of space-time. But isn't the equivalence principle the same thing as curvature of spacetime? Deflection of light has two parts: The first part is falling people measure the deflection. Why is it significant for falling people to do this and how does this follow principle of equivalence? Falling people means gravity and curvature of spacetime doesn’t play a role. This means we’ll know how much deflection is caused by the motion of the photon and general relativity? The second part is the curvature of space. For example, if you have a rod, the rod itself would bend around the Sun. These two parts are like two halves, each of it is one half the deflection.


title: Minimal Maxwell's Demon

text: I would like to understand where the waste heat is generated in the Maxwell's demon problem. To this end I've come up with the simplest scenario I can think of. If my scenario is workable I am hoping someone will be kind enough to apply the right math to it to show what is going on and why it does not work to provide a "free lunch." My scenario is as follows: Take a 1 dimensional container of length l. Start with an evenly distributed population of particles; slow red ones and fast blue ones, traveling at +v or -v, and +2v or -2v respectively. The demon sits at the boundary at l/2. He lets slow red particles at +v and fast blue particles at -2v through and keeps the opening between the two halves of the container closed otherwise. The idea of using a one dimensional container is to keep the math as simple as possible. In order for this to work the particles have to be able to go right through one another without interacting. I am imagining that if one can work out what happens in this simplest case then it should be possible to extend the scenario to a 2-dimensional container in which the line forming the barrier between the two halves of the container is made up of discrete copies of the Maxwell's Demon in my 1-dimensional scenario.


title: Extending General Relativity with Kahler Manifolds?

text: Standard general relativity is based on Riemannian manifolds. However, the simplest extension of Riemannian manifolds seems to be Kahler manifolds, which have a complex (hermitian) structure, a symplectic structure, a riemannian structure, all these structures being compatible. So my question is : What is the "simplest" theory, extending general relativity, based on Kahler manifolds ?


title: Setting up equations for a Rotational Kinematics system

text: I'm having a hard time setting up equations for the following problem: > A green hoop with mass $m_h$ and radius $r_h$ m hangs from a string that > goes over a blue solid disk pulley with mass $m_d$ and radius $r_d$. The > other end of the string is attached to a massless axel through the center of > an orange sphere on a flat horizontal surface that rolls without slipping > and has mass $m_s$ kg and radius $r_s$. The system is released from rest. ![enter image description here](http://i.stack.imgur.com/wGmxS.png) What is the magnitude of the linear acceleration of the hoop?


title: Dirac equation as Hamiltonian system

text: Let us consider Dirac equation $$(i\gamma^\mu\partial_\mu -m)\psi =0$$ as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that Dirac equation becomes Hamiltonian equation $$\dot{\psi}=\\{H_D, \psi\\}?$$ Of course, such bracket would be graded (super bracket), but if it exists this would explain on classical level why $\frac{1}{2}$-spinors correspond to fermions.


title: Charge outside Gaussian Surface doesn't contribute to Flux?

text: I roughly understand the explanation for this: any electric field line that enters the surface, must leave it, since field lines can't terminate abruptly in space. My question is, what if you have a charge $+2q$ outside your gaussian surface, and a charge $-q$ inside it? Wouldn't the field line end at the charge $+q$, and so the field lines that enter don't necessarily leave, making $+2q$ contribute a negative flux?![enter image description here](http://i.stack.imgur.com/zZsTm.png)


title: Force exerted by a capacitor on a polar object

text: I was reading about capacitors and wondered what the force an electrostatic field created by a capacitor would be on an object with a certain charge and mass. If it can exert a force on a polar object then surely it can move charged objects around. So please could someone tell me whether it is possible to do this and what the calculations are to calculate the force exerted by this electrostatic field.


title: Momentum change in collisions (Drude Model)

text: A particle suffers elastic collisions with scattering centers with a probability of collision per unit time $\lambda$. After a collision the particle is in a direction caracterized by a solid angle $d\Omega$ with probability $\omega(\theta) d\Omega$, that depends only on the angle between the intcial direction $\vec{{p}'}$ and the final direction $\vec{p}$. Assume only elastic colisions, $p={p}'$ a) Obtain the following equation of motion for the density of probability $f(\vec{p},t)$: $\frac{\partial f(\vec{p},t)}{\partial t}=-\lambda\cdot f(\vec{p},t)+\lambda \cdot \int d{\Omega}' \cdot \omega(\theta)f(\vec{{p}'},t)$ Where the integration is over the solid angle of $\vec{{p}'}$ ($d{\Omega}'=sin{\theta}' d{\theta}'d{\phi}')$ b)Show that the equation of movement of the average momentum is: $\frac{\partial <\vec{p}>}{\partial t}=-\frac{<\vec{p}>}{\tau_{tr}}$ where $\tau_{tr}$, the transport time is defined by: $\frac{1}{\tau_{tr}}=\lambda \int d\Omega (1-cos \;\theta) \omega(\theta)$ **Attempt at a solution** a) I can arrive at the given expression, so no problems here b) I start by writing: $<\vec{p}>=\int d^3p \; f(\vec{p},t)\cdot \vec{p}$ And I derive this expressions with respect to t, getting from a) that: $\frac{\partial <\vec{p}>}{\partial t}=-\lambda\cdot <\vec{p}>+\lambda \cdot \int d^3 p \; \vec{p} \int d{\Omega}' \cdot \omega(\theta) f(\vec{{p}'},t)$ And from here I don't know what to do, is there something that I'm missing or does it need some kind of trick?


title: Does photon possesses no time to cover any arbitrary distance?

text: Photon travel 8 minutes (with speed $c$) from the sun to reach the earth. Any particle (or space-ship) with velocity $0.99 c$ covers the same distance (93 millions km) within less than 2 minutes (according to SR). Does this make sense?


title: What happens when you heat vodka in a microwave?

text: Since ethanol has a lower dielectric constant than water would the water heat up and boil before the ethanol? Would the water transfer heat to the ethanol and, since ethanol has a lower boiling point, bring it to a boil before the water?


title: Is there a Hamiltonian for the (classical) electromagnetic field? If so, how can it be derived from the Lagrangian?

text: The classical Lagrangian for the electromagnetic field is $$\mathcal{L} = -\frac{1}{4\mu_0} F^{\mu \nu} F_{\mu \nu} - J^\mu A_\mu.$$ Is there also a Hamiltonian? If so, how to derive it? I know how to write down the Hamiltonian from the Lagrangian where derivatives are taken only with respect to time, but I can't see the obvious way to generalize this.