title: Conservation of energy and momentum via the continuity equation in asymmetric time and space translation

text: I am confused about energy and momentum conservation, time and space translation symmetry, and the continuity equation. Suppose we have a mass $m$ in inertial space far from any gravitational fields. Suppose the mass has an initial velocity $v$; thus, it has an initial momentum $p=mv$ and an initial kinetic energy of $T=\frac12mv^2$. My understanding of the continuity equation is we imagine a closed surface this mass passes through and we say momentum is conserved if the momentum of $m$ exiting the imaginary surface is the same as the momentum of m entering the surface. This comes about by space translation symmetry. Now, suppose during the time $m$ is within the closed surface, an impulse is applied to the mass, so that when it exits the surface, it has a greater momentum. Do we say the momentum is still conserved because we include the impulse that acted on the mass during its transit within the closed surface? Also, the same question applies to the kinetic energy the mass gains by work being done on it by a force $f$ and displacement $d$ within the closed surface. We still say energy is conserved because work was done on the mass while it was in transit within the closed surface. Correct? Now, suppose the mass $m$ starts out in a gravitational field and free falls to the earth. During its fall, it also passes through an imaginary closed surface. The momentum and the kinetic energy of the mass will have increased from its initial values prior to entering the closed surface. But, relativity states gravity is not a force, but a curving of space-time. While the mass accelerates through the imaginary closed surface, it gains energy and momentum even though there is no force or "weight" acting on it. Is it correct to say that because there was no time or space translation symmetry within this closed surface-- spacetime is curved-- that energy and momentum is not conserved? Or, do we think of a real force acting on the mass due to the gravitational field so that we can assert energy and momentum is conserved locally?


title: How can results from classical optics be obtained from QFT?

text: Recently it came to my mind, that I have some basic knowledge about QFT and know im principle how to calculate scattering amplitudes (at least for the $\phi^4$-theory), but have no idea how to understand most of the phenomena in nature. Consider for example the reflection of light on a mirror. It is clear, that I have to use QED to calculate scattering amplitudes but how can this be done? There are millions of atoms that scatter light, so I will probably have to use a statistical approach? It's not urgent but I would nevertheless be interested. At least I would like to know, if it is in principle possible, to obtain well known results like reflection or refraction directly and rigorously from (interaction) QFT. I know the arguments from Feynmans QED book and am not looking for plausibility arguments.


title: What kind of physical quantity is angular displacement?

text: Angular Displacement is neither a vector nor a scalar. What type of physical quantity it is? Are there any other examples of that physical quantity?


title: What is the solution of general relativity for our universe?

text: So I just finished off learning quantum mechanics and special relativity. I just realized that in general relativity, there is Einstein field equation which must be solved in order to talk about physical movements. But I see several solutions. So is there a thing as a solution that describes our universe perfectly at astronomical scales/macroscopic level (not quantum level)? Or do we have to solve the equation for different cases occurring in our reality?


title: What the name of the evacuated glass gadget with black and white vanes that turn when a light is applied?

text: I remember a glass device my physics teacher had at high school which   1. Contained some vanes mounted somehow on a vertical axis, which were all black on one side and white on the other   2. Was in a vacuum (partial, at least)   3. Caused the vanes to spin when a light was shone onto them I've never seen such a device since. Can anyone tell me if it has a name?


title: Dropping an object on the moon

text: If you are dropping an object on the moon would it fall on to the moon's surface or fall towards earth?


title: Why we use $L_2$ Space In QM?

text: I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space of state functions, from where this arises? and why 2-order space that assumes the following inner product: $\langle\phi|\psi\rangle =\int\phi^{*}\psi\,dx$ While there is many ways to define the inner product. In Physics books, this always assumed as given, never explains it, also I tried to read some abstract math books on this things, and found some concepts like "Metric weight" that will be minimized in such spaces, even so I don't really understand what is behind that, so why $L_2$? what special about them? Who and how physicists understood that those are the one we need to use?


title: Entropy of a two-level system

text: Consider a two-level system with energies and degeneracies $\epsilon_0 = 0, g_0=1$ and $\epsilon_1 = \epsilon, g_1=4$. I can show that the temperature at which both levels are equally populated is given by $\exp\left(\frac{\epsilon}{kT_0}\right) = 4$, at which the partition function, $q=2$ and the molar internal energy $U(T_0) = \frac{1}{2}N_A\epsilon$. This means that the entropy at $T_0$ is $S(T_0) = R\ln 2 + \frac{N_A\epsilon}{2T_0}$, right? Is there any special interpretation of this value of the entropy? Can the two terms here be described separately by something physically meaningful?


title: Where does either Bohr or Heisenberg mention the idea of the wave function collapsing?

text: Could someone reference a paragraph written either by Heisenberg or Bohr where they mention the idea of the wave function collapsing?


title: Diffusion coefficient of a crystal

text: I've been trying to work this out so I can give a hand waving argument for one of the effects I'm observing on the fly and I find myself going down a rabbit hole that seems way too complicated for what I need. Thanks for any help. I have a TiO2 rutile (so the unit cell is a body centered tetragonal cell) material. The unit cell parameters are a=b=4.5 and c=3 angstroms. I know the diffusion coefficient for oxygen along the a direction (call it Da) and the coefficient along the c direction (call it Dc). My question is: Given that I know Da and Dc, what is the diffusion coefficient in the (111) direction? While I'm at it, once I have the diffusion coefficient, how can I calculate the percentage loss of oxygen at a given distance from the surface. That is to say, say I find out that there is sufficient time for the oxygen a nanometer in to diffuse to the surface, that obviously doesn't mean that _all_ of the oxygen a nanometer from the surface will migrate to the surface. So how do I calculate what percentage _will_ migrate for a given time? If it turns out that this can't be conceptualized simply, then I suppose I'll brush off my condensed matter textbooks, but it seems to me I worked this type of problem really early on in my studies. So I hope someone can help. Thanks!


title: Can someone please explain magnetic vs electric fields?

text: I've looked through about 20 different explanations, from the most basic to the most complex, and yet I still dont understand this basic concept. Perhaps someone can help me. I dont understand the difference between the electric and magnetic force components in electromagnetism. I understand that an electric field is created by electrons and protons. This force is attractive to particles carrying opposite charge and repulsive to like-charge particles. So then you get moving electrons and all of a sudden you have a "magnetic" field. I understand that the concept of a magnetic field is only relative to your frame of reference,   1. but there's no ACTUAL inherent magnetic force created, is there?   2. Isnt magnetism just a term we use to refer to the outcomes we observe when you take a regular electric field and move it relative to some object?   3. Electrons tend to be in states where their net charge is offset by an equivalent number of protons, thus there is no observable net charge on nearby bodies. If an electron current is moving through a wire, would this create fluctuating degrees of local net charge? If that's the case, is magnetism just what happens when electron movement creates a net charge that has an impact on other objects? If this is correct, does magnetism always involve a net charge created by electron movement?   4. If my statement in #2 is true, then what exactly are the observable differences between an electric field and a magnetic field? Assuming #3 is correct, then the net positive or negative force created would be attractive or repulsive to magnets because they have localized net charges in their poles, correct? Whereas a standard electric field doesnt imply a net force, and thus it wouldnt be attractive or repulsive? A magnetic field would also be attractive or repulsive to some metals because of the special freedom of movement that their electrons have?   5. If i could take any object with a net charge, (i.e. a magnet), even if it's sitting still and not moving, isnt that an example of a magnetic field?   6. I just generally dont understand why moving electrons create magnetism (unless i was correct in my net charge hypothesis) and i dont understand the exact difference between electrostatic and magnetic fields.


title: What are the precise statements by Shouryya Ray of particle dynamics problems posed by Newton which this news article claims have been solved?

text: This recent news article (here is the original, in German) says that > Shouryya Ray, who moved to Germany from India with his family at the age of > 12, has baffled scientists and mathematicians by solving two fundamental > particle dynamics problems posed by Sir Isaac Newton over 350 years ago, Die > Welt newspaper reported on Monday. > > Ray’s solutions make it possible to now calculate not only the flight path > of a ball, but also predict how it will hit and bounce off a wall. > Previously it had only been possible to estimate this using a computer, > wrote the paper. What are the problems from this description? What is their precise formulation? Also, is there anywhere I can read the details of this person's proposed solutions?


title: Is there a subtlety to the Lorentz transformations one needs to be aware of?

text: Playing around with the four acceleration $$\left(\gamma^4_u \frac{\vec a\cdot\vec u}{c^2}\vec u +\gamma^2_u\vec a,\, \gamma^4_u\frac{\vec a\cdot\vec u}{c}\right)$$ I found the time part for frame' moving with velocity $\vec v$ along the negative $x$ axis of the other frame, using the standard Lorentz transformation $$\gamma'^4_{u'}\frac{\vec a'\cdot\vec u'}{c^2} = \gamma_V\left(\gamma^4_u\frac{\vec a\cdot\vec u}{c^2} + \frac {V}{c^2}\left(\gamma^4_u \frac{\vec a\cdot\vec u}{c^2}\vec u+\gamma^2_u\vec a\right)\right)$$ Making the primed variables from the proper frame and noting $\vec u'= 0,\,\vec V = \vec u$ this reduces to $$\begin{align*}0 &= \gamma_V\left(\gamma^4_V\frac{ a_xV}{c^2} + \frac {V}{c^2}\left(\gamma^4_V \frac{a_xV^2}{c^2} +\gamma^2_Va_x\right)\right)\\\ &= \gamma_V\left(\gamma^4_V\frac{ a_xV}{c^2} + \gamma^4_V\frac{ a_xV}{c^2}\right)\end{align*}$$ Which isn't correct, so what subtlety about the use of the Lorentz transform in this case have I missed?


title: The Double Slit Experiment - delayed measurement

text: I'm not a physicist; I'm just curious about what would happen. According to this video "Explained ! The Double Slit Experiment" (at 2:50): > "Somebody decided to leave the detectors on but just not take any data. > [...] So if it was also going to a magnetic tape - there was no magnetic > tape loaded. [...] And what do you think happed? They got this. They got the > diffraction pattern." So the act of measuring (beeing concious of the data) destroys wave-form pattern? If so lets consider these cases:   1. What if I'd throw a dice after the experiment to decide if I should look at the data or to destroy it? (e.g. look at the data if the number on dice is even)   2. What if the information about measurement would need to travel longer period of time than the particle would need to hit the wall?  To above cases: Would it mean that information travelled instantly - faster than light or that "the particle can look into the future"?


title: Amount/flow rate of N2 needed to cool substrate

text: I'm trying to cool a substrate inside a vacuum chamber with liquid nitrogen. The substrate holder is a block of copper suspended from the top of the chamber via nylon screws (for thermal insulation). A copper tube runs from the LN2 tank through the flange, through one of the substrate holder's through- hole, bend back through the other substrate holder through-hole, and exits the chamber. Upon exit, the LN2 is simply dumped into the atmosphere. The substrate holder starts at 288.2K, LN2 ~77K. The LN2 tank's line pressure is around 5 psi, and ends in standard pressure upon exit. I'm trying to calculate whether with my current setup I just described, I can actually cool the substrate (ITO coated with aluminum, with a foil of indium between it and the substrate holder surface) down to 77-90K. My problems right now are setting up the diff eqs describing the heat exchange inside the substrate holder. The flow rate of N2 inside the pipes depend on whether it would be heated to gas...I'm not exactly sure how to incorporate this into the diff eqs. I would really appreciate it if someone can walk me through how to approach this or point me to a sample calculation. Also, what would be the best way to achieve this kind of cooling? We've used a reservoir approach (having a vat of LN2 on top of the substrate holder) before with success, but it takes up a lot of space. If my current setup turns out not sufficient, can I just keep increasing the initial line pressure (to >5psi) to achieve the desired cooling? Thanks, Al


title: How Represent Waves via Complex Numbers?

text: i try to finished my thesis, (Just have a problem with the wave mechanics) this is wave function: $$\Psi(\vec x, t)=A\exp{i(\phi+\vec k.\vec x-\omega t)}$$ In mathematics, the symbol $i$ is conventionally used to represent the square- root of minus one: i.e., $i^2=-1$ In addition, a general complex number is written: $$z=x+iy$$ $$z=r|\cos\theta + i\sin\theta|=r\exp{i\theta}$$ that which means: $$\Psi(\vec x, t)=A|\cos(\phi+\vec k.\vec x-\omega t) + i\sin(\phi+\vec k.\vec x-\omega t)|$$ ok i want to know that:   1. $$A\cos(\phi+\vec k.\vec x-\omega t)=?$$   2. $$A\sin(\phi+\vec k.\vec x-\omega t)=?$$ in the case of complex numbers is: 1\. $$r\cos\theta=x$$ 2\. $$r\sin\theta=y$$ and also i want to know that what is unit of $A$ ?


title: What Would be the Experimental Signature of Composite Leptons?

text: So far, the quarks and leptons appear to be fundamental particles. But they're complicated enough that there's always been some speculation that they might be composite. What experimental evidence would be needed to show that a lepton is composite?


title: Is it Possible to Determine Radiation Levels Using Satelites?

text: Given recent events in Japan, this got me wondering. Is it possible to determine radiation levels reliably not having Geiger counters near the possible radiation contaminated zone? According to wikipedia the Chernobyl disaster was first (other than Soviet Union naturally) detected by Swedish via radioactive particles found on clothes of nuclear plant workers. Surely more efficient ways should have been developed by now.


title: Where do the choice of basis in QFT come from?

text: Hi physics stack exchange. I am new and a mathematicians - so go easy on me. I have been trying to read up on QFT in the book Diagrammatica: The Path to Feynman Diagrams, and I have a question. The construction there seems very dependent on the choice of basis. Indeed, there is often an incomming basis |0>,|p>,|p'>,|pp'>,... and a similar outgoing basis. Also when considering spin (and anti) structures it fixes some basis elements related to the representation of $\mathbb{R}^4$ to "fatten up" the basis for the Hilbert space. My question is: **Where does this choice of basis come from?** In this possibly related question it seems that the choice of basis maybe related to Eigen-vectors for the Hamiltonian, but maybe I misunderstood that question - indeed I don't understand the question but the answer seems to suggest this to me. Now.. None of the two bases (plural basis?) seems to be Eigen-spaces for the Hamiltonian, but is it then true that the incoming basis is given by a trival Hamiltonian (by which I probably means something like purely kinetic energy), which corresponds to no interactions (and similar for the outgoing basis)? Does this even make sense? I can't make this compatible in my head with the fact that e.g. the Hamiltonian in the simplest $\sigma-\pi$-model is $2\sigma \pi^2$ does not seem trivial at time $\pm$infinity - indeed it seems time independent. I have probably misunderstood something simple that makes some of this gibberish, and I would appreciate any clarifications.


title: Uses of the 'Golden Ratio' in Physics

text: What are some physics applications of the golden ratio? $$\varphi~=~ \frac{1+\sqrt{5}}{2}~\approx~ 1.6180339887\ldots$$ Does it ever function specifically as a constant in any formulas or theorems? EDIT: Original title said _Golden Radio... facepalm._ I originally asked this question at math.stackexchange but the answers there were all too abstract or useless for me.


title: Is the charge of a current carrying wire real or hypothetical?

text: Realist753 Theory Relativistic Electrodynamics assert that a current carrying wire being neutral in a laboratory frame of reference appears electrostatically charged to an observer in relative motion to that wire (“Relativistic Wire”), like an ordinary pre-charged wire would appear at rest. The theory of this apparent charge of a Relativistic Wire is covered by most textbooks dealing with Relativistic Electrodynamics.Look here: {http://chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf} by Hans de Vries. Experimental evidence Experimentally such charge has indirectly been inferred from the electrostatic potential around a Relativistic Wire. My opinion however is that for a doubtless proof of such fundamental theory it would be justified to require more credible and immediate experimental evidence of the postulated nonzero charge of a “Relativistic Wire”. Proposed Experiment Missing evidence could preferentially be obtained by means of a sliding “galvanic” contact acting as a probe* to directly pick up the electrostatic potential of a “Relativistic Wire” and adequately store the collected charge as a measure of its potential. Subsequently, the sliding contact and the probe would have to be disconnected in motion, stopped and the conserved charge be measured. A nonzero collected charge could already be regarded as indisputable proof of a nonzero charge of the wire. Question: Does anybody know if the proposed experiment has ever been done? Your comments will be welcomed.   * To avoid disturbing homopolar induction in the vacuum field around the wire the probe should be magnetically isolated.


title: How many qubits are needed for useful computation?

text: Seeing the news about 14 entangled states today @ Innsbruck: I haven't found a clear guide online to how many qubits we are aiming for a first practical quantum computer, e.g. Factorization, Search or re- implementing large scale computing problems?   1. Given the relatively few algorithms we have, and the fact that algorithms don't necessarily have to map 1:1 with the size of the domain (i.e. be multi-step), can we make any reasonable guesses for the above use cases? The Wikipedia entry for Shor's algorithm seems to state "The input and output qubit registers need ... twice as many qubits as necessary ..." so we would need 1024 qubits for common encryption in use today e.g. AES. Is this a correct understanding? references: http://en.wikipedia.org/wiki/Shor%27s_algorithm http://en.wikipedia.org/wiki/Key_size Are more info on any quantum algorithms suitable for large scale computing problems yet? e.g. 50-100 qubits for 'useful' (1999) eigen* calculations http://prl.aps.org/abstract/PRL/v83/i24/p5162_1 \- only have access to the abstract Cheers


title: How does the curve ball drag air around it?

text: In cricket or baseball there is a type of ball called the curve ball. ![enter image description here](http://i.stack.imgur.com/HRcNA.jpg) This is the top spin of the ball.I read that due to spin the ball drags the air around it due to friction in the way shown above.Can you please explain why??


title: Pressure difference in water tanks at different heights

text: Suppose there are two tanks(airtight) fully filled with water.one is kept on top of a ten storey building and one on top of a twenty storeyed one.They are NOT interconnected.Will there be a pressure difference?


title: Numerical software to manipulate a light beam in its plane wave representation?

text: Any light field can be expressed as a sum of plane waves. Such an ensemble of plane waves is called the plane wave spectrum of the light field. The plane wave spectrum is the Fourier transform of the light field in the real space representation. Since, this is such a basic technique, I wonder whether there is a standard tool, preferably open-source, with a simple interface via Python, Matlab or similar, to do the following (numerically):   * Start with a light field in real space, say a monochromatic *-Gaussian beam.   * compute the Fourier transform   * apply some operation that changes the plane wave spectrum, say a boundary between two media   * compute the inverse Fourier transfrom   * produce some output, e.g. a plot Computationally, all it takes is a library to perform the FFT. I'm looking for a framework that would wrap this along with some phyiscal concepts.


title: Why does amount of protons define how matter is?

text: My question might sound convoluted but my mind is twisting right now so my apologies in advanced. Why is it that when I have one proton and one electron it is Hydrogen a clear flammable gas, and when I have say, twelve, it is carbon the driving force of life as we know it and then we end up with 239 and we have uranium a radioactive element. How does the amount of protons affect what matter will be? Why does the amount of these particle things magically make one thing air and another cyanide? If I have one pebble it is a pebble, if I have 13 its just more of the same pebbles. What makes protons different? Sorry this is so convoluted, any reply is appreciated Thanks!


title: who will win a race between man, horse and car of same power

text: Other day I got into a chat with my friend on work power and energy where he asked an intelligence related question the question was like this > if a race was conducted between a man a horse and a car of SAME POWER then > who will most probably win the race and to his question i answered that obviously man could win it because the definition of power states that > power is the fraction of work done in a given time and as per the definition of work it is described as the dot product of force and displacement and from newton's second law we get F=ma the displacement of all the three is same as their end point. so the product of mass and acceleration must be same for all and in this situation a normal man will have less weight than horse and car so it clearly states that acceleration must be of more magnitude for man. but to my surprise he said my answer is wrong and he did'nt explained how it was wrong am i really wrong? please guide me if i am wrong in which aspect.


title: When to use which representation for an electric field

text: In class we covered three types of possibilities to evaluate the electric field for static problems. Unfortunately, most physics textbooks cover these ways without addressing the question of applicability when they introduce these equations due to historical motivation. One possibility is Gauß's law: $$\int_{\partial V} \langle E, n \rangle dS = \int_V \frac{\rho}{\varepsilon_0} dx$$ This can only be used, when $E$ does by geometrical consideration not depend on the variables that the surface integral depends on(like in spherical symmetry, when it is not a function of the angles, but just of the radius), then it can be used to determine the electric field by a charged sphere. What we can get then, is an electric field on the surface of some volume that contains a particular charge. Then we have: $$ E(x) = \frac{1}{4 \pi \varepsilon_0} \int_{\mathbb{R}^3} \frac{\rho(x')(x-x')}{||x-x'||^3} dx'.$$ This is more general in the sense that it does not require any symmetry or reduction to charges inside some volume. And finally we have $$\Delta \phi(x) = -\frac{\rho(x)}{\varepsilon_0},$$ which is the most general way to think about electrostatic problems and contains (assuming that the solution fulfills all boundary conditions) all information. I hope my understanding was correct so far. In that case, my question is: How do I distinguish boundary value problems from problems where the first two equation apply? Many problems are like: Given a sphere with a particular charge distribution, calculate the field everywhere around! What does this mean, does this mean that I should think of this as a ball of charges assembling in vacuum and the material around being vacuum too? Cause if I assume that this is a metallic sphere or a sphere made out of some material which is different from the material (probably varcuum) around, then this would give me an interface which means that my first two equations don't apply anymore, as I would get boundary conditions. ( I am talking now about this in a strict theoretical sense, maybe they would give me the right result, but for the wrong reasons). Or do these two equations also apply, if the ball is an insulator?


title: Phase factors under rotations of strong and weak isospin

text: The strong isospin raising operator changes a $d$ quark into a $u$: $$ \tau_+ \big|d\big> = \big|u\big> $$ However, for antiquarks, there is an additional phase factor: $$ \tau_+ \big|\bar u\big> = - \left|\bar d\right> $$ This phase factor is the reason the $\pi^0$ wavefunction is proportional to $\big|u\bar u\big> \- \left|d\bar d\right> $. But I don't understand why it arises. The book that I have at hand is Wong's Nuclear Physics. Given particle creation operators $a^\dagger_{t,t_0}$ and antiparticle creation operators $b^\dagger_{t,t_0}$ for hadrons with strong isospin $t$ and projection $t_0$, Wong states that $$ b^\dagger_{t,t_0} = (-1)^{t-t_0}a_{t,-t_0} $$ because "operators $a^\dagger_{t,t_0}$ and $a_{t,-t_0}$ are not Hermitian conjugate of each other without the factor $(-1)^{t-t_0}$." There is supposedly a more detailed argument in Bohr & Mottleson, which I don't have access to at the moment.   1. Why is this phase factor required?   2. Do the same symmetry arguments apply to weak isospin partners? If so, I need to revise my opinion on this previous question.


title: What's the relevance of Efimov physics?

text: Is it something unexpected?Why universality in cold atomic gases is important?What researches are looking for?Can this be useful for topological quantum computers? Can we expect a whole myriad of these states? http://arxiv.org/abs/1012.2698 thanks


title: Effect of sun turning into a black hole on earth

text: Suppose the sun would turn into a black hole. Now neglecting the effect on the living beings on the earth. would the sun suck up the earth or the earth's revolution would not be affected?


title: Distance in cosmology

text: How can we calculate the change in distance over time between (say) two galaxies that they are at rest in respect to each other? In other words, how do we modify the "classical" equation: $$ \ddot{\mathbf{r}} = -G\frac{\mu}{|r|^2}\hat{\mathbf{r}} $$ to take into account expansion, G changes over time, etc?


title: Hanging chain in a planet's gravitational field

text: The curve for a chain hanging between two poles in a uniform gravitational field is known as the catenary. Is there known an expression for the curve of a hanging chain on a planet of mass $M$ which has a gravitational field of $M/r^2$ ? Let the rope have length $L$, uniform mass-density $\rho$ and negligible thickness. The poles are a distance $D$ apart, each a distance $R$ from the planets centre. I am interested in solutions where the gravitational field may be taken to point straight down as well as when it point towards the center of the planet.


title: How to construct a 2D conformal field on a mirrored annulus with a looping pattern?

text: I would like to construct a 2D conformal field on an annulus in which the inner and outer boundaries are like mirrors, and can be approximated by regular polygons (with the same number n of mirror edges, outer and inner). I would like this field to have the property that, when a ray locally obeying classical optics (i.e. Snell's law, on these mirrors) hits an edge of an approximating polygon for the inner mirror, it gets reflected and then bent or arc'ed by the field to have an appropriate (the same?) incident angle on the outer mirror, and so on, generating a looping "flower" pattern around the annulus. (Actually, 'flower' isn't quite accurate - the petals are weird...) I would like this flower pattern to be identically traced after completing any loop around the polygon (i.e. without any "shift"). I'm also assuming that the incident points on the mirrors are midpoints of edges, and that the midpoint of any outer mirror edge is intersected by a ray from the center of the annulus through a vertex of the inner mirror (i.e. that these mirrors are rotationally shifted 180/n degrees). I'd also like to be able to draw all this in TikZ! I'm just assuming (or guessing) that any field with this property (and a "reasonable" arc for the ray) is conformal. (But I'm also interested in "unreasonable" arcs - e.g. ones that might be SLEs along field contours.) I'm also guessing that there are families of conformal fields for this, e.g. producing thicker or thinner, more or less curvy, flower petals. I must also confess that I'm quite rusty on my math & physics, so any care taken in explaining formulae would be greatly appreciated. Thanks!


title: A quantum particle in a box (with a catch)

text: I am reading Shankar's Quantum Mechanics and I am looking at the case where there is one particle inside a box, where the potential is zero inside the wall and abruptly goes to infinity outside the wall. I like the technique of differential equations used and I am wondering if we suppose there is a particle in $n$-dimensional space, then we can still use the technique used in calculating wavefunction and energy in say a 2-dimensional and 3-dimensional box.


title: Gears and efficiency/speed

text: For Christmas me and my brother got an AR Drone, the propellers are on a large gear, which is rotated by a small gear that is connected to the motor. This means the small gear (and therefore the motor) must rotate many times in order to rotate the propeller just once. Surely swapping the gears, so that the propellers are on a small gear, which is rotated by the large gear that is connected to the motor, would mean the propeller would spin faster (given that the motor is operating at the same speed as before), or that the motor could operate at a slower speed (and therefore use less energy) and maintain the same speed of the propeller as before? Also what is the advantage of using any gears at all? Why not lose the gears, and get rid of the friction between the gears and between the gear and what holding them, and the added weight?


title: Why echos cannot be heard inside the room?

text: If I go camping and shout anywhere, in the forest , or on a cliff, I usually hear the echo of my voice. Why when I shout in my room I do not hear any echos?


title: Why, intuitively, must a solution in physics be unique?

text: When solving _Laplace's equation_ or _Poisson's equation_ say, we require that the solution must be unique, which can be shown.   1. In general, what is the physics behind seeking a unique solution?    2. Are there differential equations which, for some mathematical reasons, cannot have unique solutions and hence cannot be used to model any physical phenomena?


title: How Relative Is Relativity With Respect To Visual Effects?

text: This might seem naive, but here goes. Imagine Albert and Rick, of equal mass, accelerate together to a significant fraction of light-speed (call it v) relative to Earth, enough to clearly see the effects of light aberration when looking at the stars. They expend 2 units of energy to do this. The two are now in an inertial frame of reference. Can Albert now accelerate further so that his speed relative to Rick is v, expending 1 unit of energy? How can you be in an inertial frame of reference, and still witness light- aberration effects?


title: Why do heavier objects fall faster in air?

text: We all know that in an idealised world all objects accelerate at the same rate when dropped regardless of their mass. We also know that in reality (or more accurately, in air) a lead feather falls much faster than a duck's feather with exactly the same dimensions/structure etc. A loose explanation is that the increased mass of the lead feather somehow defeats the air resistance more effectively than the duck's feather. Is there a more formal mathematical explanation for why one falls faster than the other?


title: Mathematica package for supergravity and string theory

text: I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra computations. Also, I would like this package to be able to do wedge and hodge dual, and other computation relating to forms. Can anyone suggest a specific one? I looked for atlas2, but it seems I have to pay to use it without a trial version.


title: Is a "shift in the meaning" of Accuracy and Precision occurring?

text: _Accuracy_ and _precision_ are among the most fundamental concepts in experimental physics, and, I always believed, completely unambiguous. Recently I found that the Wikipedia article on Accuracy and Precision claims that a "shift in the meaning of these terms" is occurring. My first thought was that this must be a joke, a mistake or Wiki vandalism. However, the ISO 5725-1 ( _Accuracy (trueness and precision) of measurement methods and results_ ) standard referenced in the article indeed reads > 3.7   > accuracy > > [...] > > NOTE 3 **Accuracy refers to a combination of trueness and precision.** Notably, this seems to imply that **the concept of precision is a subset of the concept of accuracy** , which is plainly incompatible with the definitions found almost everywhere else that sharply _contrast_ precision and accuracy.    My questions are:   1. Is such a "shift in meaning" really occurring in the physics/measurement community at large?   2. If yes, what is the cause of this change of terminology?


title: For the $U(1)$ problem, is the Kugo and Ojima Goldstone quartet wrong?

text: On page 96 in "Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem", _Prog. Theor. Phys. Suppl._ 66 (1979) 1, KO state the following: > Finally we should comment on the current belief that the $U(1)$ problem was > resolved by instanton. It is not correct; namely:, the instanton by itself > cannot assure the unphysicalness of the $U(1)$ Goldstone boson $\chi$ which > is contained in $J^{\mu}_5 $ because of the chiral $U(1)$ Ward identity ($ 7 > \cdot 4$ ).No one has ever proved in the framework of "instanton physics" in > a satisfactory manner that the $\chi$ really contained in the gauge-variant > current $J^{\mu}_5$is not contained in the gauge-invariant one, $j^{\mu}_5$, > although this problem has been discussed by many authors. Are Kugo and Ojima correct? I thought 't Hooft proved that the instantons solved the $U(1)$ problem.


title: From Fermi-Dirac to Maxwell-Boltzmann statistics

text: I have a little question I can't seem to find the answer to. It is as follows: When does Fermi-Dirac statistics reduce to Maxwell-Boltzmann statistics?


title: Which model of computation can be viewed as being extended by the currently most relevant models of quantum computation?

text: Which model of quantum computation resembles most closely the attempts of implementation currently being made? And which non-quantum model of computation is the conceptually closest one to the above model??


title: Magnitude of a photon?

text: I encountered the following sentence in my textbook, which I don't quite understand, and after an unfruitful google search, I still can't figure out what they mean by **magnitude** in this context: > ..."split a photon into N components with magnitude ϵ"?


title: Inclined plane question

text: An object, mass $m$ is placed on an incline, angle $\theta$. System is at equilibrium. coefficients of static and kinetic frictions are $\mu_s$ and $\mu_k$ respectively. Then: 1) What is the Total contact force on the block by the surface?? 2) Which are necessarily true? a) $tan \theta$ is less than or equal to $\mu_s$ b) $f = \mu_s N$ c)$f= mgsin\theta$ My approach to 1) total contact force will be $mgcos \theta$ (exerted by the incline as a normal reaction) + $\mu_s mgcos \theta$ (exerted by the incline in the form of friction) which are at right angles, result will be the square root of their squares, giving $mg cos \theta \sqrt{1+ \mu_s^2}$. But the answer given is just mg!!! And the explanation is that total contact force = $mg cos \theta (= N) + mg sin \theta (= f)$ $\implies$ total force $= \sqrt{N^2+ f^2} = mg \sqrt{cos^2 \theta + sin^2 \theta }$ For 2) I think all are right, except, $tan \theta = \mu_s$ but answer says b) is false! Please help me!


title: Can a link between photons that don't exist at the same time provide communication with the past?

text: They have published something about a link between photons that don't exist at the same time. Does this means that it is possible to build a device that will receive messages from itself but these messages will be received earlier than they will be sent? Can someone operating this device can win the lottery? How would you describe in numbers the bandwidth of such device? Larger than infinite? Negative?


title: Entropy of Black Hole

text: What is the relation between the entropy of rotating and non rotating Black hole?   Which one's entropy is greater?


A follow-up to this question: > Is the Casimir effect also present between two event horizons?


title: Why is the force of Friction less than the force applied on the block in this situation?

text: This is a seemingly basic mechanics problem but I'm having a dilemma in understanding what happens. You start with two blocks, one on top of the other (the bottom block has a larger mass than the top block). There is friction between the blocks, so they stick together. These two blocks rest on a frictionless surface. If I apply a force F to the top block, what happens? Drawing the free body diagram, the force F I apply is counter acted by a frictional force f because of the friction between the two blocks. Additionally, this frictional force will be opposed by another frictional force on the bottom block that forces it in the direction I applied the force. Thus, we see that the blocks will move in the direction I have pushed. HOWEVER, I can't understand why the top block will move forward as well. The force I have applied should be negated by the frictional force, but this is not the case. Clearly, the block accelerates forward despite the friction. Why is this paradox created???


title: What is an intuitive explantion for the fact that the Maxwell-Boltzmann distribution of energies is independent of mass?

text: If you take the Maxwell-Boltzmann distribution of velocities (which depends on the mass) and substitute $v=\sqrt{\frac{2E}{m}}$ you get the distribution for the energies, which turns out to be independent of mass. What physical reality does this reflect? Why is the velocity distribution mass dependent, whereas the energy distribution is independent?


title: How does capacitors provide initial high voltage for a motor?

text: While observing the water pump in my house I could see a huge capacitor connected to it. My father told me that it is to provide a high voltage of 440 V during the start-up process. But, how does a capacitor do that? From, my high school knowledge I know that a capacitor allows AC current to flow through it. But, how does it increase the voltage at the beginning for the motor to start?


title: How well is the $\rho$ and $\omega$ coupling universality measured?

text: Is there any good recent experimental data that tests whether the $\rho$ coupling constant depends only on the isospin multiplet of the produced particle? EDIT: I got a downvote, so I should explain the motivation. In the 1960s, Sakurai's idea is that the $\rho$ is the gauge boson for the isospin flavor symmetry. This idea led people to study photon-omega mixing and photon-rho mixing (the idea was omega being the massive second photon for hypercharge), and these led to the idea of describing shadow-scattering of photons off large nuclei, through the photon-vector-hadron mixing. These phenomena are discussed at length by Kurt Gottfried in 1970, as cited and explained further in Feynman's 1972 book "Photon Hadron interactions". These ideas died away with QCD, when the $\rho$ could no longer be considered an elementary particle or an elementary string state. But they were revived somewhat in the 1980s, as people began to consider hidden local symmetry, where there is an infinite tower of gauge symmetries. Hidden gauge symmetry seems sort of silly and umotivated at first, but the proper motivation is within string theory, and AdS/QCD explains how this picture can emerge, the tower of gauge symmetries are a Kaluza-Klein tower in an extra dimension, and the local-hidden-symmetry picture can appear naturally from strings. This makes all this stuff interesting again, both theoretically and experimentally. So this means we should ask the question of what is the experimental data regarding the $\rho$ meson and its couplings again, does it look like a gauge boson for isospin? I don't know how experimentalists extract coupling constants, and this is generally difficult for hadrons, but somebody might have figured out how to do this by now, and given some data somewhere. I seem to recall that there are arguments in the literature that the coupling of the $\rho$ to the pions, nucleons, etc must be the same as a gauge boson for Isospin, from general principles. I think these arguments are completely bogus. I think the only general principle which accounts for something of this sort is the necessary gauging of flavor symmetries in string theories.


title: Pair production kinematics

text: In the process $A\rightarrow B+C$ If we know the energy and momentum four vectors of B and C, then how can we find the momentum three vector of A. The particular proces I have in mind is pair production $\gamma\rightarrow e^+ + e^-$ 4-vectors for electron is $(E_1,\vec{p_1})$ and for positron it is $(E_2,\vec{p_2})$. Then for the photon all I can deduce is $E = E_1+E_2$ (energy should be conserved) and $|\vec{p}| = |E|/c$ . Where $(E,\vec{p})$ is the four momentum of the photon. Can I also find the three components of the momentum of the photon, given that I have the components of the momenta of electrons and positrons (i.e I know $\vec{p_1}$ and $\vec{p_2}$)?


title: Help understanding this forced undamped oscillator

text: I have a forced oscillating system, with driving force as $f_0\cos\omega_0 t \cos \delta t$ giving the equation of motion: $$\ddot{x}(t) +\Gamma \dot{x}(t) +\omega_0^2x(t) = f_0\cos\omega_0 t \cos \delta t$$ Notation is standard, i.e $\Gamma$ is the damping coefficient, $\omega_0$ is the natural frequency of the undamped system, i.e $ \omega_0= \sqrt{k/m}$ It is given that $\delta \ll \omega_0$ and $\Gamma =0$ The question asks for the displacement $x$ for non-zero $\delta$ to leading order in $\delta/\omega_0$. The next statement is to express it in the for $\alpha(t)\cos\omega_0 t + \beta(t) \sin\omega_0 t $ The following hint is provided: $$\cos\omega_0 t \cos \delta t = \frac{1}{2} Re\Big(e^{-i(\omega+\delta)t}+e^{-i(\omega-\delta)t}\Big)$$ * * * I don't want the solution. I cannot understand how to approach the problem. I have the equation of motion $$\ddot{z}(t) - \omega^2 z(t) = \frac{f_0}{2} \Big(e^{-i(\omega+\delta)t}+e^{-i(\omega-\delta)t}\Big)$$ I make use of the approximation $\delta \ll \omega_0$ I conduct the expansion to get $$\ddot{z}(t) - \omega^2 z(t) = f_0 \Big(1-i t\omega_0 - t^2\omega_0^2 \Big(1+\Big(\frac{\delta}{\omega_0}\Big)^2\Big)\Big)$$ But this hasn't simplified it enough to allow me to solve it. The methods I now know of solving the original equation (Green's function and variation of parameters) have not been introduced, so the author must require us to work under certain approximations. Source is Howard Georgi's physics of waves. This is not homework.


title: Can a free particle absorb/emit photons?

text: As simple as in the title.. I would like to know also some mathematics about it!


title: Will current pass without any resistance?

text: I've learned that a resistor converts some electrical energy into heat energy while the current flows through it and thus causes a power loss, but what if there's not any resistor in a circuit. Will current still flow?


title: How is the Principle of Conservation of Momentum proven using the Momentum-Impulse Principle?

text: Consider two particles moving in the same direction on the same line, $A$ and $B$, with mass $m_A$ and $m_B$, respectively. They also have velocies $u_A$ and $u_B$. They collide. After the collision A and B have velocities $v_A$ and $v_B$. I want to prove the equation for the Principle of Conservation of Momentum: $m_Au_A+m_Bu_B=m_Av_A+m_Bv_B$. So I begin: Force is the rate of change of momentum, so $F=\dfrac{\Delta mv}{\Delta t}$, so $Ft=\Delta mv$. Since the impulse on a particle is its change in momentum, $I=\Delta mv=\Delta p$. So taking partice B: $I_B=\Delta p_B=m_Bv_B-m_Bu_B$. And now A: $I_A=\Delta p_A=m_Av_A-m_Au_A$. I feel as if I'm on the right track to proving the equation, but how can I go from here? I apologise if this seems like a homework question and doesn't belong here.


title: Which is more characteristic of an element absorption or emission spectrum?

text: Absorption and emission spectrum are used to reveal the identity of an element and even to find new elements. But, which of them is more characteristic? The mission spectrum would have more lines than the no. of lines missing in the absorption spectra simply because de-excitation can occur from any higher energy level but excitation always starts from the first energy level. So is absorption spectrum more characteristic than emission spectrum?


title: What part of the fan blade actually does the noise generation?

text: I'm trying to identify the sources of noise in spinning fan blades and what causes them. Is the noise only generated by the lead edge of the blade 'cutting through' air? and different parts of it (closer to hub vs away from it) have different instantaneous speeds causing noise at different frequencies?


title: Is projectile trajectory on Earth affected by the fact that it isn't a singular point?

text: So in high school physics, we were told that projectiles traveled in a parabola, but Google searches have said that it's more like an ellipse, since the Earth isn't flat. However, I was thinking that since most projectiles stay so close to Earth, you can't really assume that gravity acts only towards the center, since gravity dictates that all particles are attracted to each other, so the core isn't the only thing on earth pulling the object "down". Is this logic valid? High School: $$d = v_{0}t + \frac{1}{2}at^2$$


title: Current flows which way?

text: Current flows through a resistor (with no direction since it is not a vector/can flow from any potential)? I thinks it is with no direction since it is not a vector. Is that right?


title: How practical is fracture mechanics?

text: I have been reading fracture mechanics recently and have encountered many beautifully elegant theories. However, one thing keeps bothering me: How practical is fracture mechanics in the real world? I want to ask this question for several reasons:   1. Many formulations (e.g. stress intensity factor) is only applicable for very simple geometry. Most problem in reality involves 3D non-planar geometry, which analytical expression might not be available, and it is not clear how to approximate them numerically.   2. In my impression (which could be wrong) fracture mechanics theories are dealing with one crack at a time. However, in practice, each sample could contain millions of cracks. Treating them one by one is not tractable.   3. Knowledge of crack geometry (at least crack length) is necessary in most of the theories in fracture mechanics. However, for brittle material, the crack is often too tiny to be noticeable before failure, making it not practical to model crack geometry in simulations. These reasons are based on my limited knowledge. I don't mean to offend any researchers in the fracture mechanics field. I am just confused about how to put the theory into practice and hope it is not just a game of mathematics.


title: Why is there a breakdown in Kolmogorov scaling in turbulence?

text: Why is there a breakdown of Kolmogorov scaling in turbulence? What causes intermittency?


title: Why are the Higgs phase and the confinement phase identical in Yang-Mills-Higgs systems?

text: If we couple a Yang-Mills theory with a Higgs field and some quarks in the fundamental representation, we can have a Higgs phase and a confining phase. However, they are indistinguishable. The Wilson loops scale according to the perimeter law, not the area law in the confining phase because of hadronization. In the Higgs phase, there is no cluster decomposition for the Higgs field because distant points have to be connected by a Wilson line with exponential falloff as the length of the Wilson line. Why are both phases indistinguishable?


title: Why are baryons equivalent to Skyrmions?

text: Baryons in quantum chromodynamics can be described as a bound state of three quarks. But they can also be described as a topological soliton of the pion field. How can both descriptions be equivalent?


title: Steady isothermal flow of an ideal gas

text: So I have a steady isothermal flow of an ideal gas through a smooth duct (no frictional losses) and need to compute the mass flow rate (per unit area) as a function of pressures at any two different arbitrary points, say 1 and 2. I have the following momentum equation in differential form: \begin{equation} \rho vdv + dP = 0\end{equation} where $v$ is the gas the flow velocity and $P$ is static pressure. The mass flow rate per unit cross section $G$, can be calculated by integrating this equation between points 1 and 2. This is where it gets confusing. I do the integration by two ways: 1) Use the ideal gas equation $P = \rho RT$ right away and restructure the momentum equation: \begin{equation} vdv + RT\frac{dP}{P} = 0\end{equation}, integrate it between points 1 and 2 and arrive at: \begin{equation} v_1^2-v_2^2 + 2RTln\frac{P_1}{P_2} = 0 \end{equation} Since the flow is steady, I can write $G = \rho_1 v_1 = \rho_2 v_2$, again use the ideal gas law to write density in terms of gas pressure and finally arrive at the mass flow rate expression: \begin{equation} G^2 = \frac{2ln\frac{P_2}{P_1}}{RT(\frac{1}{P_1^2}-\frac{1}{P_2^2})} \end{equation} 2) In another way of integrating (which is mathematically correct), I start by multiplying the original momentum equation by $\rho$ to get \begin{equation} \rho^2 vdv + \frac{1}{RT}PdP = 0\end{equation} write $\rho^2v = G^2/v$, integrate between points 1 and 2 to arrive at \begin{equation} G^2ln\frac{v_2}{v_1} = \frac{P_1^2 - P_2^2}{2RT} \end{equation} Using the ideal gas law the velocity ratio can be written as the pressure ratio to finally arrive at the mass flow rate equation \begin{equation} G^2 = \frac{P_1^2 - P_2^2}{2RTln\frac{P_1}{P_2}} \end{equation} Both the expressions are dimensionaly sound and I know that the second expression is the correct one. My question is, whats wrong with first expression.


title: Is the third spin vector of a photon always suppressed?

text: I like to tell people interested in light polarization that the photon is a vector boson for which the third spin axis, the one in the direction of travel, is suppressed due to photons being massless and traveling at _c_. It's an argument that kind of makes sense for classical physics. However, mulling over quantum physics makes me a bit more cautious. In QED for example, a photon that travels over a sufficiently short distance can have non-zero amplitudes for both superluminal and subluminal velocities. But that leads to an interesting question: Does a photon with a non-zero amplitude for subluminal travel also have a non-zero amplitude for exhibiting a real and measurable $\pm$spin axis pointed along its direction of travel? That is, does such a photon include an amplitude to behave like a true three- axis vector boson? And if so, what kind of experiment might detect that amplitude? Also, what does all of this imply for a superluminal photon amplitude? Does that amplitude imply the existence of some sort of mirror-image vector boson version of the photon? What would that even mean? And finally: How does any of this relate to fully classical circularly polarized photons? While circularly polarized photons have same symmetry as particles with spin along the direction of travel, they behave like fully classical particles that can travel indefinite distances. But by the same arguments I just made, that means they cannot possibly be true vector boson states, which would only exist as small amplitudes over very short distances! Are circularly polarized photons perhaps more accurately understood as some kind of spin-cancelling superposition of the subluminal and superluminal true vector boson states?


title: What's the heuristic reasoning for Chiral Symmetry breaking

text: In Peskin and Schroeder (page 669), and other references, the heuristic reasoning for why one would expect chiral symmetry breaking at low energies is that quark masses are small and hence it's not very energetically costly to create quark-antiquark pairs from the vacuum. These are then generated with zero net linear and angular momentum which forces the pair to have a net chirality and this breaks the chiral symmetry. Where does the requirement of low energy appear in this line of reasoning?


title: Why water in the sink follow a curved path?

text: When you fill the sink with water and then allow the water to be drained, the water forms a vortex.. And then it starts to follow a curved path downwards by effects of gravity.. Why this phenomena occurs while rain follows a straight line path (in perfect conditions) towards the ground.. I would guess that when the water molecules closest to the drain hole go through first, they create a temporary void causing other water molecules nearby (above and on the sides) to rush in and take their place each having an equal chance to fill that void (since pressure is equal in all directions at a certain point in liquids). So I was thinking more of cone like figure with water collapsing in, equally from each direction. Why the circular path??


title: Light Front Dynamics and Infinite Momentum Frame

text: What is the the relationship between Light Front Dynamics (One of the forms of dynamics pioneered by Dirac), and the infinite momentum frame? In the literature, it is claimed that the two are very different and should not be confused. This is also reiterated in L. Susskind's string theory course (available on YouTube).


title: Runge-Lenz vector and Keplerian Orbits

text: Is the loss of _closed_ Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?


title: Why do CD's shatter in a microwave?

text: Why have I heard that eggs and CD's and DVD's explode when microwaved?


title: How to teach myself physics needed at undergraduate electrical engineer level?

text: I want to learn electrical engineering on my own, specifically because I'm interested in loudspeaker design, more specifically how to design active dipole loudspeakers using DSP crossovers. I have found resources to teach myself the necessary mathematics, however I don't have a solid sense of what undergrad level physics I will need, much less how to learn it on my own. Any pointers or suggestions are greatly appreciated.


title: Modeling a list with a tunable degree of disorder/shuffling

text: Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance:   * Adding a little bit of disorder would permute a few neighboring numbers   * Adding more disorder would permute several numbers, many of them not neighbors   * Adding maximal disorder would permute all the numbers Ideally I would like to use an algorithm that has a sound statistical/information theoretic foundation. I am not sure about how to search for this. I have tried Googling things like:   * Tunable degree of shuffling   * Generating random lists of numbers with a given entropy / Kullback-Leibler distance   * Generating a list with a given level of presortedness Note that the solution is not just shuffling a given percentage of the numbers. When disorder is small, the shuffling should occur among numbers that are close. The process I am trying to model is akin to "shaking." Imagine I have a number of casino tokens ordered one after the other on top of a one dimensional table. Then I shake the table along its dimension and see in what order the tokens landed. The tunable degree of disorder I want to model corresponds to how much I shake the table. Any ideas? Many thanks!


title: Does "Crack The Whip" actually speed you up?

text: "Crack The Whip" is a game played on ice skating rinks where several individuals line up all facing the opposite end of the rink, and skate forward. When the group reaches the opposite end of the rink, the "point man" or the person on one end of the line stops, and everyone else pivots around him. Supposedly, the person on the opposite end swings around, and rockets forward at much greater speeds. However, I don't believe this is possible. Because the question remains, where would the extra speed come from? I was told that the momentum of all the people is transferred into the one person on the end. While there is a ponderous amount of outward force on the chain of people, I don't think it's possible to actually gain speed. And after watching my friends do it several times, I concluded the person on the end didn't seem to go any faster. Was it simply that the process was inefficient? Or is the theory even possible?


title: Different kinds of the same isotope

text: I apologize if this is an obvious question, but I can't find the answer anywhere. In this page: http://ie.lbl.gov/education/parent/U_iso.htm are listed the isotopes of Uranium. Some of them, for example U238 are listed many times, with "m1" or "m2" attached to the mass number. What does this mean?


title: Phonon mode in canonical and grand canonical ensemble

text: I derived the averaged energy for phonon mode with frequency $\omega$ in canonical ensemble and in grand canonical ensemble. Averaged energy derived in canonical ensemble is $E_c=\frac{1}{2}\hbar\omega+\frac{\hbar\omega}{e^{\hbar\omega\beta}-1}$. Averaged energy derived in grand canonical ensemble is $E_g=\sum_{n=0}^{\infty}\frac{\hbar\omega(n+1/2)}{e^{\hbar\omega\beta(n+1/2)-1}}$. I believe they should be the same, since observable quantity should be independent of the ensemble we choose. But how to show they are the same?? (In the following, I provide my derivation of the averaged energy. The partition function in canonical ensemble is $Z_c=\sum_{n=0}^{\infty}e^{-\hbar\omega\beta(n+1/2)}=\frac{e^{-\hbar\beta\omega/2}}{1-e^{\hbar\omega\beta}}$, so $E_c=-\frac{\partial}{\partial\beta}\ln Z_c=\frac{1}{2}\hbar\omega+\frac{\hbar\omega}{e^{\hbar\omega\beta}-1}$. The partition function in grand canonical ensemble is $Z_g=\Pi_{n=0}^{\infty}\sum_{a=0}^{\infty}e^{-\beta\omega\hbar(n+1/2)a}=\Pi_{n=0}^{\infty}\frac{1}{1-e^{-\hbar\omega\beta(n+1/2)}}$, so $E_g=-\frac{\partial}{\partial\beta}\ln Z_g=\sum_{n=0}^{\infty}\frac{\hbar\omega(n+1/2)}{e^{\hbar\omega\beta(n+1/2)-1}}$. Where a is the occupation number for each energy level.) Thank you in advance.


title: What are the coefficients of the Geiger-Nutall law dependent on?

text: The Geiger-Nutall law for alpha-particles predicts a linear relationship between the logarithm of the decay rate and the energy of the particle, and I've observed that in ln(decay rate) / (energy) plots the lines appear to have different (though similar) slopes for each isotope, therefore implying that the coefficients of the linear relation are different as well. On which characteristics of the isotopes do these coefficients depend?


title: How do you find (initial) velocity using conservation of energy?

text: Without mass; only time, distance, and height is given. For example: For this lab, the reference level was 100cm above ground therefore the height of the object was 10cm. I determined time and distance and I also found velocity using 2D kinematics. Now, however, I am required to find velocity using conservation of energy.


title: Is there a physical reason for level repulsion and avoided crossings?

text: Suppose we have a Hamiltonian that depends on various real parameters. When tuning the values of these parameters, the energy eigenvalues will often avoid crossing each other. Why? Is there a physically intuitive justification for level repulsion and avoided crossings? It would be nice to see a general argument.


title: Differentiation of the action functional

text: In the QFT book by Itzykson and Zuber, the variation of the action functional $I=\int_{t_1}^{t_2}dtL$ is written as: $$\delta I=\int_{t_1}^{t_2}dt\frac{\delta I}{\delta q(t)}\delta q(t)$$ How is this justified? In particular, why is there an integration sign?


title: Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions

text: I am using the standard symbols of $V_\mu$ for the gauge field, $\lambda$ for its fermionic superpartner and $F$ and $D$ be scalar fields which make the whole thing a $\cal{N}=2$ vector/gauge superfield in $2+1$ dimensions. Then the non-Abelian super-Chern-Simon's lagrangian density would be, $$Tr[\epsilon^{\mu \nu \rho}(V_\mu \partial_\nu V_\rho - \frac{2}{3}V_\mu V_\nu V_\rho) +i\bar{\lambda_a}\lambda_a - 2FD]$$ Clearly this is classically scale invariant.   * I would like to know of the argument as to why this is also quantum theoretically conformal (..may be there is some obvious symmetry argument which I am missing..)   * Also is it true or obvious that if the above is perturbed by a $\lambda Tr[\Phi ^4]$ potential then this might flow to a fixed point which is $\cal{N}=3$ ? And then will it still be superconformal ?  I would like to know of a way of understanding this phenomenon of supersymmetry enhancement by renormalization flow. If someone could point me to some beginner friendly expository reference regarding this.


title: Is it possible to create a hologram using X-Rays?

text: Is it possible to create a hologram using X-Rays (or other penetrating EM- waves)?


title: reflection, refraction and diffraction occur in radio waves, which one occurs the most?

text: One of the things about Radio waves is that they undergo different behaviors such as reflection, refraction and diffraction when in contact with obstacles such as walls, buildings etc. what i want to understand is that, which of the behaviors would occur the most in let's say an environment filled with trees and the slope is rough?


title: Finding Directions using moon

text: Is it possible to find directions just by looking at moon(not full bright)? I was curious to use the clue that if moon is half lit then the direction in which it is lit will it be east?


title: The acceleration of a particle in uniform electro-magnetic field

text: A particle of charge $q$ and mass $m_0$ is subject to the action of a uniform electro-magnetic field $\vec{E}=(0,E,0), \vec{B}=(0,0,B)$ and at $t = 0$ moves with velocity $\vec{v}=(v_1,v_2,v_3)$. What is the acceleration at $t = 0$ if $v_1 = v_3 = 0$?


title: Reference for solid state particle detector

text: I'm looking for a good introductory text on solid state devices for particle detection.   Thanks a lot.


title: Function of electric water pump

text: What is the function of electric water pump, i.e does it push or pull water or both?


title: Does a Weak Energy Condition Violation Typically Lead to Causality Violation?

text: In the answer to this question: ergosphere treadmills Lubos Motl suggested a straightforward argument, based on the special theory of relativity, to argue that light passing through a strong gravitational region which reaches infinity cannot reach infinity faster than a parallel light ray which does not pass through the strong gravitational region. The argument is just the standard special relativistic one, that if you can go faster than light, you can build a time-machine. To do this, you just have to boost the configuration that allows you to go faster than light, and traverse it in one direction, then boost it in the other direction, and go back, and you have a closed timelike curve. In the condition of the question, where the strong gravitational region is localized, you can do this using pre-boosted versions of the solution. Preboost two far away copies of the solution in opposite direction, one boosted to go very fast from point B to point A (at infinity) and the other boosted to go from point A to point B. Then if you traverse a path from A to B, crossing through the first boosted solution, then cross the second on the way back, you can make a CTC. I was skeptical of this argument, because the argument I gave required the Weak energy condition, not a no CTC condition. The argument from null energy just says that a lightfront focuses only, it doesn't defocus, the area doesn't ever spread out. Any violation of weak energy can be used to spread out a light front a little bit, and this corresponds to the geodesics passing through the violating point going a little bit faster than light, relative to the parallel geodesics nearby. So if both arguments are correct (and although I was skeptical of Lubos's argument at first, I now believe it is correct), this means that a generic violation of the weak energy condition which is not hidden behind a horizon could be turned into a time machine. Is this true? Question: Can you generically turn a naked violation of weak energy condition into a closed timelike curve? A perhaps more easily answerable version: If you have an asymptotically flat solution of GR where there is a special light ray going from point A to point B which altogether outruns the asymptotic neighbors, can you use this to build a time machine, using boosted versions of the solution?


title: Does gravitational differences affect the distance light travels? (a thought experiment)

text: My question is: How is light passing through different gravitational densities affected? The value of "c" is constant in a vacuum. I'm curious about if various time frames have any effect. This is the thought experiment that occurs to me. Suppose we are doing a test in two different regions of the universe. In the first region, we have an observer in a place in between two galaxies. This is a region that should have the least amount of gravitational influence, being many thousands or millions of light years between centers of mass. The second region is a place of high mass, thus high gravitational density. Suppose, for the sake of argument, that our second observer is in the middle of a Sol-sized star. Additionally, this star is transparent so we can shine light through it and it can come out the other side. Also, our observer is sufficiently protected so as not to be cooked and turned into heavier elements via nucleosynthesis. The passage of time in each region will be different, where the observer inside the star will experience time moving slower relative to the observer in between the galaxies. Higher gravity, slower time passage. To setup the model of the thought experiment: We would measure the distance of a laser beamed between points A and B, where it passes through the exact center of the two spatial regions previously described. The distance between points A and B is exactly one light second, or 299,792,458 meters. Visually, it would look something like this:               A -------> CENTER -------> B      In the low-gravity region, it is expected that a laser pulse fired from point A will arrive at point B in exactly one light second, as expected. In the high-gravity region, will a laser pulse passing through the center of the star arrive at point B in exactly one light second, or will it be delayed by passing through a region of space that has high gravity? As I am thinking through this scenario, it occurs to me that there are at least a few ways of thinking about this in terms of perspective. In the low-gravity location, I place points A and B in the same gravity as the center. However, in the high-gravity location A and B can exist in the same gravity as the center, or A and B might be points outside of the gravity region of the star's center. There are also questions about where the passage of the laser is being observed from. In the low-gravity location, I put the observer in the same low gravitational field. However, in the high-gravity context the observer could be within the same high-gravity environment or could be observer the experiment from the low-gravity perspective. The high-gravity observer would see the experiment from the context of their time frame and might get different results than the observer from outside in the low-gravity time frame. I am unsure how to reconcile these scenarios.


title: Movement of a ball on a curved ramp

text: > **Possible Duplicate:**   >  What is a natural movement of a ball on a upward curve (the two arrow lines > pointing upward) given no external force? http://i47.tinypic.com/mt55s7.jpg -See for image You drop a ball on this vertical parabola with point A as starting point and point B as ending point. What is the expected natural movement of the ball that is set into motion with no external force assuming no friction? Would it go all the way from point A to point B or halfway to point B and come to rest at the middle of the curve? I am also trying to find some evidence or literature from some text to confirm of such expected motion.. however most of the examples I see are more related to an object falling in a downward parabola or other examples on a downward projectile.


title: Does the wave function/density state actually exist?

text: I have been reading with interest the debates here on whether the wave function/density state actually collapses or not, or whether it is subjective Bayesian or objective with actual complex numbered values for each component. I have been struck, though, by the implicit assumption made by all camps that something like the wave function/density state actually exists, whether subjective or objective. What if it does not? That would render all of these debates moot. The wf/ds is a highly abstract theoretical inference of what is measured experimentally. All one measures are correlations between definite measured outcomes. Pragmatically, it has been found such correlations can pretty much only be calculated accurately within the Dirac/von Neumann two stage framework where one first postulates some abstract wf/ds evolving unitarily alternating with a collapse during measurement to the eigenspaces of some 'measured observable' according to the Born rule, whatever that really means. This makes no ontological assumptions per se; it is just what anyone needs to go through to calculate the measured correlations. Many worlds people argue wf/ds is objective with no collapse and all the branches co-exist. Copenhagenists argue for collapse. But what if the wf/ds doesn't exist? Then they are both wrong and missing the point. Other than the fact the only time wf/ds shows up is in abstract symbolic calculations, why its existence be assumed? Here, the situation differs from classical probability distributions. The probabilities are still linear for the density state, but not the wave function, but negative probabilities appear and that makes all the difference. In classical Bayesian updating, there is some leeway in when the updating happens because the different updates evolve independently and the original distribution always evolves as a nonnegative weighted sum of the individual independent contributions. In the quantum density state case, destructive interference due to oscillations between positive and negative 'probabilities' exist and the different outcomes can no longer be said to be in any way independent. Decoherence does not really explain it away because the suppression of interference is not exact, takes time, and is potentially reversible in principle. What if the density state does not exist?


title: Fuel Tank Question

text: Could some one please help me with this question as my physics knowledge does not extend this far. I have a large fuel tank with a capacity of 21000L. The tank currently is holding 2000L of fuel. On one end of the tank there are two four inch pipes where the fuel comes in at about 1000L a minute for each pipe. On the other end is a two inch pipe for breathing. Is the two inch pipe enough for the amount of fuel coming in? The only other numbers I have is the density of the fuel which is 0.7335. Thanks in advance for any help.


title: Finding out the minimum deviation angle

text: ![enter image description here](http://i.stack.imgur.com/nsFgB.png) Let a light incident on a prisom at right angle. I want to determine the minimum deviation angle. I know a relation $$ \frac{\cos i_1}{\cos r_1} = \frac{\sin i_1}{\sin r_1}$$ and minimum angle of deviation $$\delta_m = i_1 +i_2 -A$$ It can be seen that, $i_1$ is given but how to get $i_2$ and A. A is the prism angle. and $i_1 =90 $ and $i_2 $ is the angle of the outgoing ray.


title: Could the speed of light change outside our solar system

text: Theory: The speed of light changes when it enters or exits the solar system due to a difference in medium (dark matter possibly). Potential problem 1: refraction If there was a speed change at the edge of the solar system, refraction would occur. This would manifest in ways similar to the sunset effect. Solution: the sunset refraction occurs because the angle against the edge of the atmosphere is extreme. No effect is noticed at high noon. Earth's proximity to the edge of the solar system, in contrast, makes it's angle nearly perpendicular in all directions. Wouldn't this negate any sunset effect? Sub-solution: My research on refraction seems to indicate that what I'll call the "distinction level" of the edge of the mediums has an effect on the level of refraction. So that, if the edge were not solid, but rather tapered, the refraction is reduced. SO, what would be effect on light entering our solar system if the light were severely slowed--let's say by a factor of 1,000,000 times, to what it is now. What, if any, refractive effects would be observed? How much would these effects change if the tapering of the edge were severe?--Could any refractive effect be overcome by tapering? Another question, what would be the effect of the light coming from Alpha Centauri if it's system had a similar medium transition at it's edge? How would it be noticable? This picture illustrates my thoughts: ![refraction](http://i.stack.imgur.com/FSZzo.jpg)


title: Sign error in calculating the electric field of point charge

text: I have to determine the electric field of a point charge, I get a true result except for a sign. Here is my passages. $$\nabla \cdot e = \frac{\rho}{\epsilon}$$ $$e = - \nabla u$$ $$\nabla^2 u = - \frac{\rho}{\epsilon}$$ $$\frac{1}{r^2}\ \frac{\partial}{\partial r}\ \lgroup r^2 \frac{\partial u}{\partial r}\ \rgroup = -\frac{q}{\epsilon}\ \delta(r)$$ $$r^2 \frac{\partial u}{\partial r}\ = 0 \Rightarrow u(r) = \frac{f(r)}{r} \Rightarrow \frac{\partial u}{\partial r} = \frac{f'(r)}{r}-\frac{f(r)}{r^2}$$ $$ \frac{\partial}{\partial r}\ \left( r^2 \frac{\partial u}{\partial r}\ \right) = \frac{\partial}{\partial r}\ \left( f'(r)r - f(r) \right( = rf''(r) = 0 \Rightarrow f(r) = Ar + B$$ $$u(r) = A + \frac{B}{r}$$ Now I set $A = 0$ to find $B$. $$ \int _V \nabla \cdot \nabla u \,\,\, dV = \int _{\partial V} \nabla u\,\, i_n dS = \int _{\partial V} - \frac{B}{r^2} \,\, dS = - \frac{B}{r^2} 4\pi r^2 = - \frac{q}{\epsilon}$$ $$B = \frac{q}{4 \pi \epsilon} \Rightarrow u(r) = \frac{q}{4 \pi \epsilon r} \Rightarrow e(r) = - \frac{q}{4 \pi \epsilon r^2} $$ How is possible that the module of the electric field is negative? **Answer:** Thanks to Ruslan I get the answer. In Spherical coordinates, if we consider only $r$ $$ \nabla u = \partial _r u(r) \hat{r}$$ See also http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates


title: what are the practical use of LC oscillation?

text: I get the energy transfer between capacitor and an inductor in a LC circuit but I am not sure what are the practical application of it.? Can someone pls help.?


title: Quick question on astronomical units

text: I'm trying to solve for $\frac{M*}{M_0}$ and $p''$ using these two equations: Here is the lecturer's working, I worked it out several times and I got a different answer! ![enter image description here](http://i.stack.imgur.com/UAZxI.png) Surely when you use Kepler's third law, everything is in astronomical units (solar masses, yrs, arc seconds). So on the LHS of equation 3, it should be $\frac{M*}{M_0}$ instead, right? Substituting into equation 3, I get: $$3.71 + 10\log\left[\frac{1}{2T^2}\left(\frac{\theta}{p''}\right)^3\right] + 5 \log(p'') = 0 $$ $$p'' = 0.343$$ I'm not sure how the lecturer got a value of $0.086$?


title: Why does the quantum eraser seem to violate energy and momentum conservation?

text: In the literature of the quantum eraser experiment it is argued that the change in statistics of the system from non-interference to interference is due to the erasing of "distinguishing information". The preparation of the experiment almost always introduces and then erases this information via a pair of unitary actions on the system. In the specific case that the interference effect is a second order effect of single photon interference, by destroying/creating the interference one is causing a physical disturbance to the system in that it changes the measurable statistics of the system, it destroys/creates the interference pattern that is collected at a single detector/screen. If it is distinguishing information that causes this physical change, if this physical change happens in the absence of a physical cause, is it not the case that this is a violation of the law of conservation of energy? There is no "driving force". It might only be the configuration of the statistics of the system that changes (from interference to non-interference or vica versa), but certainly this is a physical change that is measurable, so it should require energy and momentum to "push" the statistics in the right direction(away from or towards constructive interference). Distinguishing information does not provide this driving force. And I know the generalized set of rules as to why quantum mechanics is suppose to be energy and momentum conserving, it has to do with the invariance of H under dislacements. This does not explain the specific case of quantum erasure which seemingly defies conservation.


title: Does the number of left handed chiral quark superfields always equal half the number of quark flavours?

text: In Weinberg's "The Quantum Theory of Fields Vol III" page 267 we're told that $n_f = 2N_f$. Where $n_f$ are the number of flavours and $N_f$ is the number of left chiral quark superfields (or the number of corresponding left chiral anti-quark superfields). This implies that the number of left chiral quark superfields is half the number of quark flavours. I've become a little reliant on the above relation to explain why beta functions are sometimes written differently for the same theory. For example I use it to explain the equivelance between equation \begin{align*} b_0 = 3N_C - N_f \end{align*} in Notes on Seibergology page 117 and equation \begin{align*} b_0 = 3N_C - (1/2)N_f \end{align*} in Supersymmetry and Beyond page 3 (where in the latter $C_2 (G)$ has been substituted for $N_C$). Both these equations are supposed to describe $N=1$, $SU(N_C)$ SQCD beta functions but they look different. The reason for this, I decided, was that in the first equation we're using $N_f$ as the number of left chiral quark superfields whilst in the latter equation $N_f$ corresponds to $n_f$ in the first paragraph of this question. In other words $N_f$ in the second equation actually means the number of flavours. Substituting $n_f$ in place of $N_f$ in the second equation then using $n_f = 2N_f$ shows that these two equations are actually the same. This seemed to tie things up. However, Duality in Supersymmetric Yang-Mills Theory page 17 has the equation \begin{align*} b_0 = 3N_C - N_f \end{align*} where it explains on page 15 that $Nf$ is the number of flavours of quarks (we should substitute $N_f$ for $n_f$ using the notation established in the first paragraph of this question). It also explains on this page that we're indeed working with $N=1$, $SU(N_C)$ SQCD. So this seems to mess things up. Has the last paper just forgotten to divide by two and explained $N_f$ in an incorrect manner or am I missing something fundamental? I realise it's most likely the latter.


title: Additional boundary conditions for inclined flow?

text: I am solving an inclined flow problem, and am stuck. The problem is to find the volumetric flow rate of inclined flow in a square channel. Once I have the velocity profile, I can just integrate over that to get the flow rate. Letting the x-axis be along the direction of flow, I start with Navier-Stokes: $$\rho v_x \frac{\partial v_x}{\partial x} + \rho v_y \frac{\partial v_x}{\partial y} = \rho g \sin \theta + \mu \left( \frac{\partial^2 v_x}{\partial x^2} + \frac{\partial^2 v_x}{\partial y^2} \right)$$ $$\rho v_x \frac{\partial v_y}{\partial x} + \rho v_y \frac{\partial v_y}{\partial y} = \rho g \cos \theta + \mu \left( \frac{\partial^2 v_y}{\partial x^2} + \frac{\partial^2 v_y}{\partial y^2} \right)$$ No pressure terms since it's a free fluid. I found in a textbook the solution for inclined plane flow (but my problem is inclined flow in a square channel). In that solution, $\frac{\partial v_x}{\partial x}$ and $v_y$ are assumed to be 0, which gives $$-\frac{\rho}{\mu} g \sin \theta = \mu\frac{\partial^2 v_x}{\partial y^2}$$ which is easy enough to solve with the boundary conditions $v_x\big|_{y = 0} = 0$ and $\frac{\partial v_x}{\partial y}\big|_{y=L} = 0$. However, I don't know why they just assume $\frac{\partial v_x}{\partial x}$ and $v_y$ are 0; where does that come from? The fluid is flowing under the influence of gravity so I would think $v_x$ is increasing along x (imagine if you roll a ball down an inclined plane), and I would also think a free flow would decrease in height (L) as it travels. I mean, if you continuously dump water at the top of the incline, you're going to have a thicker water "height" at the top I would think... And even if I accept that those assumptions are true, I don't know how to extend the problem from a plane to a square channel. There's no z-flow anyway, so I don't need any $v_z \big|_{z=0}=0$ or $\big|_{z=W}=0$ boundary conditions anyway. So the solution would be the same...


title: Understanding Normal Force Change

text: _I know this has been asked around, my question is a bit more specialized towards my personal problem._ If I have an object the magnitude of the weight is usually equal to the normal force, right? I could be mistaken but from what I have read the normal force is the force the object is feeling opposite to the $(mass*gravity)$. If that is the case, and I put my hand on the object does my Force get added to the object's weight and thus the normal force of that object increases? Therefore if I keep adding hands to the object will the normal force keep compensating? Also is the normal force the negative charged electrons repelling each other (electromagnetism)? ![enter image description here](http://i.stack.imgur.com/sPXjk.jpg)


title: Spectroscopy: clarification about doppler shift

text: I've just begun to study spectroscopy, and I need a clarification about the Doppler Effect. Considering this graph: ![enter image description here](http://i.stack.imgur.com/h8s8B.png) could you explain me how I can see the doppler shift related to the deeper peak and how I can calculate it? I'm confused because I haven't a course of Spectroscopy and this aspect was treated very very quickly in another course... is the doppler shift the inverse of the FWHM of the peak?


title: How far into space does one have to travel to see the entire face of earth?

text: Virgin Galactic will take passengers aboard SpaceShipTwo as high as 65 miles above the surface of the earth. But from this altitude, passengers will only be able to see a certain segment of the curvature of the earth through windows as large as 17 inches in diameter. How much further into space would SpaceShipTwo have to travel to give passengers a view of the entire sphere of earth through one of these windows?


title: Why is $r'/r^2 = -1/r$?

text: If $r=r(t)$, why is $\frac{r'(t)}{(r(t))^2}$ = $\frac{1}{r(t)}$ where $'$ denotes the derivative? I saw it in a lecture. Can you please explain?


title: iPhone compass not being affected by current

text: As you probably know, electrical current and magnetic fields are close friends. In an iPhone there is a compass, however there are also lots of cables and in all of them, or at least in most of them passes a current. How come the current doesn't drive the compass away (and far) from the real north?


title: Alternative ways to take particle tracks photographs in a cloud chamber

text: I know that the most common type of particle tracks photography is in photographic plates, but i'm using a cloud chamber and I would like to know if there are alternative ways to take photographs of the particle tracks in a cloud chamber.


title: Will the black hole evaporate in finite time from external observer's perspective?

text: There is the problem that is bothering me with the black hole evaporation because of Hawking radiation. According to Hawking theory the black hole will evaporate in finite time because of quantum effects randomly producing particle-antiparticle pairs on the opposite sites of horizon. However, the gravity causes the time dilatation, which goes to infinity on the horizon itself, so the arbitrarily small amount of time from horizon's perspective is going to be infinitely long from external observer's perspective? So, from which perspective is the time the black hole will evaporate calculated? If it is calculated from horizon's perspective, it would mean, the black hole will never evaporate from the external observer's perspective?


title: Is the equivalence principle strictly fulfilled by general relativity?

text: The equivalence principle states _The outcome of any local experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime._ Any real local experiment needs some finite space, since nobody is a point particle himself. In principle I will always feel some deviation. Since in (pseudo-)Riemannian geometry I can only change to flat coordnates in a single point $p$ of the spacetime manifold (and not in a finite neighborhood), is the deduction right, that the equivalence princpil is only fulfilled by general relativity in an approximative sense?


title: Is it possible to overload a lightning rod?

text: A couple of weeks ago we had a big storm roll through the Chicago area. I watched as the city's skyscrapers were struck multiple times by lightning throughout the night and told my coworker about it the next morning. That got us both thinking, is there a maximum load that a lightning rod/lightning dissipation system can handle? Is it possible to overload or burn out a rod on a building like the Sears Tower? How massive/long-lasting of a lightning strike would you need for that to happen? (This is also posted on the Earth Sciences SE where someone suggested I post it here)


title: Why do almost all nuclear reactions release energy?

text: I'm just wondering why **almost all nuclear reactions release energy** , in a typical way, the mass defect is transformed into energy ? Is there a nuclear reaction that gains mass (resp. energy)? or most nuclear reactions always produces energy ? Your answer would be more helpful if you provide examples. Thanks.


title: In layman's terms, what is a quantum fluctuation?

text: What causes it and how does it occur? If you do post some mathematics, please explain what each term means too please.


title: Is (0,0,0) an undefined vector?

text: I'm not sure what to make of the direction of a vector with components (0,0,0). Is it an undefined vector?


title: Wolff vs Swendsen Wang Algorithm

text: Following the orginal paper of Swendsen Wang, their dynamical critical exponent $z$ is about $z=0.35$, whereas the Wolff Algorithm seems to have $z=1.19$. When I calculate the Correlation time though, I get another result but I am not sure if it is correct. ![Correlation Time](http://i.stack.imgur.com/1ZXFx.png) My Question: 1) What are the correct dynamical exponents and where can I get them 2) lets assume the exponents I found are correct, why is the wolff algorithm considered to be better if the exponent is much higher


title: Is 4-velocity normalized to -1 even for non-geodesic timelike curves?

text: In Hartle's General Relativity book ("Gravity"), one of the problems (chapter 8 problem 6) is to prove that $g_{\mu\nu}u^\mu u^\nu$ is conserved along geodesics (really not hard to show), where $u^\mu$ is the 4-velocity. My question is: Isn't it true that $g_{\mu\nu}u^\mu u^\nu$ is equal to $-1$ for _any_ timelike curve whether it is a geodesic or not? This follows (I think) from $$ g_{\mu\nu}u^\mu u^\nu = g_{\mu\nu}\frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\tau} = \frac{g_{\mu\nu}dx^\mu dx^\nu}{d\tau^2}=\frac{ds^2}{d\tau^2} = \frac{-d\tau^2}{d\tau^2} = -1. $$ Am I wrong about this? Why should we need the geodesic equation to prove this if it's true for any timelike curve?


title: How can I estimate confidence intervals around the forecasted temperatures for future days?

text: Weather.com will happily give me temperature predictions for the next ten days, but no indication of how reliable those predictions are. So if I want to plan something for a week from today, or four days from today, I don't really know whether there's much information in the forecasts. My personal, unscientific (and certainly unreliable) experience says there's not, but there's plenty of variation in the forecasted temperatures, even between days 9 and 10, so the weathermen are not simply falling back to the long-term averages for the time of year. I'm hoping for a rule of thumb here (so my question is different from this theory-heavy discussion from two years ago). Conceivably something as simple as a fixed interval size for each number of days in the future could work, although I could imagine there being low-hanging fruit in, for example, atmospheric pressure or the proximity of the location being forecasted for to water.


title: Where are the ice rings in X-ray crystallography located?

text: I threw this image of one of my protein crystal's diffraction pattern (not the greatest) on a poster, and was wondering where (what reciprocal dimension) the ice rings are located as it might be a useful reference (or talking point). While I can find information about water ice's unit cell parameters (4.5 Å, 7.3 Å), I'm not sure if these are where the reflections would be located (the inner two rings seem far too close for that disparity, and I believe the outer two rings are at a much higher resolution (< 3 Å) ![enter image description here](http://i.stack.imgur.com/FTPb4.png)


title: Non-separable solution for the Schrödinger equation

text: Schrödinger solutions are usually if not always of the type: $\psi=\operatorname{T}(t)*\operatorname{X}(x)$ (we use the separation of variables method to arrive at the time independent Schroedinger equation). I was trying to find a non-separable solution. To this purpose I tried the following method: compose the product T(t)*X(x) into another function. For example: $\sinh(\operatorname{T}(t) \cdot \operatorname{X}(x))$ or $\ln(\operatorname{T}(t) \cdot \operatorname{X}(x))$ or $(\operatorname{T}(t) \cdot \operatorname{X}(x))^2$ and so on. Then I try first time derivative of $\psi = \mathrm{second}$ position derivative of $\psi$ (trying to find a solution for the null potential. In addition I know I need a constant but it's for simplification). I arrive at a differential equation. I try simple solutions for one of the functions like $\operatorname{T}(t)=t$. I get to a very difficult differential equation that can't be solved even with a look at: http://www.amazon.com/Handbook-Solutions-Ordinary-Differential- Equations/dp/1584882972 If there any obvious non separable solution that I am missing?


title: Density matrix and irreducible tensor operators

text: I'm reading those lecture notes on atomic physics. Yesterday I posed a question on reducible tensors, and today I have a question on their relation to the density matrix. If there's any information missing, please let me know so that I could provide it. Please observe the following test from the script: > The density matrix ρ can be expanded in the basis of the irreducible tensor > operators $T^{(K)}_Q$ according to $$\rho = \sum\limits_{K = > 0}^{2F} > {\sum\limits_{Q = - K}^K {{m_{K,Q}}\,{T_Q}^{\left( K \right)}} }\quad \quad > (8.29)$$ where $T^{(K)}_Q$ is given by the formula $${T_Q}^{\left( K \right)} = \sum\limits_{M,M'} {{{\left( { - 1} \right)}^{F - M'}}\left\langle {F,M;F, - M'|K,Q} \right\rangle \left| {F,M} \right\rangle \left\langle {F,M'} \right|}$$ At a later part the writer shows how he derives the spin-1/2 system density matrix from the first equation as follows > Consider as a first example the decomposition of the density matrix of spin > 1/2 particles. According to Eq. (8.29) it is given by $$\begin{array}{c} > \rho = \sum\limits_{K = 0}^1 {\sum\limits_{Q = - K}^K > {{m_{K,Q}}\,{T_Q}^{\left( K \right)}} } \\\ = {m_{0,0}}T_0^{(0)} \+ > \sum\limits_{Q = - K}^K {{m_{1,Q}}\,{T_Q}^{\left( 1 \right)}} \\\ = > \frac{1}{2} + \sum\limits_{Q = - K}^K {{m_{1,Q}}\,{T_Q}^{\left( 1 \right)}} > \end{array}$$ Now I have a few questions: 1- Where did that 1/2 in the last line come from? How is it calculated? 2- How can you calculate the other terms systematically? 3- Can you provide the same calculation for spin-1 and spin-3/2 particles? I want to learn the generalized process. 4- Could you please put any of all this in the frame of Liouville's equation? I'm having a hard time imagining an equation of motion with spins that way. Thank you for any efforts.


title: Bell State Measurement From Parametric Down Conversion Source

text: My question is about whether or not there exists any scheme to distinguish between symmetric and antisymmetric Bell states from entangled pair of down converted photons. State of Down Converted photons \begin{equation} |\psi>=(\alpha|H>|H>+\beta|H>|V>+\gamma|V>|H>+\delta|V>|V>) \end{equation} Now, I want to know is there any way to convert this state to anti-symmetric Bell state.AN experimental scheme is what I desire.


title: How to predict how much data to collect

text: > The same question on CrossValidated Apologies if I'm being a bit vague in what follows, I've been asked to keep certain aspects of the experiment confidential for the time being. An analogous experiment would be like trying to 'see' the ebb-and-flow of the tide (0.5 day period) by locating a photon detector at the bottom of the ocean (though of course this wouldn't work and is silly, but the principle is at least quite similar.) Hope that clarifies it a bit, let me know if not. I'm currently in the planning stages of this experiment that I am hoping will detect a 0.155% signal variation (relative magnitude) within a resonable time frame (less than 6 months ideally.) I've calculated the rate of (usable) data will be around 68 events per day, though it should be stressed this is a random variable. Now I'm trying to work out - **how many days will I need to run the detector for to see the variation with a confidence level of 3σ?** Some other details that may (or may not) be relevant include: the variation in the signal is expected to be sinusoidal with a period of 0.5 days. For this reason I reduced my useful event rate to 34 (Ie half) as clearly there is no variation to see when the sinusoidal signal is at or close to the mean value. I've been googling for a method to predict the size of a data set necessary to see such a small signal variation but have come up with nothing. I would be extremely grateful for any hints / tips anyone could offer.


title: paper about black branes and implications to 4d black holes

text: This paper makes a case for piezoelectric response (electric dipole moment under mechanical oscillations) of black branes. This paper does not make an implication of their results for 4D black holes (do their results apply or not apply to them?). Can someone explain if this implies something for usual 4D black holes in De Sitter space? Do "standard" black holes have such a response as well?


title: Commutation relation of $J^2$ and $R(\alpha,\beta,\gamma)$

text: If $R(\alpha,\beta,\gamma)$ is the Rotation operator and $\alpha,\beta,\gamma$ are Euler angles and $J$ is the total angular momentum then how to get to this: $$[J^2,R]~=~0?$$ This is stated in Zettili's book Quantum Mechanics.