title: Why the kilogram is not defined?

text: > **Possible Duplicate:**   >  Why do we still not have an exact definition for a kilogram? I was thinking about SI units. I found the following definition for the base units:   * **Meter** : distance covered by light in 1/299792458 seconds.   * **Second** : duration of 9192631770 periods of the radiation corresponding to the transition between two levels of fundamental state of 133-Cesium.   * **Kelvin** : 1/273.16 of the thermodynamic temperature of water triple point   * **Mole** : Number of atoms in 0.012 kg of carbon 12   * **Candela** : [...]   * **Ampere** : [...] I searched the definition of the kilogram and I found only this one: > Mass of the international prototype of kilogram. Why such definition? It is impossible to well define the kilogram? Why? By my point of view the mass of the prototype will change a little with time. Is this effect considered? And what about definition of mole: it is based on kilograms, so also mole definition is "impossible"?


title: Symmetric potential and the commutator of parity and hamiltonian

text: In one dimension - How can one prove that the Hammiltonian and the parity operator commute in the case where the potential is symmetric (an even function)? i.e. that [H, P] = 0 for V(x)=V(-x)


title: Can radioactive isotopes stay unstable after beta decay?

text: Say you had a very radioactive element in a confined area: could that element (hypothetically speaking) go through beta decay, then, once it has too many protons could it immediately go through electron capture to become that same radioactive element OR become another unstable element that will again go through beta decay?


title: Self-sustained vs. non-self-sustained discharge systems

text: I don't quite understand what a self-sustained discharge is. I figure it means that the processes involved are self supporting and generate themselves, so that I don't have to put energy into the system and generate an outside voltage at the electrodes. Can an experimental device ever by fully self- sustained? If yes, wouldn't that mean I can't control when it's running or now?


title: Bouncing ball simulation computer science

text: In my Computer science class I was given a problem where I have to simulate a bouncing ball using "real physics". I have been trying to find a equation that will simulate the height of the bounce given a gravity and an arbitrary mass. And I will need to calculate the next bounce and it's height. A lot of the equations I've found require a time. But I don't really care about a time, all I want is to get the next height after the previous bounce until it finally hits height of 0 or close to it. I haven't taken a physics class since high school( 5 years ago) and that was basic physics.


title: What is the format for "local catalog" files used by JSkyCat?

text: I am trying to use JSkyCat to mark a set of coordinates on a FITS image, and have found the dialog for choosing a catalog file to load. However, I am having trouble finding any documentation on what format it expects (and my guesses have been unsuccessful).


title: Do the stars imaged by a telescope even exist at present?

text: I know that we now have telescopes which can capture the images of the stars and galaxies millions of light-years away from us. Does the telescope capture the past image of the star, i.e. the light which it emitted centuries ago? What guarantee is there that the star is still alive? What basis do organizations like NASA plan missions for evading such stars?


On Earth, North is determined by the magnetic poles of our planet. Is there such a thing as "North" in outerspace? To put it another way, is there any other way for astronauts to navigate besides starcharts? For instance, if an astronauts spaceship were to be placed somewhere (outside of our solar system) in the milkyway galaxy, would there be a way for them to orient themselves?


title: Human power on treadmill

text: On an elliptical treadmill a regular person can easily burn 1000 calories in one hour (treadmill reports calories burnt). This translates into: $$(1\times 10^3\mathrm{cal/hr}\times 4.2\times10^3\mathrm{J/cal})/3.6\times 10^3\mathrm{s/hr} \approx 1.2 \; \mathrm{kW} \approx 1.5 \; \mathrm{hp}$$ On the other hand, Wikipedia says "A trained cyclist can produce about 400 watts of mechanical power for an hour or more..." Is the problem that the treadmill gives wrong numbers? Or it is true that running using legs and arms - on elliptical machine or cross-country skiing which seems to be similar - a human can produce a lot more mechanical power than cycling? I thought the maximum power is set by the cardiovascular system, so it would be the same, running or cycling.


title: Coulomb barrier and proton evaporation

text: Why is it that neutrons evaporate from nuclei more easily than protons do? Intuitively, since protons are electrostatically repelled (in addition to whatever nuclear forces they have in common with neutrons), one would expect protons to be ejected more readily than neutrons. (Maybe this is even what does happen for small nuclei, but apparently not large nuclei.) It seems to be said in common parlance that the Coulomb force/barrier acts to contain the protons. Which is counter-intuitive. On the other hand, at least some textbooks acknowledge the coulomb force trying to push protons away from others in the nucleus, and so they infer that the nuclear force (e.g., residual strong force) must act more strongly on protons than what it does on neutrons. (At least in big nuclei, "beta stable nuclei", nuclei with an excess of neutrons..) So how does this nuclear force distinguish between protons and neutrons?


The equation of state for a perfect fluid is that $p=\omega \rho c^{2}$, where $p$ is the pressure, $\rho$ is the density, $c$ is the vacuum speed of light, and $\omega$ is called the equation of state parameter. $\omega$ may be constant or varying in time. I'm looking for broad answers (and references if possible) to the following:   * Why is it important that the equation of state parameter of dark energy is measured?   * What will it tell us?    * What are the implications?


title: Why do we need the concept of dark energy to explain the expansion of the universe?

text: Why can't the expansion of the universe be thought as the Big Bang itself still in progress? Why do we need to introduce dark energy? The Big Bang was powerful, and that explosion itself could still be continuing right?


title: Higgs boson/field symmetries and local symmetries

text: In the SM with gauge group U(1)xSU(2)xSU(3), those factors are associated to the gauge bosons associated with a local symmetry and the Higgs field provides masses to the elementary fermions AND the W,Z bosons (the photon is inert) through SSB. My question is, the Higgs boson has (likely) a mass of about 127 GeV, what kind of symmetries prevent the Higgs to become very heavy through quantum radiative corrections? SUSY can make the work, but is there ANY clever alternative symmetry that protects the Higgs particle to become a superheavy particle via quantum corrections to the mass? I believe that the (minimal) Higgs boson has NO local symmetry associated to it, as far as I know...


title: Does the photon-phonon interaction always rotates the photon polarization of 90°?

text: I'm reading about the acousto-optic effect and on the Acousto-Optical Tunable Filters on particular and wanted to understand the physics under its working. I found this paper http://dx.doi.org/10.1016/S0079-6727(03)00083-1 where they talk about the interactions of polarized light within a crystal. They say > "For instance, if the incident radiation is an ordinary ray (o-ray), it will > be converted into an extraordinary ray (e-ray) upon interaction with the > acoustic wave." and a few paragraphs later > "Considering the entering o-ray [...], photons interact with phonons [...] > and are converted to e-rays by a 90° polarization rotation." They do not explain the origins of this polarization rotation (and I imagine that it's beyond my knowledge) but is this rotation of 90° always true and why of 90° particularly?


title: Question on Newton's law

text: I have heard my friends referring to quantity ma as the "force of acceleration" whereas my teacher told us it can't be referred as so. Is it correct to refer that quantity a force? If not, how can we better describe this quantity?


title: How much energy needed to push a volume of water?

text: I am trying to solve a situation, where I'd like to know how much energy would be needed to push a mass of water out of a container. Here's an image to help understand: ![enter image description here](http://i.stack.imgur.com/3tyr0.png) The water tank has a height of 2 meters, length of 6 meters, and width of 4 meters. If a piston, much like a coffee press but watertight, pushes the water with only the hole on top of the container, as shown in the drawing, as an exit point, how much energy would be needed for that device to go all the way to the other side of the container? Assuming the hole is 1 square meter, if that can help. I understand there are a lot of forces to take into consideration, such as friction, hydrostatic pressure, and more, but I'm trying to figure out if it would require a lot of energy or would it remain minimal? What is the force that will require the most energy? Hydrostatic pressure? If there is a formula that would enable me to figure this out, that is all I'm asking, I can try and do the math myself, but I can't figure out where to start! Thanks a lot for the help!


title: How to measure a qubit in a random basis

text: Let a two dimensional system be in the state $\phi=|0\rangle\langle0|$, for any basis $M$ spanned by the orthogonal vectors $|\psi_0\rangle,|\psi_1\rangle$, we can measure $\phi$ in basis $M$ and obtain "0" and "1" with probabilities $p_0=\mathrm{tr}(|\psi_0\rangle\langle\psi_0|\phi)$, $p_1=1-p_0$. My question is, if I want to select $M$ randomly, is there some commonly understood way of choosing a random basis? My second question is, what would be the distribution of $p_0,p_1$ resulting with this random selection of the basis?


title: How does a wave packet acts rigidly?

text: Particles can be represented as wave packet. So how do particles get scattered? Waves superimpose on one another, they don't bounce off of on one another.


title: Does positronium have a stable crystalline phase?

text: This is a long shot, but while the 100YSS conference is going on at Houston, i haven't been able to get a grip on myself and think in other, more mundane and short-term rewards as normal people do. The main thing that has been taking up my mind is scalable ways to stabilize and store positronium in a way that the mass of storage device is negligible to the antimatter fuel It is known that excited Ps atoms with high n (rydberg or rydberg-like) have estimated lifetimes of the order of years. Since positronium seems to be quite reactive (di and tri-positronium molecules have already been observed) I've been wondering if it could be possible to grow large crystals from positrons and electrons in a simple cubic lattice, where **Na** and **Cl** in the lattice being replaced by $e^{+}$ and $e^{-}$. > **Question:** is possible that positronium can have a crystalline bulk phase > with enough ion distances to avoid annihilation? The reason why i'm interested in positronium and not antihydrogen, which looks relatively easier to manipulate, is that proton-antiproton annihilation is extremely messy, with more than half of the mass-energy decaying into end products like neutrinos, which won't contribute anything to kinetic energy. In contrast, positronium decays in relatively soft gamma rays of 511 KeV (and 380 KeV for orthopositronium) that in theory we could reflect with extremely low grazing angles with efficiencies up to 90% **As an addendum to the larger question of positronium storage methods,** i can't avoid mentioning that there have been other ways proposed over the years to keep the antimatter from touching the walls. If we want to store positron and electron separated, we have to deal with the Brillouin density limit that affects all existing and future Penning traps ($10^{12} e/cm^{3}$ for a field of 1 Tesla), so a simple calculation shows that a cylindrical container with weight ratio of 1 between container and antimatter masses, with 100 Tesla and 10 cm of thickness _will have to have a radius of $10^{12}$ meters, roughly the radius of Neptune orbit!_ so in order to explore more viable alternatives, we are forced to consider only neutral antimatter (unless we find materials able to sustain over large regions magnetic fields 5-6 orders of magnitude higher than the current state of the art) This report gives a nice overview of some of the alternatives that have been explored, the most interesting is paraelectricity (which is an effect where induced electric fields create virtual mirror charges on the wall that repels charges and possibly dipoles). Quantum reflection between antimatter BEC and wall is also mentioned, but i have reservations toward this one, since even if positronium BEC will form theoretically at higher temperatures (roughly 1-10 Kelvin), it is still complex to keep a large mass of BEC isolated enough from the environment (think of accelerations on a hypothetical ship) to make this a viable alternative. Basically if you sneeze, you and your ship will become a mininova. There is one patent online proposing using photonic bandgap crystals to disallow the decay band of rydberg positronium, but it seems to me that requires cavities that are of the order of one wavelength of the decay radiation, which put us again in a scenario with low ratios of container-fuel masses PS: Glad i've finally written this down, hopefully i'll be able to take my mind off a bit from this subject


title: Considering the wave function is not 'real', what is interfering?

text: I find the idea of the wave function being 'just' a collection of numbers (probabilities) quite alluring, and elegant in explaining away the whole 'collapse' business (see Luboš' answer to this question). I realize though, you can only stretch an analogy so far. Yes, learning location of a wanted criminal does not in fact 'collapse' his wave function, but is there any analogy which explains wave function interfering with itself (as per double split experiment)?


title: Is time dilation an illusion?

text: It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth would be moving relative to the clock on the spaceship, and since time always dilates and never goes faster regardless of the direction of relative motion, the clocks on earth should register less time than the clock on the spaceship. Is this true? Whenever there is a fast-moving object such as a rocket do all clocks on earth really become slow? If the rocket with the clock landed after moving at relativistic speed, would its clock and the earth's clock again show the same time since during its travel both appeared slow to each other? Or is all this just an illusion, ie. the clocks just appear to be slow to each other but in actually run at normal speed, and neither is behind when the rocket actually lands?


title: Calculate time dilation with Lorentz transformation

text: It is possible to calculate the time dilation with Lorentz transformation? So with the equation $$t'=\gamma(t-\frac{x v}{c^2}) \tag{1}$$ in which $\gamma$ is the Lorentz-Factor? In an exercise I have succeeded. So why can be calculated with the equation $(1)$ the time dilation? What is the reason?


title: Is time dilation real?

text: If a body with an accurate clock is moving away from A which is stationary, then the time in B would be slower than that in A. Since relative to B A would have an equal velocity time in A would be slower than that in B. This results in a contradiction. This is the argument given in this website. Can someone say how this argument is wrong from a deeper study of SR.?


title: Is aging independent of time progression when relativistic effects are taken into account?

text: I have been trying to understand Einstein's principle of relativity for quite some time. I have at least I believe, understood the notion that time is relative and can actually 'change' relative to some frame of reference close to c. My question is, time is actually a variable that we invented based on how we thought about it; it's the progression of events, life and existence itself. So when, we say in Twin Paradox, one of the twin when he comes back to Earth is younger, how can that be possible? Again, it is true time would slow for him during his travel in space but that's because of the way we defined time and consequently its limitations close to c. How can that affect his physical structure (aging process)? Time should be independent of his personal physique.


title: Is time dilation an illusion? Variation on the twins paradox

text: Consider the twins paradox with a slight variation: Twins A and B are in separate space ships both capable of going at the speed of light instantly (i.e. without any acceleration). Both ships are stationary relative to each other in intergalactic space facing in opposite directions. They synchronize their clocks. Then Twin A sees ship B zooms off to the "right" at the speed of light, and ship B travels a round trip of 8 years. Twin A sees ship B recede away from him at the speed of light (in fact, ship A just disappears). When ship B returns, Twin B's clock will show he has been gone 8 years. But from Twin B's perspective, it's ship A that zooms off to the "left" at the speed of light, does an 8 light year round trip, and according to Twin A's clock, he has also been gone 8 years. So they both would agree that one has been away from the other 8 years, and both have aged the same amount of time. It would seem clocks do not actually run slower as they move closer to the speed of light. So is time dilatation just an illusion?


title: The real meaning of time dilation

text: Is this true or false: If A and B have clocks and are traveling at relative velocity to each other, then to B it APPEARS that A's clock moving slower, but A sees his own clock moving at normal speed. Similarly, to A it APPEARS that B's clock is moving slower, but B sees his own clock moving at normal speed. If the above is true, then both A seeing his own clock moving at normal speed and B seeing his own clock moving at normal speed means that in reality both clocks are moving at normal speed, and neither has slowed down, whereas the other person's clock APPEARING to move slowly is merely an illusion. Now is this true or false: If A and B have clocks and are traveling at relative velocity to each other, then A sees his own clock move slowly (compared to the speed of the clock when A was at rest with respect to B) and B sees his own clock move slowly, so that in reality both clocks are moving slowly, but they still remain synchronized (since both are slow by the same amount) If the above statement is not true, then why do muons decay slowly when moving fast? [it could only be possible if the muon saw its own clock as moving slowly. If we saw the muon's clock moving slowly, but the muon saw its own clock moving at the normal rate, then the muon would decay at the normal rate, and not slowly] Can anyone please explain where I went wrong?


title: How does cold fusion work?

text: I understand that in regular fusion, you use high levels of heat to accelerate atoms to speeds high enough to overcome nuclear force. What method would be used to achieve cold fusion?


title: What is the name of the principle saying it is meaningless to talk/ask questions that can not be measured/tested?

text: Watching quantum mechanics lectures and it was mentioned that it is pointless/meaningless to try to talk/question things that can not be tested/measured. Is this a principle? And if so what is it's name? Also does this apply to questions other than Quantum mechanics? E.g. does it make sense to ask if earth was the only object in universe if gravity would still exist? Although it seems intuitive to answer yes, yet it is something that can never be tested/verified. It seems almost as meaningless as to ask if the universe was only made of a unicorn would it have gravity? As an analogy consider glottogony, at some point it was banned as it seemed to be an unanswerable problem. http://en.wikipedia.org/wiki/Origin_of_language


title: How does a snowflake "know" to form symmetrically?

text: > **Possible Duplicate:**   >  Why are snowflakes symmetrical? Under ideal situations, a snowflake forms into near perfect hexagonal symmetry. How? For instance, when a water molecule moves towards the edge of the snowflake, how does it "know" where to place itself so that the crystal formed matches the other five points?


title: ATLAS and CMS calorimeters

text: I was reading this interesting recent review on arxiv about particle identification: Particle Identification In figure 2, there is an interesting comparison between the CMS and ATLAS calorimeter performances. I hope the paper author won't mind if I reproduce the image here: ![](http://img809.imageshack.us/img809/1180/calo.png) You see that the CMS EM calorimeter has much better resolution than the ATLAS one, and I'm certain that this is due to the almost unfair comparison between an homogenous and a sampling calorimeter. No surprise here. On the other hand, the ATLAS hadronic calorimeter has much better resolution than CMS's. 1) Why is that? Is this just a by-product of the reduced size of the CMS hadronic calorimeter? 2) Are those resolutions final or can the collaborations make them better when they have more data? How?


title: How can I infer the topology of a quantum state (or band) from its Chern number?

text: Whereas I can calculate the **Chern number** of a quantum state (or band) from the integration of the Berry curvature in all space. How can I infer the topology of the quantum state from this result? What is the physical meaning of a quantum state with non-zero Chern number?


title: Some sort of light reflection

text: One morning I woke up to a text message and picked up my phone but I was not yet fully awake and my eyes had not really gotten its focus. When I stared at the phone I saw two phones. Which is obviously just a depth perception and missed focus. There is even and art form called stereogram and its fun to play with sometimes , which is what I was doing, because there was some interesting light coming through the window. In the corner of my eye I even caught a glimpse of the visible light band spectrum. So I was looking at the two phones. One real and the other a recreation of the other, and they were exact copies of each other ( as they should be ). But when I titled my head, a light reflection would pass over the real one but not its doppelganger. However the original light reflection was still showing even though the real phone had tilted showing another reflection. Does anyone know what this phenomenon this?


title: Unsolved entanglement problems

text: What are the current most important _theoretical_ problems on quantum entanglement? What is that we don't yet understand about how it works? (Not considering interpretation etc problems)


title: Why did this glass start popping?

text: I remember a while ago my father dropped a glass lid and it smashed. It looked something like this. When that happened, for about 5 minutes afterwards, the glass parts were splitting, kind of like popcorn, and you could hear the sound. I was just wondering why this happened, and the particles didn't just sit quietly in their own original parts?


title: Electromagnetic weapons: power?

text: I essentially have three questions concerning weapons based on EM waves or more generally.   1. Focusing on the weapons using radio-waves and/or micro-waves, what power do these types of weapons need to radiate to generate the described effects?   2. How easy or difficult would it be to make your own weapon or to acquire one. As I understand it from the wikipage, only the US army is known to have such weapons, so I suppose it is not something you could easily make unless you have a physics lab at your disposition.   3. We live in a world where the "amount" of radio-waves and micro-waves that pervade our space is impressive. Isn't there any danger to be expected from these waves, considering that weapons can be built based solely on concentrated pulses of EM waves? Could something apparently as benign as a cell phone or a WiFi connection have the same effects, even though they would require longer exposition? I am aware that studies, also this link and this one, have been done, and they seem to be either inconclusive or answering in the negative. Yet, I have this nagging doubt. I am aware that the question is bordering on questions of medicine and physiology as well as engineering rather than pure physics, but I'm not sure where else to ask.


title: Can radio waves be formed into a pencil beam?

text: Laser beams are said to have high "spacial coherence". This means that the beam is highly concentrated even at long distances (low spread). Can this be achieved with radio waves (much longer waves) or is it due to laser's  stimulated emission?


title: Could ball lightening be a form of plasma?

text: With regard to the recent arXiv article: J. D. Shelton, _Eddy Current Model of Ball Lightening_   http://arxiv.org/abs/1102.1224 I wonder if this is a reasonable explanation of ball lightening, or if there is such an explanation. The paper is somewhat technical and E&M is one of my worst subjects. Please feel free to edit this question to one better suited, or if you don't have the rep, add a comment suggesting changes.


title: Quantum Entanglement and Inflation

text: Is it possible that the process of quantum entanglement creates new space time? If two entangled particles' quantum states cannot be described individually, even if they are separated to us, is it possible that observation causes the space time they occupy to "separate"? Hence the near instantaneous information transfer? Could this also cause inflation in some way?


title: What is a D-brane?

text: I know that in string theory, D-branes are objects on which open strings are attached with Dirichlet boundary conditions. But what exactly is a brane? Are they equally fundamental objects like string? If so then do they also vibrate? If the visible universe itself is not a brane then what is the dynamics of these branes within the universe? Do individual D-Branes interact, collide? Can an open string tear itself off from the D-brane? If so what are the results?


title: Detection Angles in Bell-type Experiments

text: Bell-type experiments look at the violation of this inequality: $|S|\leq 2$. where $S=E(a,b)-E(a,b')+E(a',b)+E(a',b')$ and $E$ is the correlation function. Mathematically, the maximal violation of the inequality is reached when $|S|=4$ (because the bounds of $\cos \theta_{ab}$ are $\pm 1$). However, wherever I look in the literature it says that experimentally, quantum states produce a violation up to $|S|\leq 2\sqrt{2}$. That is Tsirelson's bound. The detector settings are always given in intervals of $\frac{\pi}{8}$ radians. A very common set-up in degrees is: $a = 0$, $a' = 45$, $b = 22.5$, $b' = −22.5$. They seem to take it for granted that this is THE configuration for maximal violation, without an explanation (I think I'm missing something). Why can't the mathematical maximum be achieved experimentally? Thanks in advance! :)


title: Why does measured pressure change over time in closed hose with temperature gradient

text: I have a 4' hose that is closed at one end and connected to a Airdata Test Set (precise control of pressure) and a high accuracy pressure monitor on the other end with a T and valve. The valve allows the Airdata Test Set connection to be closed off resulting in a hose connected to the pressure monitor and closed at the other end. The valve is a high quality needle valve. The pressure monitor is a a Druck DPI 142. Half the length of the hose is in a temperature chamber controlled to 70 C. The Druck connected end is outside the chamber at roughly 22 C. When the airdata test set is commanded to a pressure of 1300 mb and allowed to settle for 30 seconds or so, then the valve closed, the pressure reported by the Druck drops over 20 minutes or so with a decreasing rate of change. The airdata test set draws air from the room when operating. The hose is ~0.190" ID neoprene, Saint-Gobain P/N 06404-15. The temp chamber, hose, etc, are given 1 hour to thermally stabilize prior to commanding the pressure to 1300 mb. The difference between initial pressure and stable pressure is ~18 mb. Why does the pressure take 20 minutes to stabilize?


title: Value of G, gravitational constant

text: if the universe is a 0 energy universe, could the value of G be worked out through summing up the strong, weak and electromagnetic force strengths for an elementary particle up to an infinite distance, and take the value of the negative energy gravity provides as that value in reverse? Or at the very least the value of the sum of the force of gravity and the cosmological constant?


title: Why do we use operators in quantum mechanics?

text: In classical mechanics, physical quantities, such as, e.g. the coordinates of position, velocity, momentum, energy, etc, are real numbers, but in quantum mechanics they become operators. Why is this so?


title: Do all planets have an electric charge?

text: Do all planets have an electric charge? If yes, is positive or negative? And how much each magnitude? I have read some articles which really confused me. Some of these articles said that all planets have a negative charge and the sun has a positive charge. Some other articles said the the exact opposite.


title: Quantum Field Theory without LSZ, how is it possible?

text: Most modern texts spend some time deriving the LSZ reduction formula that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you are calculating. Yet some earlier texts and even some modern texts (e.g. "Student Friendly Quantum Field Theory" by R. Klauber) seem to skip right past this, working everything out in the "interaction" picture. It seems there must be something going wrong with this latter procedure, but I am not quite able to put it together.


title: Can you confirm 2 simple statements about vaporization?

text: Vaporization is an interesting engineering subject, but unfortunately much about it has always been unclear to me. Recent research of mine has brought my mind to link _vapor pressure_ to _boiling_ and _partial pressure_ to _evaporating_. So I would just like to confirm the following two understandings of mine:   1. **VAPOR PRESSURE** is the pressure needed to "mechanically" keep a liquid from **BOILING**. The composition of the air exerting the pressure doesn't matter.   2. When an evaporating substance's **PARTIAL PRESSURE** equals its **VAPOR PRESSURE** , "statistically" it stops **EVAPORATING**. Thank you.


title: $\mathcal N=2$ Weyl multiplet and chiral superfields in 4d

text: It is more or less known that a given antisymmetric tensor $F$ in two indices can be written in terms of spinorial indices, splitting into self-dual and anti-self-dual parts $$ F_{\mu\nu} = F_{\alpha\beta} (\sigma_\mu)^{\alpha\dot\alpha}(\sigma_\nu)^{\beta\dot\beta} \varepsilon_{\dot\alpha\dot\beta} + F_{\dot\alpha\dot\beta} (\sigma_\mu)^{\alpha\dot\alpha}(\sigma_\nu)^{\beta\dot\beta} \varepsilon_{\alpha\beta} .$$ My question is the following: start from (equations 5.3 and 5.4) $$ W_{\mu\nu}^{ij} = T_{\mu\nu}^{ij} - R_{\mu\nu\lambda\rho}\theta^i\sigma_{\lambda\rho}\theta^j + \cdots $$ which is self-dual in Lorentz indices $\mu\nu$ and antisymmetric in $\mathrm{SU}(2)$ indices $ij$. Then it is squared to $$W^2= \varepsilon_{ij}\varepsilon_{kl} W_{\mu\nu}^{ij}W_{\mu\nu}^{kl}.$$ How do I see (possibly using the first equation above) that this is the same as a tensor (formula 4.1 and below) $W_{\alpha\beta}$ with self-dual $T$ as top component, where $\alpha$, $\beta$ denote symmetric spinor indices and $$W^2=W_{\alpha\beta}W_{\alpha'\beta'} \varepsilon^{\alpha\alpha'}\varepsilon^{\beta\beta'} ?$$


title: What does "carry a representation" mean (in SUSY algebra)?

text: I come from a maths background and am struggling with some of the more physical texts on SUSY. In particular they claim that the fermionic generators $Q_A^i$ **carry** a representation of the Lorentz group. What does this mean? I have never heard the word 'carry' applied to representations in a mathematical framework. I would appreciate it if someone could   1. give me a general mathematical definition of this term   2. explain specifically why it is used in this context (see edit below) **Edit** : most books I have read note that $$[Q_A, J_{ab}]= (b_{ab})_A^BQ_B$$ and use the super-Jacobi identity to conclude that the structure constant matrices $b_{ab}$ form a representation for the Lorentz algebra. They **use this** to immediately conclude that $Q_A$ "carry a representation" of the Lorentz group. What is the logic here?


title: How momentum/energy is distributed in a elastic collision?

text: We know from conservation of momentum or energy that energy (lets think about one quantity at a time) is conserved before and after collision. But how the energy is distributed between the bodies? I mean $1+3=4$ otherwise we can say $2+2=4$. Which distribution would be preferable?


title: Gravitational lensing of massless photons

text: I recently got a more complete proof of photons having no mass. (I knew it before, but now I _really_ know it.) But now, I'm curious how gravitational lensing can occur without a mass to act on. I have heard that space is like a sheet and gravity works because the more massive an object is, the more it bends space. I heard that when I was five years old. When I got older I questioned how that would work, seeing as space is 3-dimensional. The answer I eventually cobbled together from a plethora of excellent resources was this: > Gravity is like a point light source. At the center, you have the most > intense light. As you move outward the intensity decreases with the square > of the distance. Like light, gravity radiates in all directions > simultaneously. This works well for me, and I still believe it to be accurate. However, when I was thinking about photons, I realized that you cannot apply a force to an object without mass. At least, you can't by standard Newtonian thinking. This is because $F=ma$. With no mass, you can have no force. Alternately, you could rearrange to $\frac{F}{m}=a$. With no mass, and no force, you can have no acceleration. **_Yet gravity is able to refract light._** How is this possible? Like $E=mc^2$, does this only apply to a specific set of conditions?


title: AC through a pure inductor

text: _I've studied the AC circuit for an ideal inductor in many physics books. After deriving the final equation for current the integration constant $C$ is assumed to be $0$ by giving inadequate reasons. In this question I seek for an adequate reasons._ Suppose an ideal AC voltage source is connected across a pure inductor as shown: ![i](http://i.imgur.com/aevwKxN.jpg) The voltage source is$$V=V_0\sin(\omega t).$$ From Kirchhoff’s loop rule, a pure inductor obeys $$V_0 \sin(\omega t)=L\frac{di}{dt},$$ so $$\frac{di}{dt}=\frac{V_0}{L} \sin(\omega t)$$ whose solution is $$i=\frac{-V_0}{\omega L}\cos(\omega t)+C$$ Consider the (hypothetical) case where the voltage source has zero resistance and zero impedance. > In most of elementary physics books $C$ is taken to be $0$ for the case of > an ideal inductor. $$\text{Can we assume that } C \neq 0?$$ >   1. (To me this is one of the inadequate reasons). This integration > constant has dimensions of current and is independent of time. Since source > has an emf which oscillates symmetrically about zero, the current it sustain > also oscillates symmetrically about zero, so there is no time independent > component of current that exists. Thus constant $C=0$. > >   2. (Boundary condition) there might exist a finite DC current through a > loop of wire having $0$ resistance without any Electric field. Hence a DC > current is assumed to flow through the closed circuit having ideal Voltage > source and ideal inductor in series if the voltage source is acting like a > short circuit like a AC generator which is not rotating to produce any > voltage. When the generator starts, it causes the current through the > circuit to oscillate around $C$ in accordance with the above written > equations. > >


title: Initialize a traveling wave in a 1D gas?

text: I am trying to initialize a **traveling** wave for a 1d simulation as one can see from the attached figure. ![enter image description here](http://i.stack.imgur.com/J0iOi.png) Such that it will be **traveling to the right**. However, I cannot initialize the right velocity profile, and this makes the initial pressure distribution tends to be more uniform to reach the same pressure of the surrounding fluid ! Can any one provide some support?


title: Magnetic field in the Centre of Circular loop wire with Current?

text: By biot-savart: $$\bar{H} = \frac{I}{4\pi} \oint \frac{d\bar{l} \times \bar{r}}{r^{3}}$$ so $$\bar{H} = \frac{I}{2a} \hat{n}$$ Please, explain the last implication. I cannot find such integral to match the results. The radius of the loop is $a$. The current is $I$. $d\bar{l}$ is a vector along the perimeter.


title: Can a black hole be formed by radiation?

text: I'm trying to find out if black holes could be created by focusing enough light into a small enough volume. So far I have found (any or all may be incorrect):   * Maxwell's equations are linear, dictating no interaction of radiation.   * The Kerr effect and self-focusing has been observed in mediums, but not vacuums.   * Masses bending light have been observed per general relativity.   * Photons are said to have no rest mass, just energy and momentum (???).   * General relativity seems to provide for energy to energy interaction. This leads to a more specific question: Does radiation or energy curve space like mass curves space?


title: Comparing scales of atomic level objects to scales of everyday size objects

text: I am trying to come up with everyday size objects comparisions of atomic scales items, e.g. if a proton probability cloud was of size basketball how far would the next atoms to it be? reason being is to give an idea of the space in between the atoms and giving student some idea of relative atomic object sizes. Looking for examples of how does dnsity of materials can be reflected in this comparsion scheme, for example comapring a dense material to a relatively far less dense material and much closer the basketball sized atomic cloulds would relatively be closer to each other. PS : No models of everyday objects as analogy to atomic structure will be used, only relative distances of the structures is the main objective.


title: Relativistic centripetal force

text: The thought randomly occurred to me that a circular particle accelerator would have to exert a lot of force in order to _maintain the curvature of the trajectory_. Many accelerators move particles at fully relativistic speeds, and I want to ask how that affects things. Why does this matter? Well, if I understand correctly, a particle in the LHC moving at $0.999 c$ would be _dramatically_ more difficult to keep moving in the circle than a particle moving at $0.99 c$. Reading Wikipedia, I was delighted to find a fully specified problem within a single paragraph. http://en.wikipedia.org/wiki/Large_Hadron_Collider > The LHC lies in a tunnel **27 kilometres** (17 mi) in circumference, as deep > as 175 metres (574 ft) beneath the Franco-Swiss border near Geneva, > Switzerland. Its synchrotron is designed to collide opposing particle beams > of either **protons at up to 7 teraelectronvolts** (7 TeV or 1.12 > microjoules) per nucleon, or lead nuclei at an energy of 574 TeV (92.0 µJ) > per nucleus (2.76 TeV per nucleon). I can (or Google can) calculate the proton case to come to $0.999999991 c$. In order to correctly calculate the force that the LHC must exert on it, do I need to start from $F=dp/dt$, or can I get by with $v^2/r$ times the relativistic mass? I'm not quite sure how to do the former. **Question:** Say I have 2 protons, both moving so fast they're going almost the speed of light but one has twice the energy of the other. They move side- by-side and enter either an electric or magnetic field that causes them to accelerate perpendicular to the velocity vector. Is the radius of curvature mostly the same for the two, or is it different by a major factor (like 0.5x, 1x, or 2x)? I want to read some comments from people who understand these physics well. The particles beyond a certain energy are all going _almost exactly_ the same speed. Is it still okay for me to say they have the same "acceleration" too? They just happen to have absurdly huge inertia compared to the same particle at a more modest fraction of the speed of light. Is this the correct perspective?


title: Is the existence of electromagnetic standing waves dependent on the observers reference frame?

text: If I take two plane EM waves travelling in opposite direction e.g. $E = E_0 \sin(kx-\omega t)$ and $E=E_o \sin (kx + \omega t)$, they sum to give a standing wave with a time-averaged Poynting vector of zero. If I use the appropriate special relativistic transformations to derive how these fields appear to an observer travelling at $v$ along the x-axis, I find that one E-field is diminished, one is boosted, whilst at the same time one wave is blue-shifted and the other red-shifted. These waves do not sum to give a standing wave in the moving frame of reference and have a non-zero time- averaged Poynting vector. So, is the phenomenon of a standing wave dependent on the frame of reference of the observer?


title: Viability of Dysons bladeless fans?

text: Do Dyson's bladeless fans produce enough air pressure to cool say an air conditioning unit and do they produce a vortex pressure like a bladed fan?


title: Estimating Partition functions

text: I have a finite state ensemble with an energy functional (you can think of it as an ferromagnetic Ising model if you like), and I need very careful estimates of the partition function. What methods are available to me to get reasonable estimates (in reasonable temperature regimes) of $Z(\beta)$?


title: Should a neutron fall faster than a proton?

text: If you drop a proton and a neutron in a gravitational field, they both fall, but the proton has a charge and accelerating charges radiate energy, so that leaves less kinetic energy for the proton and by this reasoning, it should fall more slowly than a charge-free object. The issue is discussed but not in the terms above in Peierls's "Surprises in Theoretical Physics" in the chapter "radiation in hyperbolic motion", but I didn't understand the chapter well enough (or at all) to apply it to my version of the question. Peirls also refers to Pauli's Relativity book (section 32 gamma) but while Pauli claims there is no radiation from uniform hyperbolic motion, he does say there is radiation when two uniform rectilinear motions are connected by a portion of hyperbolic motion. So I take it that would mean a proton at rest which falls for a second and then is somehow forced to maintain its newly acquired downward velocity from the fall without speeding up any further would have radiated.


title: Undergraduate-friendly reading material on the multiverse?

text: I'll be teaching a seminar for first-year undergraduates next year. The idea of my university's first-year seminar program is to expose students to exciting ideas and important texts in a somewhat interdisciplinary way. My course will focus on three epochs in the history of cosmology in which our ideas about the size of the Universe underwent radical expansions: the Copernican revolution, the early 20th century, and the present / recent past. I have a lot of ideas for good undergraduate-friendly readings on the first two topics, but not so many for the last one. One idea I want to get at with them is that recent theories suggest that the observable Universe is a small and perhaps not even typical fraction of the entire Universe. I'd even love to get them arguing about the anthropic principle while I'm at it. So my question is this: Can you suggest good books, articles, etc. for me to consider in the syllabus for this course? Because of the interdisciplinary nature of the course, I'm happy to consider fiction, philosophy, and history as well as straight-up science. (For instance, Borges's story about the Library of Babel has a nice metaphorical connection to some of these ideas.) Just remember that these are kids fresh out of high school -- they're not ready for _Phys. Rev. D_!


title: What forces are at work causing sand to migrate to the centre of a spinning bucket of water?

text: A bucket is filled with water and a handful of sand. The water is then spun. Why and what forces are in play which cause the sand particles to congregate in the centre of the bucket?


title: Motion of Object in Rotating water

text: Water inside bucket is rotated (by spoon or something) to flow in circular motion. An object kept in the bucket tends to be at the center of the bucket. Why is that?


title: Mixing a cup of tea and break of centrifugal force

text: > **Possible Duplicate:**   >  Vortex in liquid collects particles in center Why when you mix a cup of tea with a teaspoon, tea-craps collect in the center of cup, instead of goes near the walls?


title: Why tea dust in a cup of tea seems to concentrate in the bottom center?

text: > **Possible Duplicate:**   >  Vortex in liquid collects particles in center Sorry for my bad English. :-) Hello ! Here is my question : If you enjoy some cup of tea, you may see that there are some tea dust in suspension in your cup. If you turn your spoon in the liquid, the tea will rotate, and the dust will concentrate in the bottom of the cup (because the dust is denser than the water) but too in the center ! This is conter intuitive for me. The dust have to spread near the sides of the cup, because it's more denser than the water ! No ? Edit : We can think to the centrifugation of the blood. When the blood is collected from a people, the pocket pass into a centrifuge (? do you see what I mean ? top of the pocket in the center, bottom of the pocket near the walls) and the diverse parts of the blood finish separated in function of their density. But the denser, the closer of the bottom of the pocket...


title: Why is electric flux defined as $\Phi = E \cdot S$?

text: Flux, as I understand it, is the amount of substance passing through a particular surface over some time. So, from a simple perspective, considering photons that go through some virtual surface $A$ (or $S$, doesn't matter). They have a fixed speed in vacuum, $v=299,792,458$ $\text m/\text s$. To simplify even further, they're all hitting the surface head-on. So, if we wanted to figure out how many photons go through the surface, we conclude that at a constant velocity they will only pass through the surface if they are in the volume bounded by sweeping the surface area along the velocity vector (perpendicular to the surface, the opposite of its normal) a distance $d$ in the alloted time $t$: $d = vt$ So the flux volume is well-defined as $V(t) = Avt$. We could just look for a period of unit time and "drop" the dependency on time. But even then, it's useless if we cannot sample photon volume density $\rho_p$ to determine how many photons occupy a unit volume in order to determine the actual flux. That makes sense: $$\Phi = \rho_pV(t)$$ And now comes along the electric flux and thwarts my understanding of the whole notion completely. An electric field is generated when a charge is dropped somewhere in space. Any other charge, especially idealized point charges, placed in its vicinity would experience a force exerted on them by the source charge, its magnitude modulated by the amount of charge. So, the electric field maps points in space with force vectors (ie. a vector field) whose direction and magnitude is parametrized by the interaction between the source charge and the point charge. And this electric flux is defined as $\Phi = E \cdot S$ (I'll use $\Phi = E \cdot A$) and I just cannot interpret the semantics of this dot product, the product's dimensionality is not what I've come to expect from the notion of flux ($\text{Vm}^{-1}$ or any other). **How does this in any way show how much electric field flow goes through a surface? Furthermore, what is this vague thing called electric field flow? It seems like it is completely disconnected.** I've tried expressing it in different ways from the derivation of the expression of an electric field, which makes sense (non-vector form, dropped unit vector): $$E = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}$$ I've intentionally separated the inverse square of the distance and the $4\pi$ which is, I presume, a part of the normalization factor (steradians of sphere) -- but I noticed that together they forge the area of a sphere $A_r = 4\pi r^2$. This way, I could see the expression as the uniform charge density distribution on the surface of a sphere, scaled by the vacuum permittivity. $$E = \frac{Q}{A_s\varepsilon_0}$$ And then, due to presumed uniformity, by multiplying by an arbitrary area, I could get the flux, the amount of charge(?) flowing through a particular surface in unit time(?): $$\Phi = E \cdot A = \frac{Q}{A_s\varepsilon_0} A $$ I could see that as flux, but I'm really not sure can I really reinterpret parts of the normalization factor and the inverse-square of the distance into the area of a sphere. From the perspective of voltage over distance it makes absolutely no sense to me. Any help would be appreciated.


title: A Simple Explanation for the Schrödinger Equation and Model of Atom?

text: I tried reading the Wikipedia article to no avail - I simply cannot understand the Schrödinger Equation (what does each of the variables mean, especially the wave function), and the Schrödinger Model of the Atom. Could someone explain in simple words how this entire thing works and its consequences/conclusions in Physics? ![enter image description here](http://i.stack.imgur.com/wykwd.png)


title: Hydrostatics , work Power and Energy

text: If a servant lifts 10 cubic meter of liquid from a tank, which is at a depth of 40m . If the work done by him is 1600J, then find the density of the liquid (g = 10 m/s^2)


title: Combining ±% with ±dB in measurement uncertainty

text: Firstly apologies if this is not the correct place to post this but wasn't sure which site would be good to ask regarding about measurement uncertainty calculation. I am trying to calculate the combined measurement uncertainty, however the uncertainties I want to combine are using different scales: Carrier level uncertainty: ±0.5dB (logarithmic) Modulation uncertainty: ±5% (linear) Converting either from one format to another will not give me a simple ±value in the other format What is the best way to combine these uncertainties?


title: Does boundedness of observables in the Haag-Kastler axiomatization rule out interactions?

text: In an interacting theory I expect there to be caustics, resonances, and other situations in which _some_ observables would give an infinite experimental result. Of course, these are idealized states and observables -- if a real device's measurement results are quite accurately modeled by such an observable, and we created a state in which its expected value is large enough, the device would be destroyed. An idealized world in which models never predict infinite results seems somehow different from the world we live in. Even though experiments never return the measurement result "infinity", they do return the measurement result "I'm so sorry, I'm breaking now, it's bigger than you thought it could be". The Wightman axioms do not require operators to be bounded, and to me seem much better for it. QFT as it's used in practice isn't constructed within the Wightman axioms, but it's much less constructed within the Haag-Kastler axioms, and, it seems to me, particularly for this reason. I take boundedness to mean that all the eigenvalues of an operator in its action on a Hilbert space of idealized Physical states are required to be finite. This is much stronger than requiring the expected values of an operator to be finite for a dense subset of the Hilbert space (or other, relatively weaker, requirements). It's certainly mathematically more convenient to use bounded operators (because we don't have to keep track of for which states we get a finite result for a given measurement, because they all do), but is that enough? At least, is this acceptable as part of a major attempt to axiomatize theoretical Physics? Is it obvious enough to be an axiom? I'm prompted to ask this question in this way by a comment in Doplicher's "The principle of locality: Effectiveness, fate, and challenges" J.Math.Phys. 51, 015218 (2010), http://arxiv.org/abs/0911.5136, which I'm reading this morning, where he sets out on the first page (2nd page in the arXiv) that "In quantum mechanics the observables are given as bounded operators on a fixed Hilbert space", which seems a specially sanitized version of QM, insofar as it rules out position, momentum, and energy observables. Finally, this question is asking, as always, have I got something (very) wrong?


title: exterior electric field on a capacitor

text: Has it been observed that charged high capacitance capacitors do generate a strong positive electrostatic charge on their exterior insulating surfaces? Has it been observed that charged high capacitance capacitors attract exterior negative electrostatic charges to their exterior insulated surfaces?


title: In a large city how much hotter on average is it outside due to the air conditioning of all the buildings?

text: Title pretty much states the question. How much hotter do air conditioning units make it outside in a large city like NYC, Chicago, etc?


title: Qubit (Qdit) equivalence with bits/bytes/Kbytes/

text: **What is the conversion factor for qubits (qudits) to bits/bytes in classical information theory/computation theory?** I mean, how can we know how many "bits/bytes" process, e.g., a 60 qubit quantum computer (quamputer), are equivalent to classical bits (dits)?What about memories and velocities in "attaniable" quantum computers versus classical current memories and computer velocities(GHz)?


title: Symmetry and conservation laws related to baryon number, lepton number and strangeness

text: According to Noether's theorem, _Every continuous symmetry of the action leads to a conservation law._ For example, conservation of linear momentum corresponds to translational symmetry, conservation of angular momentum corresponds to rotational symmetry. My question is on the conservation of baryon number, lepton number and strangeness. What type of symmetry does imply when the above mentioned quantities are conserved in a system?


title: Induced current in parallel wires

text: Consider two parallel wires of finite radius. When a current is applied to one of the wire for a short period of time, what is the current induced in the other wire? Applying Maxwell's equations, it seems that there is a change in magnetic field perpendicular to the second wire, and as a result, the induced current has a nontrivial distribution which averages somewhat to zero. Is this correct? Intuitively, I had instead expected a simpler result similar to the case of two coils of wires placed side by side.


title: Scale Factors via Ellipsoidal Coordinate System Scale Factors

text: In Morse & Feshbach (P512 - 514) they show how 10 different orthogonal coordinate systems (mentioned on this page) are derivable from the confocal ellipsoidal coordinate system $(\eta,\mu,\nu)$ by trivial little substitutions, derivable in the sense that we can get explicit expressions for our Cartesian $x$, $y$ & $z$ in terms of the coordinates of some coordinate system by simply modifying the expressions for $x$, $y$ & $z$ which are expressed in terms of ellipsoidal coordinates. Thus given that $$x = \sqrt{\frac{(\eta^2 - a^2)(\mu^2 - a^2)(\nu^2 - a^2)}{a^2(a^2-b^2)}}, y = ..., z = ...$$ in ellipsoidal coordinates, we can derive, for instance, the Cartesian coordinate system by setting $ \eta ^2 = \eta' ^2 + a^2 $, $\mu^2 = \mu'^2 + b^2$, $\nu = \nu'$, $b = a\sin(\theta)$ & letting $a \rightarrow \infty$ to get that $x = \eta'$, $y = \mu'$ & $z = \nu'$. Substitutions like these are given to derive a ton of other useful coordinate systems. I don't see why one shouldn't be able to use the exact same substitutions on the scale factors. Thus given $$h_1 = \sqrt{\frac{(\eta^2 - \mu^2)(\eta^2 - \nu^2)}{(\eta^2 - a^2)(\eta^2 - b^2)}}$$ I don't see any reason why the exact same substitutions should not give the Cartesian scale factors, namely that $h_1 = 1$ in this case, yet I can't do it with the algebra - I can't get it to work. You get these $a^4$ factors which you just cannot get rid of, thus it seems like one can't derive the scale factors also by mere substitution... Now it might just be late & that I've worked too much, hence my question is: **Is it possible to get the scale factors for orthogonal curvilinear coordinate systems by simple substitutions into the scale factor formulae for the ellipsoidal coordinate system, analogous to the way one can derive the formulae for Cartesian components in terms any 'standard' orthogonal coordinate system by substitutions into the formulae for them expressed in terms of ellipsoidal coordinates? If not, why not?** If there is then the gradient, divergence, Laplacian & curl become extremely easy to calculate in the standard orthogonal coordinate systems, & working separation of variables for all the standard pde's becomes immensely easier, if not I'd have to derive the scale factors by differentiation of completely crazy formulas (at least there's an easy way to remember any formula in $\vec{r}(u^1,u^2,u^3) = ...$ from which we can derive the scale factors thanks to Morse & Feshbach!!!) Thanks for any help possible.


title: Why the red-shift of distant galaxies is considered to be the effect of expanding spacetime?

text: Why it's not explained just by Doppler redshift caused by faster movement of those galaxies billions of years ago when that light was emitted? Would the speeds of the galaxies necessary for Doppler redshift to explain all of the observed galaxies redshift be unreasonable or is there something else that prevents such explanation to be sufficient?


title: Proof that 4-potential exists from Gauss-Faraday field equation

text: This is a problem concerning covariant formulation of electromagnetism. Given $$\partial^{[\alpha} F^{\beta\gamma]}= 0 $$ how does one prove that $F$ can be obtained from a 4-potential $A$ such that $$F^{\alpha \beta}=\partial^{\alpha} A^{\beta} - \partial^{\beta} A^{\alpha} $$


title: What does "nearly infinite mass" mean?

text: I am sure this is a silly question, but I was reading something that described the pre big-bang universe as having "nearly infinite mass." How can something be "nearly" infinite? The term seems to make no sense.


title: What does Brian Greene mean when he claims we wont be able to observe light from distant stars due to the universe's expansion?

text: Brian Greene in this TED talk about possible multiverse, claims tomwards the end (At around 18:00 mark) this statement. 'Because the expansion is speeding up, in the very far future, those galaxies will rush away so fast, we wont be able to see them, not because of technological limitations, but because of the law of physics.' This seems to me against the basic premise of relativity, namely that two objects are moving so fast away from each other that their relative speed is greater than that of light. Can anybody explain whether he really meant what I understood, and if not what he really meant.


title: How widespread is the meme "QM is counterintuitive" in academic physics?

text: I have recently entered university -- studying CS -- and I have spoken to many physics students on campus. Most of these -- when propmted -- will gladly proclaim that QM is counterintuitive, and not something you are supposed to understand. To my knowledge, no one proclaims similar things about, e.g. Relativity, that is just difficult mathematics; but we have the rubber sheet analogy and all that. Do any professionals share this opinion? Are we purposefully imparting it on the students? Where does this meme originate, historically?


title: How would one show that a nonabelian field strength tensor transforms in a certain way under a local gauge transformation?

text: How would one show that the nonabelian ${F_{\mu\nu}}$ field strength tensor transforms as ${F_{\mu\nu}\to F_{\mu\nu}^{\prime}=UF_{\mu\nu}U^{-1}}$ under a local gauge transformation? Rather than going through this in a very manual manner (i.e., gauge transform ${A_{\mu}\to A_{nu}^{\prime}}$ and use the explicit expression for ${F_{\mu\nu}}$), it was suggested to me to show first that ${D_{\mu}\to D_{\mu}^{\prime}=UD_{\mu}U^{-1}}$ and then gauge transform the commutator relation ${\left[D_{\mu},D_{\nu}\right]}$ for ${F_{\mu\nu}}$: ${\left[D_{\mu},D_{\nu}\right]\psi\left(x\right)-gF_{\mu\nu}\psi\left(x\right)}$.


title: Understanding What A Wakefield Describes?

text: I am trying to understand the some of the properties of wakefields, namely the energy change. So, as a preface I am interested in primarily the wakefield due to electron beams as they progress through a curved section (the eletcrons radiate strongly when they are in circular motion). There are two main/simple regimes:   1. When the wakefield is constant and not dependent on how far Δθ the electrons have traversed, we have a wakefield like so: $$\frac{dE}{sds}(z) $$ Which to my understanding (which I am very certain of) describes the $$\frac{dE}{ds}$$ (the change in energy per distance traveled along its curved trajectory) for a given z (position along the eletcron beam, where zero is defined as the certer of the eletcron beam which we can consider to be gaussian-ly distributed). 2 When the wakefield is not constant and is dependent on how far Δθ the eletcrons have traversed, we have the wakefield like so: $$\frac{dE}{ds}(z,θ) $$ Where this describes the $$\frac{dE}{ds}$$ (the change in energy per distance traveled along the curved trajectory) for a given z (position along the eletcron beam) and θ (the amount the eletcrons have traversed). Now, the main difference between 1 and 2 is the fact that for two $$\frac{dE}{ds}$$ is changing wrt θ (is some function of theta). If you were to integrate regime 1, wrt ds from 0 to L (the total path length), then you would get the total energy change through the curved region as a function of z: $$ Etotal(z,θ) $$. Now this is where I start getting confused: If we turn our attention to regime two with θ dependence. WHat do we have when:   1. We integrate $$\frac{dE}{ds}(z,θ) $$ wrt to θ from 0 to θ (thet total travesrved angle of teh eletcron beam)? We would have something like $$\frac{dE}{ds}(z) $$ which is still a function of ds (the path travesersed).   2. We integrate $$\frac{dE}{ds}(z,θ) $$ wrt to the path ds? We would now have something like $$Etotal(z,θ) $$ which is still a function of θ. Any help on conceptually understanding this would be greatly appreciated! I have been at it for days!


title: Impact of friction on a fallen body

text: If a body travelling at speed falls to the ground through an arc from a certain height (someone walking who trips, for example), how does friction of the ground surface affect the forces impacting upon the body (treating it as a point mass) when it reaches the ground? How can the net forces on the body and the net vertical impact velocity be calculated?


title: N-body forces in classical mechanics

text: For a system of two interacting particles `1`, `2` we get from the conservation of momentum $$ \dot{\bf{p_1}} + \dot{\bf{p_2}} = 0$$ and from conservation of angular momentum $$ \bf{r_1} \times \dot{\bf{p_1}} + \bf{r_2} \times \dot{\bf{p_2}} = 0$$ so $$ \bf{F_1} = -\bf{F_2} $$ and $$ \bf{r_{12}} \times \bf{F_1} = 0 $$ where $ \bf{r_{12}} = \bf{r_1} - \bf{r_2} $ is the separation between particles. So basically only central forces $\bf{F}=\bf{F}\left(|\bf{r_{12}}|\right)$ are allowed. But for a system of three and more interacting particles we don't have such restrictions. E.g. for 3 particles $$ \bf{F_3} = -\bf{F_1}-\bf{F_2}$$ and $$ \bf{r_{13}} \times \bf{F_1} + \bf{r_{23}} \times \bf{F_2} = 0 $$ (two more likewise expressions for `(21,31)` and `(12,32)`). And this is, I believe, as far as one can get in general case. We can expand $$ \bf{F_1} = \bf{F_{1,2}} + \bf{F_{1,3}} + \bf{R_1} $$ where $\bf{F_{1,2}}$ and $\bf{F_{1,3}}$ are for two-body interactions, but no one forbids the existence of 3-body force $\bf{R_1}\left(\bf{r_{12}}, \bf{r_{23}}, \bf{r_{31}}\right)$. Are there any known examples or I am missing something?


title: What is the linearized form of relativistic hydrodynamics?

text: **What I'm looking for:** Let $\vec{W}$ be the vector of conserved variables for a 1-dimensional, adiabatic, (special) relativistic, electrically neutral fluid. (Yes, something that simple!) I'm looking for a paper that derives the form of the matrix $A$ that linearizes the evolution equation. That is, $$ \partial_t \vec{W} \approx A \partial_x \vec{W}. $$ Alternatively, the matrix $B$ that does the same for the conserved variables will work: $$ \partial_t \vec{U} \approx B \partial_x \vec{U}. $$ These matrices are useful in fluid computations for several reasons. I need more than just the eigenvalues (used in certain solvers) - I also need the eigenfunctions. I've found plenty of papers that treat the nonrelativistic case (for one of many, many examples, see the appendices of Stone et al. 2008, ApJS 178 137) both with and without magnetism. I've found some papers that just quote a few eigenfunctions for relativistic MHD, but these are often the ones that are interesting only with magnetism in play. I'm looking for whatever paper derives these matrices in the rather simple case I'm dealing with. An answer that gives the derivation would be nice, but I'm also trying to locate the relevant literature. In particular, I would like a paper addresses the physical reliability/usefulness of the linear approximation. **Background:** There are three primitive variables defining my fluid: rest-mass density $\rho$, velocity $v$, and pressure $p$. By convention, these variables are combined into a vector $\vec{W} = (\rho, v, p)^\mathrm{T}$. Many approaches to evolving fluids deal with the equations in flux- conservative form. Here, the conserved variables are \begin{align} D & = \gamma\rho && \text{(lab-frame density),} \\\ M & = Dh\gamma v && \text{(relativistic momentum),} \\\ E & = Dh\gamma - p && \text{(relativistic energy).} \end{align} Here I define \begin{align} \gamma & = \frac{1}{\sqrt{1-v^2}} && \text{(standard Lorentz factor),} \\\ h & = 1 + \frac{\Gamma}{\Gamma-1} \left(\frac{p}{\rho}\right) && \text{(enthalpy),} \end{align} where the ratio of specific heats $\Gamma$ is assumed to be constant. These are often combined as $\vec{U} = (D, M, E)^\mathrm{T}$. Along with the vector of conserved quantities, we can define the vector of fluxes $$ \vec{F} = \begin{pmatrix} Dv \\\ Mv + p \\\ M \end{pmatrix}. $$ Then we have the relation $$ \partial_t \vec{U} + \partial_x \vec{F} = 0, $$ which is used as the basis for most Riemann solvers and many fluid codes in general.


title: Question regarding centripetal force and tangential force

text: I was asked to think of a situation where a car driver only feels centripetal acceleration, but exerts no tangential acceleration. The first thing that came to mind was orbit, where the satellite does not need to speed up but be caught by the gravity of Earth, and keeps orbiting around it. So, my question is this. I tried to consider a case where a car is driving towards a loop with no friction so that it will not need any tangential acceleration, but the centripetal acceleration is not constant due to gravity. One of my friends told me that a banked road can do the same thing as orbit, but I did not understand his explanation at all. I cannot imagine a car moving in circles on a banked road without accelerating tangentially. Can someone explain me this kinematics ?


title: What would be the effective resistance of the ladder of resistors having n steps

text: I'm a tutor. This is a high school level problem. In high school, every one have might have solved a problem of effective resistance of a ladder of resistors having infinite steps. Now the problem is little different. what if it has `n` steps instead of infinite steps. How to calculate effective resistance in that case?![enter image description here](http://i.stack.imgur.com/n1eIX.jpg)


title: General Physics II Practice Question

text: I have a test in a few hours, and my professor gave us a practice test, and I'm stuck. Could you give me a hint as to how to approach this problem, equations I could use. It's an algebra based class so I'd avoid using calculus equations. Thank you. _Three thin infinite wires carrying currents I in the same direction go perpendicularly to the paper sheet that they intersect at the points forming an equilateral triangle of side L. Calculate the force acting on each wire per unit length. What is the direction of the forces?_


title: Partial and total time derivatives of the Hamiltonian

text: When does the total time derivative of the Hamiltonian equal the partial time derivative of the Hamiltonian? In symbols, when does $\frac{dH}{dt} = \frac{\partial H}{\partial t}$ hold? In Thornton & Marion, there is an identity in one of the problems, for any function $g$ of the generalized momentum and generalized coordinates, the following is true: $$ \frac{dg}{dt} = [g,H] + \frac{\partial g}{\partial t},$$ where H is the Hamiltonian. It seems to me that if we let $g = H$, then, since the Hamiltonian clearly commutes with itself, then $\frac{dH}{dt} = \frac{\partial H}{\partial t}$ is always true. Is this the correct way to look at it?


title: Physical meaning of Laplace-Beltrami eigenfunctions?

text: The eigenfunctions of Laplace-Beltrami operator are often used as the basis of functions defined on some manifolds. It seems that there is some kind of connection between eigen analysis of Laplace-Beltrami operator and the natural vibration analysis of objects. I wonder, is my intuition true? What is the physical meaning of Laplace-Beltrami eigenfunctions? For now, I only know that the eigenfunctions of the Laplace-Beltrami operator are real and orthogonal, thus they could be used as the basis of functions on the manifold where the functions are defined.


title: Any liquid metallic alloys which are safe to handle with bare hands?

text: http://en.wikipedia.org/wiki/Liquid_metal describes some alloys which are liquid at room temperature containing gallium, and sodium-potassium. We are advised not to handle them, and mercury, with unprotected skin. Are there any which are safe (as safe as, say, alcohol or glycerine)?


title: How does ultrasonic horn produce a convection current in the water?

text: When I was using ultrasonic horn in a beaker, I notice that there are convection currents in the beaker and stir up my substance. I don't understand why it produce water current, I thought that it will just vibrate like the ultrasonic bath. So why does ultrasonic horn create water currents? Thank you.


title: Why are interacting noncommutative quantum field theories with space-time noncommutativity unitary?

text: Can anyone explain in a simple manner why interacting noncommutative quantum field theories with space-time noncommutativity of the Moyal bracket sort are unitary? Thanks.


title: Specific differential equation in RLC circuit

text: I have been studying differential equations in RLC circuits: **_(a generator with fixed EMF $=E$,a capacitor $C$, an inductor with inductance $L$ and internal resistance $r$, and a separate resistor $R$)_** with the elementary cases accounting for $q$ (the charge on the capacitor), $V_c$ its voltage or$i$ the current flowing through the circuit (such as $\ddot q+\frac{R+r}{L}\dot q+\frac{q}{LC}=E$). I've been trying to find such a differential equation for the compound voltage $V_{L,r}=V_L +V_r=ri+L\frac{di}{dt}$, which didn't seem to satisfy the criteria for a "regular ODE": $\fbox{$\ddot V_{L,r}+\frac{R}{L}\dot V_{L,r}+\alpha V_{L,r}=\frac{\alpha r}{L}e^{-rt/L}\int e^{rt/L} \ V_{L,r} \ dt$}$ with $\alpha=\frac{-Rr}{L^2}+\frac{1}{LC}$ I started with trying to express $i$ through $V_{L,r}$ as all relevant voltages are expressed in $i$ (resistor), $q$ (capacitor) and $\frac{di}{dt}$ ($V_{L,r}$). At first through this relation by applying regular ODE properties: $V_{L,r}=ri+L\frac{di}{dt} \rightarrow \fbox{$i=\frac{1}{L}e^{-rt/L} \int e^{rt/L} \ V_{L,r} \ dt$}$, and then replaced in : $E=V_{L,r}+Ri+\frac{q}{C} \rightarrow 0=\frac{dV_{L,r}}{dt}+R\frac{di}{dt}+\frac{i}{C}$ and obtained the aforementionned DE. Should I be using any other physical relation


title: What do the various journals and publications bodies offer for their subscriptions?

text: I would like to abide by the site policies on not asking open-ended/chatty questions so if someone feels there is a better location or wording for this question, please feel free to modify it as appropriate. I am normally a big fan of open source/open access work and I believe I have learned a great deal from such sources. There is an open-access journal question here. Nonetheless, there are times where I really do want a specific article that is not available through non-commercial means. I am currently studying to return to school (in other words I don't have access to an institutional subscription) for a physics PhD and reading published work is becoming increasingly important to me. As a result I am considering subscribing to one of the big publishing houses (Elsavier, ScienceDirect, Science, Nature, etc.). Before I spend that kind of money, I would like to know what other physicists think of these organizations and who offers the best value. If I decided to opt for a subscription, which would be the best? Is a subscription even the best idea, or should I perhaps buy individual articles as needed? PS - I know the answer to these questions depends on the area of interest, my interests lie in quantum field theories and the like, but feel free to answer for your particular area of expertise.


title: What is supposition of equilibrium? How do Rayleigh, Jean know the electromagnetic wave in equilibrium behave?

text: In a cavity of dimension L, the wave must give zero amplitude at the wall, means wave equation has zero amplitude. Why? Answer from hyperphysics "since a non-zero value would dissipate energy and violate our supposition of equilibrium. To form a standing wave, the reflection path around the cavity must produce a closed path." 1) what is supposition of equilibrium? 2) in 3D, how do we know $$E=E_0sin\frac{n_1\pi x}{L}sin\frac{n_2\pi y}{L}sin\frac{n_3\pi z}{L}sin\frac{2\pi ct}{\lambda}$$ from link http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html


title: Lasers can demagnetize ferromagnets?

text: How is it possible to demagnetize a magnet with a laser? Source: http://www.helmholtz- berlin.de/pubbin/news_seite?nid=13657&sprache=en&typoid And the paper: http://prb.aps.org/abstract/PRB/v88/i21/e214404 How does this work?


title: Why an infinitely measuring apparatus in gravity is not possible?

text: In the discussion of the amplituhedron paper (arXiv:1312.2007), there is the following discussion in paragraph 14.outlook (page 28): > Quantum mechanics forces us to divide the world in two pieces - an infinite > measuring apparatus and a finite system being observed. However for any > observations made in a finite region of space-time, gravity makes it > impossible to make the apparatus arbitrarily large, since it also becomes > heavier, and collapses the observation region into a black hole. Can one elaborate this point? Is this related to coordinate invariance?


title: Effect of waters changing specific gravity on objects apparent weight placed in liquid

text: My goal is to monitor the change in specific gravity of a liquid over a period of time. My question is: What are the appropriate formula for determining expected apparent weight of an object immersed in a liquid where the liquids specific gravity g/ml is expected to change? EG. If I were to take an object who's density is 2.6 (average for glass) weighing 100 grams and plunk it into distilled water I believe I should expect an apparent weight should be roughly 61.53 grams. Please let me know if I am just horridly wrong. So then if that distilled waters density/specific gravity were to change say to 1.010, would my new apparent weight of the object be 61.15 grams? My math is not solid in this. I'm basically using ratios in order to produce these answers. Please for the sake of simplicity if you are to choose to answer leave out extenuating circumstances such as temperature of the liquid/object and possible compression of the object due to pressure. If you do chose to add extenuating circumstances I would ask to add those concepts as tertiary answers. I'm sure that my question is probably very basic, but grasping the concepts has proven perplexing to me. I am probably not using the correct search. Your help in this simple question is greatly appreciated.


title: Why do nearsighted people see better with their glasses *rotated*?

text: If you are nearsighted (like me), you may have noticed that if you _tilt_ your glasses, you can see distant objects more clear than with normally-positioned glasses. **If you already see completely clear, you can distance your glasses a little more from your eyes and then do it.** To do so, rotate the temples while keeping the nosepads fixed on your nose, as is shown in the figures. As I said, starting with your glasses farther than normal from your eyes, you can observe the effect for near objects too. (By _distant_ , I mean more than 10 meters and by _near_ I mean where you can't see clear _without glasses_ ) **Note that if you rotate more than enough, it will distort the light completely.** Start from a small $\theta$ and increase it until you see blurry, distant objects more clear. (You should be able to observe this at $\theta\approx20^\circ $ or maybe a little more) When looking at distant objects, light rays that encounter lenses are parallel, and it seems the effect happens because of oblique incidence of light with lenses: ![enter image description here](http://i.stack.imgur.com/QpPys.png) The optical effect of oblique incidence **for convex lenses** is called coma, and is shown here (from Wikipedia): ![enter image description here](http://i.stack.imgur.com/lIUw6.png) I am looking for an explanation of how this effect **for concave lenses** (that are used for nearsightedness) causes to _see_ better. One last point: It seems they use plano-concave or convexo-concave lenses (yellowed lenses below) for glasses instead of biconcave ones. ![enter image description here](http://i.stack.imgur.com/s3HdJ.png)


title: Heisenberg picture usage - Merzbacher 14.106

text: I am trying to understand a line in the quantum mechanics book by Merzbacher, specifically the second line of equation 14.106. The problem is a forced quantum harmonic oscillator. The Hamiltonian operator in the Schrodinger picture is $H_S(t) = \hbar \omega_0 (a^{\dagger}a + 1/2) + \hat{x}f_x(t) +\hat{y}f_y(t)$ Here $\hat{x}$ and $\hat{y}$ are the quadratures of motion of the oscillator, ie. dimensionless position and momentum. In other words $a = (1/\sqrt{2})(\hat{x}+i\hat{y})$ If we define $f(t)\equiv -f_x(t)+if_y(y)$ we can rewrite the Hamiltonian as $H_S(t) = \hbar \omega_0 (a^{\dagger}a + 1/2) + af(t) + a^{\dagger}f^*(t)$ The thing that I don't understand is that Merzbacher goes from the previous equation to $\bar{H}(t) = \hbar \omega_0 (\bar{a}^{\dagger}(t)\bar{a}(t) + 1/2) + f(t)\bar{a}(t) + f^*(t)\bar{a}^{\dagger}(t)$ where the overbars indicate Heisenberg picture operators. The question is, how does he do this? Since the Schrodinger picture Hamiltonian is time dependent and doesn't commute with itself at different times, the conversion from Schrodinger to Heisenberg pictures isn't simple. Can someone explain how this is done? My approach is to say that the propogator in the Schrodinger picture is some operator $T(t)$, ie. $T(t)$ propagates the Schrodinger picture state vector forward from time 0 to time $t$. Then I define the Heisenberg picture operators by $\bar{A}(t) \equiv T^{\dagger}(t)A_S(t)T(t)$ Using $i\hbar \dot{T}(t) = H_S(t)T(t)$ you can show $i\hbar \frac{d\bar{A}(t)}{dt} = \left[ \bar{A}(t), H_S(t) \right] + T^{\dagger}(t)(\partial A_S(t) / \partial t)T(t)$ Suppose we want to solve for $\bar{a}(t)$. The Schrodinger picture operator $a$ has no time dependence so the equation of motion is $i\hbar \frac{d\bar{a}(t)}{dt} = \left[ \bar{a}(t), H_S(t) \right]$ If the Schrodinger picture Hamiltonian commuted with itself at different times this would be simple to work with, because _in that case_ $H_S(t)=\bar{H}(t)$. We would then be able to use the fact that $\left[\bar{a}(t), \bar{a}^{\dagger}(t) \right] = 1$ to evaluate the commutator on the right hand side of the equation of motion. However, in the present problem this is not the case so I don't know how to compute the commutator.


title: Orbital of Hydrogen molecule

text: does anybody here know an analytical approximation of the bonding hydrogen orbital MOLECULE? I am looking for a good approximation to this orbital, that might be in some textbooks to get an impression how this whole concept of bonding antibonding works?


title: Maximum electron momentum in $\beta^-$-decay

text: This _should_ be easy, but I think I have a mind-block... For $\beta^-$-decay, what is the maximum possible momentum for the electron? The two equations I can use are conservation of energy and conservation of momentum, but I have three unknowns: Momentum of electron, nucleus and anti- neutrino, so what am I missing? Could I just set the kinetic energy of the nucleus to zero and work from there?


title: How can I simulate a model electronic hole?

text: Suppose I can solve time-dependent Schrödinger equation for several 1D particles (currently 3). I'd like to see, what an electronic hole is and how it behaves — in a series of numerical experiments. I know that a hole is lack of electron in a sea of occupied electron states, but I think I don't quite understand, what it really is: do I need to have electron repulsion to see any useful effects? Do I need much more electrons for such a simulation than 3? What initial conditions should I use to _see_ the hole? I'm thinking of using a model "crystal" potential with 3 cells — would this be enough? As an example of what I'd like to actually see is exciton, namely how its wave packet wanders across the crystal. For an electron in conductivity band, taken as a wavepacket, I'd expect it to look like increase in probability density in the place where the wavepacket is located, and for hole it might be a similar decrease in charge density, so I guess the exciton should look like an increase of charge density in a wave packet and decrease around this wave packet. Is it right? Or is it actually invisible as a charge density? Another example would be seeing excitonic states in band gap, but for this I don't really understand, what to compare it with — should I use some single- particle approximation to compute band structure without excitonic states, and then after computation of true energy states search for extra states in band gap, or how should I go about finding them?


title: Free HEP dataset for teaching and demo purposes?

text: I'm wondering if there are any free particle physics datasets out there, for use in teaching, demonstrations, developing analysis techniques etc.. I'm looking for data events e.g. as ROOT trees or in a similar format, together with a standard set of background events and postprocessing, or maybe even a simple framework with detector simulation to create my own events. I'm not looking for the very "raw" data, but something you could do a simple analysis on, like plot the dilepton mass and see resonances. The kind of experiment doesn't matter that much, as its for illustration purposes (can be e+e-, pp, medium or high energy). Publishing raw data is common in other areas or fundamental (non-applied) research, especially in government-funded astronomy experiments. Imaging my astonishment when I started in this field that you couldn't just download "the data" from www.cern.ch as a torrent :-). For collaboration-political reasons, and because the data is considered too ununderstandable for laypersons, it is tightly controlled by the experiments. Yet, internally, especially on mature collaborations, you often have "the (processed) dataset", "the standard MC", "the standard corrections and uncertainties", and writing a simple analysis (for demonstration, not for publication) boils down to just writing custom code for event selection, so it should be entirely possible for a physics student or even an interested layperson to make a little sense of the data. So, I believe that at least one of the now closed experiments (LEP, Tevatron, Hera, ...) might have published their framework and data, but I couldn't find anything on the net. Does anyone know of such a case?


title: Black Hole evaporation through virtual couples at the horizon

text: I read about vacuum energy. It explains the Hawking radiation, the black hole necessary radiation: > Physical insight into the process may be gained by imagining that particle- > antiparticle radiation is emitted from just beyond the event horizon. Vacuum > fluctuations are always created as particle–antiparticle pairs. The creation > of these virtual particles near the event horizon of a black hole has been > hypothesized by physicist Stephen Hawking to be a mechanism for the eventual > "evaporation" of black holes. Is this "insight" supposed to make us to think that   1. the virtual pair created is a part of black hole so that when half flies away then the BH mass is reduced? The article on vacuum energy says that the vacuum energy is an underlying background energy that exists in space throughout the entire Universe. So, it is not related to the black holes, though one particle of the couple may create the salute that you may consider as BH evaporation, it actually covers up the fact that the **second particle flies into the BH, increasing its mass**.   2. Why do we believe that the receding half of the couple does not fall back to the Black Hole? Yes, it has escaped the horizon but the (pretty strong) BH gravitation is still in action, and it is only few neutons less than $\infty$ because we are still almost at the horizon initially. This means that to actually escape and not to fall back into BH, the speed of the receding particle must be virtually infinite. I doubt that it is likely that you will have many such virtual particles right at the event horizon. It is much much (Almost surely) more likely that **"escaped" half of the couple will also eventually fall onto the black hole, increasing its mass**. So, considering the virtual particles of vacuum energy, we find two ways to add mass to the BH. Why do they call it BH (mass) evaporation?


title: What is the temperature of the surface and core of a neutron star formed 12 billion years ago now equal to?

text: In what part of the spectrum is it radiating? In the infrared, in the microwave? Or is not radiating anymore at all? In russian: Чему сейчас равна температура поверхности и ядра нейтронной звезды, которая образовалась 12 миллиардов лет назад? В каком диапазоне она сейчас излучает? В инфракрасном, микроволновом? Или не излучает вообще?


Why is electric flux through any closed surface $q/\epsilon_0$? In schools we are only taught of its simplest case, i.e. flux through a sphere with charge centered at origin. And then it is generalised to all closed surfaces. Is there really any proof of flux through all closed surfaces.


title: Einstein action and the second derivatives

text: I have naive question about Einstein action for field-free case: $$ S = -\frac{1}{16 \pi G}\int \sqrt{-g} d^{4}x g^{\mu \nu}R_{\mu \nu}. $$ It contains the second derivatives of metric. When we want to get the Einstein equation (which doesn't contain the third derivatives), we must use variational principle. The variation of "problematic" factor $R_{\mu \nu}$ (which contains the second derivatives) is equal to $$ \delta R_{\mu \nu} = D_{\gamma}(\delta \Gamma^{\gamma}_{\mu \nu}) - D_{\nu}(\delta \Gamma^{\lambda}_{\mu \lambda}). $$ So the corresponding variation of action may be rewritten in a form $$ \delta_{R_{\mu \nu}} S = -\frac{1}{16 \pi G}\int d^{4}x \sqrt{-g}\partial_{\lambda}(g^{\mu \nu}\delta \Gamma^{\lambda}_{\mu \nu} - g^{\mu \lambda}\delta \Gamma^{\sigma}_{\mu \sigma}). \qquad (1) $$ Then one likes to say that it is equal to zero. But why it must be equal to zero? It isn't obvious to me. After using the divergence theorem $(1)$ becomes $$ \delta_{R_{\mu \nu}} S = -\frac{1}{16 \pi G}\int dS_{\lambda} \sqrt{-g}(g^{\mu \nu}\delta \Gamma^{\lambda}_{\mu \nu} - g^{\mu \lambda}\delta \Gamma^{\sigma}_{\mu \sigma}). $$ Why it must be equal to zero? It is metric, not physical field, even if Christoffel symbols refer to the gravitational field, so I don't understand why it must be equal to zero at infinity.


title: Quantum version of the Galton Board

text: If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. http://mathworld.wolfram.com/GaltonBoard.html ![Galton Board](http://i.stack.imgur.com/ll7PE.gif) What kind of distribution would one see, if the particles would obey the laws of quantum mechanics (as a thought experiment) ? Wouldn't interference effects lead to a different distribution than the normal distribution?


title: Explicit calculation of bosonic string Weyl invariance at one loop

text: I have been trying to do all the calculations in the Green, Schwarz and Witten Superstring Theory textbook. At the end of chapter 3, the author did one-loop calculation for Weyl invariance for the bosonic string, in section 3.4.2 and 3.4.5. In the latter section more fields were included, and not much calculation detail was given. The actions are $S_1=\frac{-1}{4\pi\alpha'}\int d^2\sigma\sqrt h h^{\alpha \beta}\partial_\alpha X^\mu \partial_\beta X^\nu g_{\mu \nu}$ $S_2=\frac{-1}{4\pi\alpha'}\int d^2\sigma \epsilon^{\alpha \beta}\partial_\alpha X^\mu \partial_\beta X^\nu B_{\mu \nu}$ $S_3=\frac{1}{4\pi}\int d^2\sigma \sqrt h \Phi (X^\rho) R^{(2)}$ I consider those one-loop calculations to be very good exercise, but as a beginner in string theory I find myself not able to do them. Therefore may I ask if there are some notes/papers in literature that give explicit calculation or point out key steps? Thank you very much!


title: Is there a general term for the situation where an improperly chosen measurement range results in a bias?

text: For example, consider the following measurement: A sensor can measure a specific physical quantity, and has a range of $0$ to $100$. All values above $100$ will be shown as 100. We now take the following measurements: $78$, $100$, $82$, $94$, $100$, and we conclude that the average is $90.8$. However, the true values were $78$, $112$, $92$, $94$, $105$, resulting in the true average of $94.2$. Both end results are in the valid measurement rage, but individual measurements are not. Can we call it saturation? It has a similar meaning in photography, but in mathematics it seems to have a completely different meaning.


title: The thermodynamics of heating water in a rigid container

text: When the pressure on the liquid surface is less than the vapor pressure of the liquid at a given temperature, the liquid will start to evaporate. This is common sense. The problem is more difficult when the liquid and its vapor are heated inside a rigid container, with the specific volume of the mixture less than the critical specific volume: ![enter image description here](http://i.stack.imgur.com/ESHNv.png) According to my professor's notes, the level of the liquid in the container would fall. Why? What is the physics (or the thermodynamics) behind this? If a mixture is heated in a constant volume what happens to it? I know that it will not boil completely because it would attain equilibrium pressure with its vapor soon enough, but how do we fix the state when it would stop boiling? Why is it that if the specific volume of the mixture is less than the critical specific volume, the level of the liquid will fall when heated?


title: Centre of mass, integral

text: I was answering a question on proving the parallel axis thereom for angular momentum and came across this: $$\int Yy'dm=Y\int y' dm=0$$ Where the position of the center of mass of an object is given by $(X,Y,Z)$, $(x',y',z')$ is a position relative to the centre of mass and m is the mass of the object. My text book (Introduction to classical mechanics) says that this is due to the definition of the centre of mass. There are two things that I don't understand firstly why is $Y$ independent of mass whilst $y'$ is not? and secondly please can you explain what definition of the centre of mass they are using to get the reslut above? I really have no idea to the answer for either of these questions?


title: Optical signal filters

text: Are there any optical filters which filter the signal's frequency and not based on the wavelength of the light? So what I mean is, if I have a modulated/pulsating light signal riding on a large DC offset, is there some way I can filter out the DC offset using optics alone? I've tried searching the internet for this but this is obviously hard since I don't know which keywords to use... "optical filters" are always based on filtering the spectrum of light, not on the temporal signal. Would appreciate any help and/or discussions/debates about this, thanks a lot!


title: Liquid Column "Recoils" in a Sealed Cylinder When Hit by a Piston -- Is it Possible?

text: Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to the system), the liquid in the cylinder exists in equilibrium with its vapor at the vapor pressure of the liquid, applicable at room temperature. Suppose that the bottom of the cylinder is fitted with a piston. Note that the system is still sealed. Now imagine that the piston moves upwards. The liquid column moves upwards, the volume the vapor occupies decreases, but the vapor still exists at the vapor pressure of the liquid (assuming that thermodynamic equilibrium can be achieved fast enough). What's interesting is when the piston move downwards. If the piston moves at a slow speed, the liquid column should stay "on top of" the piston (without any "gap" between the column and the piston). Now, if the piston moves downwards fast enough (or when the downward acceleration is high enough), the liquid column shall "leave" the piston, and a "packet" of vapor shall be formed between the piston and the liquid column. (Please refute the former claim if you think it's wrong.) Why? if the "friction" between the cylinder walls and the liquid column is negligible, and the liquid column is already in a state of free-falling, there is no mechanism to "pull" it downwards further anymore. Now, imagine that the piston moves upwards again. Then the liquid column shall "collide" with the piston. Will it "stick" to the piston, as in an inelastic collision, or recoil, as in an elastic collision? _P.S. After thinking for a while, I think it is not at all an easy question to answer. Now whether the liquid will "recoil" (not "slosh", which implies that the liquid changes shape) depends on how momentum is transferred from the piston to the liquid column. Please refer to the youtube video for the "beer bottle trick". If the cavity formed at the bottom is a "vacuum", which is probably the case, then when the liquid "smash back", the atmospheric pressure shall press on the liquid column, and most probably it will not "recoil". On the other hand, if the cavity formed is gas-filled, then the kinetic energy from the liquid (which is trying to "smash back" on the glass bottle) may be dissipated to the gas (in the original gas-filled cavity), through the formation of many tiny cavitations (claim: the latter claim is not sound; I am just guessing). For as long as the impact is "dampened", a recoil will not happen.   Indeed there are many ways in which a liquid may dissipate energy, because it's formless/shapeless, and there's viscosity in the picture. The more "flexible" it is to energy dissipation, the less likely it is to recoil._


title: Redshift Dependence in the Spatial Orientation of SDSS Galaxies having Redshift 0.19 to 0.20

text: Does redshift depend on the spatial orientation of SDSS galaxies with redshift in the range 0.19 to 0.20 ?


title: Rotate a long bar in space and get close to (or even beyond) the speed of light $c$

text: Imagine a bar spinning like a helicopter propeller, At $\omega$ rad/s because the extremes of the bar goes at speed $$V = \omega * r$$ then we can reach near $c$ (speed of light) applying some **finite** amount of energy just doing $$\omega = V / r$$ The bar should be long, low density, strong to minimize the amount of energy needed For example a $2000\,\mathrm{m}$ bar $$\omega = 300 000 \frac{\mathrm{rad}}{\mathrm{s}} = 2864789\,\mathrm{rpm}$$ (a dental drill can commonly rotate at $400000\,\mathrm{rpm}$) $V$ (with dental drill) = 14% of speed of light. Then I say this experiment can be really made and bar extremes could approach $c$. What do you say? **EDIT** : Our planet is orbiting at sun and it's orbiting milky way, and who knows what else, then any Earth point have a speed of 500 km/s or more agains CMB. I wonder if we are orbiting something at that speed then there would be detectable relativist effect in different direction of measurements, simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity, simply because $V = \omega * r$ What do you think?