title: Winding number in the topology of magnetic monopoles

text: I am reading on magnetic monopoles from a variety of sources, eg. the Jeff Harvey lectures.. It talks about something called the winding $N$, which is used to calculate the magnetic flux. I searched the internet but am not being able to understand the calculation done in this particular case. $g=-\frac{1}{8}\int_{S^2_\infty} Tr([d\hat{\Phi},d\hat{\Phi}],\hat{\Phi})$ Then the author says that > Now $\Phi$ restricts to a map $\Phi : S_\infty^2 → S^2$ , where the target > is the unit sphere in $su(2)$. This map has some degree $N$ , and it is easy > to verify that the right-hand side of the above equation is $−2\pi$ times > this. Therefore $g = −2\pi N$ . What is $N$, the winding number also called as the degree on the map? By what i have learnt, it is the number of times you wind an object unto the another, then shouldn't the integral be $N*4\pi$, as $4\pi$ is the surface area of $S^2$.


Is there any scientific evidence that demonstrates why time passes? Or is it just an opened question?


title: Is there more mass in stars or interstellar medium?

text: From what I gather the interstellar medium has about about 1 atom per cubic centimeter. But on the other hand, as they say, "Space is big, really really big" So if it is known (or at least theorized about) what percent of the universes matter is in the following: black holes, stars, and interstellar medium?


title: Where can I find information on space navigation, and the people who pioneered it?

text: I'm doing a paper for school about space navigation. It's an interesting subject, but upon searching google, all I could find were non-detailed explanations of astrophysics that I think are meant for children, and a few somewhat-more-detailed articles about other subjects. I remember learning about the subject in high school physics class, and I remember there were people that were credited for there work in space exploration. Who are those people? My paper is specifically about 'navigating', ie determining when to leave the Earth, where the spacecraft is headed, and where certain astronomical objects will be when the spacecraft gets there. I'm looking for articles (or any information) on the work that goes into that, and the people who should be credited for that work, and for pioneering it.


title: cause of maximum kinetic energy and elastic potential energy at the same point of a transverse wave in a string

text: Suppose a string element oscillating transversely in _SHM_ having both kinetic energy and elastic potential energy travels with velocity $u$. Let $y(m)$ be the amplitude. When it reaches $y(0)$, it has max. $K.E.$ and elastic $P.E.$ together at the same time. But in _SHM_ , when the kinetic energy is max. the potential energy is min. but in the string it is contradicted. Does transverse wave violate _SHM_ and if not why at the same time it has both K.E. and P.E. maximum unlike _SHM_?


title: Why 1 Month LHC Magnet Cooling Times

text: An often quoted figure is that the LHC magnets take a month to completely cool and a month to warm. There is never an explanation as to why that is. I can conjure any number of reasons (slow changes to prevent stress, very low temperature deltas, gremlins can hold their breath for 29 days, etc) but I can't find any facts. I don't suspect the answer will be complex, but I'd just like to know why it takes a month and not, say, 14.6 hours.


title: Does diamond dust conduct heat as well as diamond?

text: Diamond is one of the best thermal conductors you can get. If the diamond is crushed into dust and spread out over a flat surface, but still held fairly compact (for instance in a small petri dish), would it still conduct as well as before?


title: Is tension always constant throughout a rope of mass in equilibrium?

text: Let's say we have a meter stick with a single rope attached to it. One end of the rope is attached to one end of the meter stick, the other end of the rope is attached to the opposite end of the meter stick. By hanging the rope from a beam in the center of the rope, the meter stick (which is attached to the rope) balances perfectly flat in equilibrium as it hangs from the rope. Now, say the rope is not hung perfectly in its center, and as a result the meter stick accelerates from its perfectly horizontal position to an almost vertical position. (Does this make sense so far?) At this point where the meter stick is now at rest at an angle which is at a diagonal (the actual angle is irrelevant, we could say perhaps 5 degrees off the vertical, just to clarify to the reader), is the tension in the rope still constant among the two halves of the rope? How can it be, when it appears that so much more of the meter stick's weight is being held up by one end of the rope?


title: does a rocking kettle cause the water to boil more slowly?

text: When I boil water in the kettle on my electric stove, sometimes it rocks back and forth making an annoying sound at a frequency of about 6Hz. When that happens, I move the kettle slightly to make it stop rocking. It occurred to me that although my motivation is to stop the annoying sound, it might also make the water boil slightly faster because the energy that had been wasted in maintaining the oscillation of the kettle is now being directed elsewhere. I am supposing that this energy is transferred to the kettle because the bottom of it is now in more constant contact with the electric heating element.   To test this theory, I am thinking that I could experiment by boiling the water each morning (as I already do) and note the time it takes to boil, the ambient temperature and the temperature of the water, and make sure that the exact same amount of water is in the kettle each morning. By noting whether the kettle vibrates or not, but without adjusting it, I could see if I can statistically disprove the null hypothesis that there is no correlation between the kettle boiling and the time it takes to boil.   Is there anything missing from the proposed design of the experiment, and/or is the answer already well known?


title: How long does the 2nd pot of water take to boil right after the 1st one finishes?

text: Say I have a pot of water that boils in 20 minutes, at whatever temperature. If I leave the fire on, take the pot off, pour the hot water into a container, refill the pot with tap water and put it back on the fire. How long will the 2nd pot take to boil and why?


Single photons: Is there a 90° offset of the electric to the magnetic component in the direction of propagation? ![Electromagnetic wave](http://i.stack.imgur.com/ksHYn.png)


title: Number theory in Physics

text: As a Graduate Mathematics student, my interest lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications of Number theory to physics. I have heard Applications of linear algebra and analysis to many branches of physics, but not number theory. Waiting forward in receiving interesting answers!


title: Will the increasing rate of expansion of the universe eventually result in Hawking Radiation suddenly occurring everywhere?

text: The universe is expanding at an ever increasing rate. Virtual particles are being created and then destroyed everywhere at every moment. As space expands even faster, will a time come when these virtual particles will be ripped apart before they can destroy each other, much like what happens at gravitational event horizons. Does this mean that the universe will at this point find itself suddenly full of Hawking radiation, almost as if a new "Big Bang" had occurred?


title: Time-dependent Schrodinger equation from variational principle

text: In the paper, "Density-functional theory for time-dependent systems" Physical Review Letters 52 (12): 997 the authors mentioned that the action $$ A= \int_{t_0}^{t_1} dt \langle \Phi(t) | i \hbar\partial / \partial t - \hat{H}(t) | \Phi(t) \rangle \tag{1} $$ provides the solution of time-dependent Schrodinger equation at its stationary point. Wikipedia  called (1) as the Dirac action without further reference. If I do a variation, indeed the stationary point of action (1) gives $$ i \hbar\partial / \partial t | \Phi(t) \rangle = \hat{H}(t) | \Phi(t) \rangle $$ However, from path-integral point of view, the least action principle is only a limiting case when $\hbar \rightarrow 0$. In general, there is no least action principle in quantum mechanics. My question is, how to reconcile these two aspects? What does vary of action (1) mean?


title: Is "real" antimatter (odd under C, P, T) unphysical?

text: A positron is odd under charge conjugation and parity reversal but nevertheless even with respect to time reversal. Is a theoretical positron which would be odd under all three symmetries (C, P, T) physical?


title: What is light cone singularity? Has it any relation with light like singularity?

text: I thought light like singularity is where the geodesics end on a lightlike hypersurface and can't be extended anymore. I guess its different than light cone singularity. Lot's of places have mention of it, but I wanted to know its definition for sure.


title: Why do electrons drift in an ideal conductor, since there's no field?

text: Suppose a simple circuit with a **DC voltage** source and a **resistor**. The voltage of the source will be situated over the resistor. So the **electric field** (which is the gradient of the potential) will be constant in the resistor (if you assume a linear potential function in the resistor), and will be equal to **zero in the conducting connections**. Since **electrons** are **drifted** because of an **electric field** (with Newton's second law and Lorentz' law for the force), what keeps them drifting in the ideal conductors? Or do they just keep their velocity they got in the resistor, and don't decelerate because there's no resistance there? What would mean that the electrons **obtain their velocity within the resistor** , which sounds a bit paradoxal... Where's the loop in my argumentation, or am I just right?


title: spin parity $J^P$ notation

text: In particle physics, when you read $J^P$, does it mean Spin parity or total angular momentum parity? I know that the letter $J$ is used for TOTAL angular momentum but I think I read somewhere that sometimes it is meant spin when used in this $J^P$ notation.


title: What does a curved natural log graph suggest?

text: Sorry if this is rather simple, but I've only just started learning about using logarithms in experimental physics. I did an experiment to test the amount of time it would take for an amount of water to leave a burette. I used the starting volume of water in the burette as a control variable, $50cm^3$. I recorded the time it took for the a given volume of water to be left in the burette. For example, $10cm^3$ left took a time of roughly $71\mbox{s}$; $45\mbox{cm}^3$ left took roughly $6\mbox{s}$, and then many values in between. I would expect this to represent exponential decay, seen as different concentrations and masses of water in the burette would have different effects on the speed of the water leaving the burette. (Correct me if I'm wrong.) So I plotted a graph of volume against time and it showed exponential decay, but it was only very slightly curved, but curved nonetheless. So I decided then to plot a graph of $\ln\left(V/\operatorname{cm}^3\right)$ against time/s. However, this did not produce a straight line. If I were to follow the plotted points with a curve, the gradient of the line would have been negative and increased in negative 'magnitude'. I'm meant to analyse the extent of whether or not my experiment shows exponential decay. I'm quite stuck, because my original graph shows very slight decay, whereas my log graph isn't a straight line. Does the fact that the log graph doesn't produce a straight line show that there isn't exponential decay? Does it not matter? Would it have been straight had there been very few experimental errors/uncertainties (there would have been a lot)? So I guess, fundamentally, my question is: What does the curved line on my natural log graph suggest?


title: Can Quantum Stealth be Real?

text: I've recently heard about this new material called Quantum Stealth which is suppost to be a replicate of Harry Potter's 'Invisibilty cloak' . Apparently the material, bends light waves around a target which allows complete invisibility. Is all this true?


title: Earth's magnetic field

text: I'm dealing with a problem here. Today my professor asked us a question : How should a metallic wire move in Earth's magnetic field such that she gets maximum potential difference in it's ends: a) Horizontally b) Vertically c) Normal in the magnetic field lines Can anyone help me with this question? Thank you !


title: When is the Fermi surface a surface of constant mean curvature?

text: Fermi surfaces are surfaces of constant energy in reciprocal space. They provide information about the properties of a material in solid state physics. Constant mean curvature surfaces are a superset of minimal surfaces, which minimize area and have zero mean curvature. Soap bubbles are surfaces of constant mean curvature. The two certainly coincide in the case of a sphere, but must they always coincide? If so, why? Is there a sharper constraint that Fermi surfaces must obey as well? I found a few papers that mention the two as connected, but they never establish the exact connection between the two. Preliminary literature review: Mackay, Alan L. Periodic minimal surfaces, 1985. > Minimal surfaces are found, as mentioned above, in soap films . . . The > surfaces of constant energy in reciprocal space, used in solid state physics > for finding the Fermi surface, are very similar. Mackay, Alan L. Periodic minimal surfaces from finite element methods, 1994. > Fermi surfaces, which are surfaces in reciprocal space, are closely related > to nodal surfaces.


title: Relation between symmetry factors

text: In $\phi^3$ theory, the generating functional for interacting field theory is given by: $$ Z_1(J) = \sum_{V=0}^{\infty} \frac{1}{V!} \Big[ \frac{iZ_g g}{6} \int \Big( \frac{1}{i}\frac{\delta}{\delta J}\Big)^3 d^4 x \Big]^V \times \sum_{P=0}^{\infty} \frac{1}{P!} \Big[ \frac{i}{2} \int J(y) \Delta(y-z) J(z) \, d^4 y \, d^4z \Big]^P $$ [Reference: Srednicki: eqn. (9.11)] Let, for specific values of $V$ and $P$ we get some terms from it. One of them is a disconnected diagram consisted of two connected diagrams $C_1$ and $C_2$. The disconnected diagrams symmetry factor is, say, $S$; that is the term for disconnected diagram has a numerical coefficient: $\frac{1}{S}$. Now we write the term for disconnected diagram according to the eqn (9.12): $$ D = \frac{1}{S_D} \prod_I (C_I)^{n_I}$$ where $n_I$ is an integer that counts the number of $C_I$ ’s in $D$, and $S_D$ is the additional symmetry factor for $D$. Here, $S_D = \prod_I n_I !$ In this case is this true: $S=\frac{1}{n_1!} \times \frac{1}{n_2!} \times C_1$'s symmetry factor $\times C_2$'s symmetry factor?


title: Where did the concept of energy come from?

text: Energy seems to me to be a very abstract thing, and while it clearly works out very nicely, I don't understand how anyone would have thought to come up with it. Where does the concept of energy find it's roots, and how was it settled down on as a 'useful' quantity as opposed to something else?


title: Stability of rotation of a rectangular prism

text: I've noticed something curious about the rotation of a rectangular prism. If I take a box with height $\neq$ width $\neq$ depth and flip it into the air around different axes of rotation, some motions seem more stable than others. The 3 axes which best illustrate what I mean are: (1) Through the centre of mass, parallel to the longest box edge. (2) Through the centre of mass, parallel to the shortest box edge. (3) Through the centre of mass, parallel to the remaining box edge. It's "easy" to get the box to rotate cleanly around (1) and (2), but flipping the box around (3) usually results in extra twisting besides the rotation around (3) that I'm trying to achieve (obviously a "perfect" flip on my part would avoid this twisting, which is why I call it an instability). If you're not quite sure what I'm talking about, grab a box or book with 3 different side lengths and try it out (but careful not to break anything!). What's special about axis (3)? ![enter image description here](http://i.stack.imgur.com/yzD8c.png) Image taken from Marsden and Ratiu.


title: Red shift/blue shift: how would it appear to a fast-moving observer?

text: I've read sci-fi stories in which a spaceship crew, moving at some significant fraction of 'c', observes stars ahead as bluer, stars behind as redder, stars to port and starboard as...well, you get the idea. This seems wrong, though I'm not sure if it is. Seems to me the red/blue shifts would only be apparent with spectroscopic analysis, not to the naked eye. Yes? No?


title: Why are only logarithmic divergence relevant for the Callan-Symanzik equation? Intuitive understanding?

text: I may be wrong, but it seems that only logarithmic divergences need to be retained when using the Callan-Symanzik equation, finding running couplings, etc. Why is this the case? Is there some simple intuitive understanding for why the logarithmic divergences are most important for these applications?


title: Why not shoot a marble sized spacecraft at the moon?

text: I was thinking about the Google XPrize for Space Travel the other day. In order to claim the prize of building a robot that goes to the moon, travels 500m, and relays data, I had the idea of building a tiny vessel the size of a marble and shooting it at the moon with a railgun. The theory is that since the mass of the marble-sized craft is only a fraction of the size of a regular shuttle, it should take exponentially less energy to get it to the moon. So, if you could aim it right, and shoot it with enough power to escape Earth's gravity (Let's say it weight 1oz) couldn't you shoot your own vessel to the moon with essentially a potato launcher? Why does this not work?


title: About Shor's error correcting algorithm

text: * In this paper, http://arxiv.org/abs/1301.4504 in equation 4.1 in what sense are the two states a "9-qubit state"? I did not understand this counting.    * Can someone explain what are the different $X_i$ and $Z_i$ in 4.2? How is say $X_1$ Pauli matrix different from $X_8$ and so on?    * And what is the non-trivial thing that happened in equation 4.2? (aren't the two kets on the LHS and the RHS the same?)  * * * It would be great to hear of any other general insights/explanation people might have about this section 4.


title: Why is the space-time interval squared?

text: The space-time interval equation is this: $$\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2-(c\Delta t)^2$$ Where, $\Delta x, \Delta y, \Delta z$ and $\Delta t$ represent the distances along various coordinates according to an observer, and $\Delta s$ is the space-time interval. All observers agree on the space-time interval, it is constant. My question is **why is it squared?** If we had in equation like this: $$\Delta s'=\Delta x^2+\Delta y^2+\Delta z^2-(c\Delta t)^2$$ $\Delta s'$ would be constant as well. It would also never be imaginary. It would have units of $[length]^2$ instead of $[length]$ though. Is there a theoretical or practical reason that we define the space-time interval based on squaring, or is it just to make it look similar to Pythagoras' theorem/give it simpler units or something else entirely?


title: daylight length variation from year to year

text: I am doing some calculations to see how many hours of light does a specific location (identified by latitude and longitude) has in a specific day of the year. Contrary to my expectations I get a slight variance for different years. See the data calculated for this point in Svalbard (77.553604,23.670272) in the same day for different years. The values are calculated using the same formula and the same coordinates.               2005-02-22  5.84500     2006-02-22  5.76472     2007-02-22  5.68389     2008-02-22  5.60222     2009-02-22  5.85472     2010-02-22  5.77472     2011-02-22  5.69389     2012-02-22  5.61250      Is this normal and why so?


title: Spectroscopic notation $s$, $p$, $d$, $f$, $\ldots$

text: $s$ is _sharp_ , $p$ for _principal_ , $d$ for _diffuse_ , $f$ for _fundamental_. Where do all those term come from? I do not see any link with the corresponding shapes.


title: Optics of the eye - do we see Fourier transforms?

text: I've recently been learning about Fourier optics, specifically, that a thin lens can produce the Fourier transform of an object on a screen located in the focal plane. With this in mind, does the lens in a human eye produce a Fourier transform on the retina? Any help appreciated


title: Why do we use time-dependent regions in this derivation?

text: I'm studying fluid mechanics and I have the following doubt: on the book, the author first deduces the differential form of the equation of balance of momentum. First he argues that if the fluid is ideal and is contained in a region $D\subset \mathbb{R}^3$ and if the pressure is $p : D\times \mathbb{R}\to \mathbb{R}$ then the stress force per unit volume is $-\nabla p$ and the body force per unit volume is $\rho \mathbf{b}$ (with $\mathbf{b}$ being the body force per unit mass). In that case the law becomes $$\rho \dfrac{D\mathbf{u}}{Dt} = -\nabla p + \rho\mathbf{b}$$ Then with some manipulations he derives the integral form of the law. Basically he considers a **fixed** region $W$ and consider the total momentum contained in $W$ as $$\int_W \rho \mathbf{u} \ dV$$ In that case the integral form can be obtained differentiating that. So, we gain the following law: $$\dfrac{d}{dt}\int_W \rho \mathbf{u} \ dV = - \int_{\partial W} (p\mathbf{n}+\rho \mathbf{u}(\mathbf{u}\cdot \mathbf{n}))\ dV + \int_W \rho \mathbf{b} \ dV$$ This law is over a fixed region. So we choose a region on the fluid, compute the momentum inside it and see how it varies as the fluid flows through it. Now, to assume as little differentiability as possible, the author proceeds to obtain one integral form of the law directly from basic principles. If $\varphi$ is the fluid flow map, $\varphi_t = \varphi (\cdot, t)$, then he states the following: $$\dfrac{d}{dt} \int_{\varphi_t(W)} \rho \mathbf{u} \ dV = \mathbf{S}_{\partial \varphi_t(W)} + \int_{\varphi_t(W)} \rho \mathbf{b} \ dV$$ Where $\mathbf{S}_{\partial \varphi_t(W)}$ is the total force at time $t$ exterted on the fluid contained in $\varphi_t(W)$ by means of stress on its boundary $\partial \varphi_t(W)$. This is quite clear: we pick a region, look at the mometum and the rate of change of momentum should be equal to the total force applied to it. Now this region is **time-dependent**. That is, instead of looking at a fixed region and at the fluid flowing through it, the author is following a chunk of fluid that moves with time. My question is: why, when deriving the integral form of the balance of momentum law from the differential form, we consider a fixed region and why, when stating it from basic principles, we consider a region varying with time? Is there some connection between this and the differences between the Lagrangian and Eulerian points of view?


title: Center of mass, center of gravity of a spoon

text: I went to a restaurant yesterday and while I was eating dessert, I saw a **standard stainless steel spoon (note the alliteration!** ) balancing on a plate. It was balancing on its handle, and I started wondering, Why is that particular point the center of gravity for the spoon? Thanks.


title: Angular speed of the planets

text: Do all the planets in our solar system have the same angular speed? Physics teacher says yes, my research is not crystal clear. I want to make sure I have the right information for future reference.


title: Regarding state of Klein-Gordon field

text: In regular quantum mechanics of particles, I have the Schrodinger evolution picture for a **general state** $$ i\hbar \frac{d}{dt} \left|\psi(t)\right> = \hat H \left|\psi(t)\right> $$ then we take the inner product with respect to $ \left< x\right| $ to obtain the equation in the position representation. $$ i\hbar \frac{d}{dt} \psi(x,t) = -\frac{\hbar^2}{2m}\nabla^2\psi(x,t) - V(x)\psi(x,t) $$ where $$ \psi(x,t) = \left< x |\psi(t)\right> $$ and $$ \left< x |\hat H|\psi(t)\right> = -\frac{\hbar^2}{2m}\nabla^2\psi(x,t) - V(x)\psi(x,t) $$ In the case of quantum fields, the position and momentum and demoted from operator status to simply paramaters and the field operator (here for KG real field) is given by $$ \hat \psi(\vec x) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2\omega_p}} \Bigl[\hat a(\vec p) e^{i\vec k. \vec x} + \hat a^\dagger(\vec p) e^{-i\vec k. \vec x} \Bigr] $$ in the Schrodinger picture. The states are generated from vacuum by the operator $$ \hat \psi(x) \left|0\right> = \int \frac{d^3p}{(2\pi)^3}\frac{1}{2E_p}e^{-i\vec p.\vec x} \left|\vec p\right>$$ Now what exactly are these states, are they eigenstates of some operator (seems like the field operator) or quite arbitrary ? In what representation is the field operator given here ? EDIT : I think I understood the first part of the question, these states are the eigen-states of Hamiltonian of the field. But the question about the choice of basis of the operator still remains.


title: Why is there a size limitation on animals?

text: Why is there a size limitation on human/animal growth? Assuming the technology exists for man to grow to 200 feet high, it's pretty much a given that the stress on the skeletal structure and joints wouldn't be possible to support the mass or move...but WHY is this? if our current skeletal structures and joints can support our weight as is, wouldn't a much larger skeletal structure do the same assuming it's growing in proportion with the rest of the body? And why wouldn't a giant person be able to move like normal sized humans do? (I'm honestly thinking Ant Man, or even the non-biological sense of mechs/gundams/jaegers)...I'm just having a hard time grasping why if it were possible to grow to gigantic sizes or create giant robots, why it then wouldn't be possible for them to move.


title: Why does the echo of the last chord appear to rise in pitch

text: I - and others - observe that when a musical performance ends, the echo of the last chord appears to rise in pitch by up to a quarter tone while the echo decays. This effect appears to be independent of the type of performance - orchestral or choral. I am tempted to assume that this is related to what is known in electro-acoustic circles as Space Echo, but I cannot see why this should occur.


title: How would charge be distributed in charged conductors if the Coulomb law was not ${1}/{r^2}$?

text: Would the excess charge on a conductor move to surface until the electric field inside become zero if the Coulomb law was for example $\frac{1}{r^3}$? If yes, would the distribution $\sigma(x,y)$ be different from when it is $\frac{1}{r^2}$?


title: Small question about accuracy and precision

text: Let's say I have a law like this, $$D=\frac{c}{r}$$ where $c$ is a constant, $r$ a distance in meter. my measures of $r$ are [$0.02m$, $0.01m$], then $<r>=0.015m$ and $\delta r = \pm 0.005m$. So now if I want to calculate $D+\delta D$ should I use $+\delta r$ or $- \delta r$ in my equation? because if I use $+\delta r$ I get a smaller value than if I use $-\delta r$ since $r$ divide $c$ edit: in my real problem I have a lot of data, all is fine when I use the minus delta. I just want to be sure...


title: What would be the real-world implications of the Kessler Syndrome?

text: I recently read about the Kessler Syndrome and am thinking about writing a story set in a world suffering from it. In the interest of realism, I am curious about the secondary effects which would be produced by this kind of scenario.   * About what distance would the debris cloud reside? How deep would it be?   * Would the debris cloud destroy satellites? Some satellites? All satellites? Could you build a satellite which would survive it?   * What would be the effects on the ground? Would there be frequent meteor showers? Would the meteor showers cause damage? Would the sun or stars be obscured?   * How long would the cloud last? How could it be manually eliminated? I understand that there are a huge number of variables here, and that many of the answers depend upon how the syndrome got its start. I'm just curious about the best-case and worst-case scenarios. For the best-case scenario, imagine that the International Space Station explodes. For worst-case, imagine that 433 Eros is in geosynchronous orbit and explodes. I also understand that this is a subjective question. I am trying to make it a good subjective question.


title: What equation describes the wavefunction of a single photon?

text: The Schrödinger equation describes the quantum mechanics of a single massive non-relativistic particle. The Dirac equation governs a single massive relativistic spin-½ particle. The photon is a massless, relativistic spin-1 particle. What is the equivalent equation giving the quantum mechanics of a single photon?


title: In interferometry, what is the origin of the name "Airy function"?

text: In interferometry (specifically, in the domain of Fabry-Perot cavities), the function $$f(\phi) = \frac{1}{1 + F \sin^2 \phi}$$ , which describes the shape of the resonant structure of the cavity, is often called the "Airy function" (for instance, in Wolfram Mathworld). However, it is obviously quite different from the special functions Ai(x) that usually go by that name. This function resembles probability density function of the wrapped Cauchy distribution. **How did it get the name "Airy function"?** I've heard that Fabry and Perot gave it this name in one of their original papers (maybe this one? PDF, in French, which I can't read), in honor of (the same) George Biddell Airy who had earlier considered similar interferometers. It would be great if someone could help ferret out the first reference to that function by this name.


title: Vanishing of Weyl Tensor Contraction

text: Within the context of Einstein space-times, we know that the contraction of the Weyl tensor across a set of indices always vanishes, like so : $$C{^{\alpha }}_{\mu \alpha \nu }=0$$ From a purely mathematical standpoint this should be straightforward ( but perhaps tedious ) enough to prove from the definition of the conformal tensor in terms of the Riemann tensor and its contractions. However, I am wondering what the physical and/or geometric meaning and significance - if any - of this vanishing contraction really is ? I am a very visual person and learner, so an intuitive geometric understanding of this would be very helpful to me.


title: Does non-mass-energy generate a gravitational field?

text: At a very basic level I know that gravity isn't generated by mass but rather the stress-energy tensor and when I wave my hands a lot it seems like that implies that energy in $E^2 = (pc)^2 + (mc^2)^2$ is the source of gravity. If the total energy of a particle contributes to the generation of a gravitational field, that seems to imply some strange things. For example, you could accelerate a particle like an electron to such a high velocity that it has enough momentum / kinetic energy to collapse into a black hole. An observer traveling with the electron would see an electron and stationary observers would see an arbitrarily massive black hole flying by. These observations seem to be contradictory. The same would be true of an extremely high energy photon. Another consequence is that a stationary particle could appear to have so much mass that it could attract / deflect the trajectory of a rapidly moving observer. It seems odd that at low velocities you wouldn't even notice a stationary electron as you pass it by but at high velocities the gravitational field you observe could be significant enough to alter your path. Am I correct that non-mass-energy generates a gravitational field? If it does, how are these strange observations like a particle looking like a black hole in one reference frame but not another reconciled?


title: Will accelerating a massive particle generates a blackhole?

text: I have a naive question about blackhole. If I accelerate a massive particle very close to the speed of light, the particle will have large energy-momentum tensor. Will it become a blackhole?


title: Relativistic Black Hole?

text: So recently, looking at high energy particles through the lens of General and Special Relativity has peaked my interest. One thing I was considering, using the electron as the first example, is as follows: If gravity is the result of mass (stress-energy tensor), and as particles approach the speed of light, their mass is increased as measured by an outside observer (A) by a factor, $ \frac{1}{\sqrt{(1-(v/c)^{2})}} $. The mass of the electron, $ m_{e} $, is $ 9.109 \times 10^{-31} kg $, and the radius is $ r_{e} = 2.818 \times 10^{-15} m $. Given the Schwarzschild Condition is: $$ r_{s} = \frac{2Gm}{c^{2}} $$. Observer A, due to the Lorentz dilation, will measure a dilated mass term that is increasing monotonically as a function of the electron's velocity. The mass that observer A will then measure is: $$ m_{A} = \frac{m_{e}}{\sqrt{(1-(v/c)^{2})}} $$. Combining the Swarzschild Condition with the mass as measured by A, we attain a relation between the mass that observer A measures with the particle's velocity, accounting for relativistic effects. This allows me to now pose the question that given the Schwarzschild radius is the electron radius, at what velocity does the mass increase to the point where the electron, as seen by observer A, become a black hole? This also leads to the more conceptual question of what are the implications of simultaneity in this situation? If the electron's mass is still $m_{e}$ in it's own frame, then shouldn't the electron not really turn into a black hole? Of course, this whole argument falls apart if the derived speed is greater than $c$. I went own to calculate that. I found that speed to be: $$ v = \sqrt{c^{2}-\frac{4G^{2}m^{2}_{e}}{r^{2}_{e}c^{2}}}$$ The velocity at which an object of a given radius and mass would become a black hole. To my disappointment, this came out to be $8.988 \times 10^{16} m/s $. Over twice the speed of light. I have yet to calculate the velocity for more massive objects, such as stars ( which could theoretically reach relativistic velocities as the result of being flung by a galactic collision ). Either way, if this velocity is attainable for anything, what would simultaneity say about this?


title: reletivistic mass as seen by different observers

text: Imagine there are two observers $A$ and $B$ and a particle $P$. $A$ and $B$ are at about the same point, $P$ is some distance away. From $A$'s point of view, $P$ has velocity $V$ and $B$ has velocity $-V$.                         P---->                    A          <----B      Suppose $A$ and $B$ have the same rest mass $m$ and $P$ has rest mass $m_P$. It seems to me that $A$ will observe a gravitational force between $P$ and $A$ of $F_a$ and between $P$ and $B$ of $F_b$ with $F_a\neq F_b$ because the relativistic masses of $A$ and $B$ are different. However, B will observe forces $F_a'$ and $F_b'$ and it seems to me that $F_a' \neq F_a$ and $F_b' \neq F_b$ because $A$ and $B$ observe different relativistic masses for everything involved. I've tried demonstrating $F_a=F_a'$ on paper and gotten into a tangle. Intuitively, I think this equality is false and expect the difference to be resolved elsewhere. I have a qualitative understanding of general relativity, but can't handle tensors etc. Can this be explained with high-school maths?


title: Gravitational atraction of fast object

text: Let's imagine a asteroid that travels with 0.99999999999999999c. (I know it's impossible). Anyway... Relativistic mass of such object would be almost equal to earth's stationary mass. Now let's imagine that such object passes closely to me (assuming I'm immortal etc.). According to $F_g=GMm/r^2$ (Where M is relativistic mass of this asteroid and m is my mass) such an object would attract me. So would I gravitate after it? Would I gain it's speed constantly falling on it? Or maybe it would just pulled me for a moment, but then I would return to my ol' good non-relativistic speed in "everyday reference system"? Or maybe something else would happen? What happens with gravity of relativistic, NON ACCELERATINNG objects? (Let's assume that there's something that makes this asteroid speed constant).


title: If a 1kg mass was accelerated close to the speed of light would it turn into a black hole?

text: I'm a big fan of the podcast Astronomy Cast and a while back I was listening to a Q&A episode they did. A listener sent in a question that I found fascinating and have been wondering about ever since. From the show transcript: > _Arunus Gidgowdusk from Lithuania asks: "If you took a one kilogram mass and > accelerated it close to the speed of light would it form into a black hole? > Would it stay a black hole if you then decreased the speed?"_ Dr. Gay, an astrophysicist and one of the hosts, explained that she'd asked a number of her colleagues and that none of them could provide a satisfactory answer. I asked her more recently on Facebook if anyone had come forward with one and she said they had not. So I thought maybe this would be a good place to ask.


title: Does influence on gravity increase with mass when velocities approach the speed of light?

text: In other words, when a particle's mass increases significantly as it approaches the speed of light (c), does its influence on gravity increase, and if so, does it increase proportionally?


title: Can a single particle create a black hole?

text: Let us suppose a particle with so much energy $ E= h \frac{c}{\lambda} $ so $ \lambda $ is smaller than Planck's length ? Would it be possible? I mean if the particle has so much energy then its mass would be very huge and would itself collapse into a black hole This means that we could not 'see' what is beyond the Planck's length because a very energetic particle would turn into a micro black hole before reaching 'Planck's lenght' am i right? Is this fact supported by SR and GR? what would be then the Einstein equations ? $ R _{a,b} =0 $?


title: Can a black hole form due to Lorentz contraction?

text: > **Possible Duplicate:**   >  If a 1kg mass was accelerated close to the speed of light would it turn > into a black hole? Imagine, a rod of length **L** is moving with velocity approaching the speed of light with respect to a human observer on Earth. Due to Lorentz contraction, the rod will observed to be very short. And since all laws of physic hold true in every frame of references, the gravitation law which state the force acting is inversely proportional to square of distance between them, will be acting between various part of the rod. Now, as velocity approach **c** , **L** will approach 0. This should cause an enormous gravitational force enough to form a black hole. Isn't this suggesting a black hole can be formed when the object velocity comes near the speed of light? According to the rod's frame of reference, it will see itself as stationary and a man who observe it is moving, so according to the rod, the human must be a black hole. Isn't this a paradox?


title: Large-N factorization of single-trace operators

text: Does anyone know where I can find a pedagogical explanation of large-N factorization in SU(N) gauge theories or nonlinear O(N) sigma models (in the latter case the trace corresponds to a dot product). The reference I am using is Polyakov's gauge fields and strings. However, I find the explanation of large-N factorization there quite opaque. Thanks.


title: What is the amplitude of the limit cycle of the van der Pol oscillator?

text: In the second edition of _Classical dynamics of particles and systems_ by Jerry B. Marion, it is said that the van der Pol equation $$\ddot{x}-\mu\left({x_0}^2-x^2\right)\dot{x}+{\omega_0}^2x=0$$ where $\mu$ is a positive parameter of small value, has a limit cycle with amplitude $|x_0|$ (I'm paraphrasing this from the first edition in spanish) and he even illustrates it as ![Marion van der Pol illustration](http://i.stack.imgur.com/AU9dy.png) In newer editions this has been removed, but they add nothing new whatsoever. From the vdP equation alone it seems that this is right, but I noticed that the limit cycle does not have this amplitude in any $\mu$ case, e.g. for $\mu=0.1$ and $x_0=1$, the plot in phases space looks like (in Mathematica) ![van der Pol with $\\mu=0.1$, $x_0=1$](http://i.stack.imgur.com/4s2dl.png) I tried different values and the behaviour is the same, e.g. for $\mu=5$ and $x_0=9$, the plot for position in time is ![van der Pol with $\\mu=5$, $x_0=9$](http://i.stack.imgur.com/6DDgq.png) In both cases the amplitude seems to be $2|x_0|$. I think I intuitively understand what's going on by seeing the field lines of the oscillator and how it changes behaviour (damping) when it crosses $x=x_0$, e.g. for $\mu=1$ and $x_0=2$, ![van der Pol with $\\mu=1$, $x_0=2$](http://i.stack.imgur.com/LFXcL.png) **But how can I find the _real_ amplitude of the limit cycle and why is it not simply $|x_0|$ as the van der Pol equation suggest?**


title: How is the torque reaction in a four-stroke engine produced?

text: Assuming we have a plane with a propeller driven by an engine like this one . How would the torque reaction be generated if the piston is aligned with the plane center of mass? What I mean is, where are the reaction forces located, in which part of the engine?


title: Has the speed of light changed over time?

text: Could someone judge my (stoner) hypothesis that the speed of light has changed over time -- ie. as the universe has expanded in volume light has slowed down, perhaps going so far as back to the big bang when it was infinitely fast and there was no time because everything happened at once etc. Thinking that the speed at which information can propagate through the universe is linked to the size of it seems intuitive to me. My question -- is there an easy disproof of this? Would Einstein have to be wrong? Does it violate anything supposedly more fundamental such as quantum or string theories? Do any current experiments invalidate it? If not can you show me in any case why you think its unlikely. # Edit 8/24 I'm accepting Mark M.'s answer but will post this here because there is a character limit on comments @Mark M thanks, good answer but. as someone whos only read some popular physics, and should leave this to the experts, im still muddled in my personal theory. i dont see why you should need two units to measure the speed of light. the thing i have a hard time wrapping my head around is the relation of time and distance. they seem like they could fundamentally be the same thing. if you say time is measured fundamentally by the vibration of so and so quantum object in space....why cant we just measure that vibration distance as the constant... ill repeat myself to try to be clear... there is a certain minimum distance that particles have to go to interact with each other ....... if it wasnt vibrating there wouldnt be time,its what creates the illusion of time...so instead of talking about speed or c as distance/time.... cant we simply talk about that distance a quantum object vibates....I'll lead up to my point.....perhaps there can need be only one constant here, and that is the physical size of the universe. a tiny metal tuning fork doesnt appear to be vibrating at all but if you blew it up to the size of the empire state building the metal rods would move from window to window. perhaps as our universe expanded in size the length of that minimum vibration (perhaps infinite at point zero) would have expanded, and therefore created the illusion of time and the speed of light, which, as the universe expands, will continue slowing down. perhaps we are like a big balloon and we have been blown up and all the fields/particles-without-size are vibrating more and more in that space.. am i missing something obvious here?


title: Curl of a vector field with two different systems of coordinates

text: Let $$\mathbf{H} = H_x \mathbf{u}_x + H_y \mathbf{u}_y + H_z \mathbf{u}_z$$ be a vector field whose components are defined with respect to the unit vectors $\mathbf{u}_x$, $\mathbf{u}_y$ and $\mathbf{u}_z$, so in the $(x,y,z)$ system of coordinates. **Question 1** : If we computed its curl in a _new_ system of coordinates, that is $(x' = x, y' = y, z' = -z)$, how would we do it? $$\nabla \times \mathbf{H} = \mathrm{det} \begin{vmatrix} \mathbf{u}_{x'} & \mathbf{u}_{y'} & \mathbf{u}_{z'}\\\ H_x? & H_y? & H_z?\\\ \displaystyle \frac{\partial}{\partial x'} & \frac{\partial}{\partial y'} & \frac{\partial}{\partial z'} \end{vmatrix} $$ In other words, which quantities should we put in the second line? $H_x$, $H_y$ and $H_z$ are along $\mathbf{u}_x$, $\mathbf{u}_y$ and $\mathbf{u}_z$ and _not_ $\mathbf{u}_{x'}$, $\mathbf{u}_{y'}$ and $\mathbf{u}_{z'}$. **Question 2** : And if we would like to keep $H_x$, $H_y$ and $H_z$ in the second line, which would be their meaning in this computation? These questions are strictly relative (but not equal) to my previous one.


title: Will humid air mitigate airborn dust due to neutralization of static electricity?

text: I have came to understand that humid air will help prevent electrostatic forces that can propel dust and cause it to cling to surfaces. My first question: is this above statement true? If the answer to the first question is true, then please continue: I have attempted to find designs for the various types of humidifiers but have not been successful. After examining a simple facial steamer and using some thought experiments, I have a crude design to propose, but am open to any other proposed designs reasonable for DIY construction. I understand there are many method to vaporize water. My current design is to have a stainless steel, rectangular tank with all sides enclosed and two holes drilled in the top. One hole will be used for inbound air while the other hole will be connected to a fan which will pull humid air out. On the bottom of the tank will be attached a flexible silicone heater that will heat the water to X temperature and enhance evaporation. My second question: is this design effective? My third question: given the simplicity of the proposed design, are any other designs better for DIY?


title: Length of wire required for solenoid to produce desired magnetic field

text: In a question: > To construct a solenoid, you wrap insulated wire uniformly around a plastic > tube 12cm in diameter and 50cm in length. You would like a 2.2 A current to > produce a 2.6 kG magnetic field inside your solenoid. > > What is the total length of wire you will need to meet these specifications? In the provided answer: $$NC = nL C = (\frac{B}{\mu_0 I}) L (\pi d)$$ Where:   * $N$ is total number of turns   * $n$ is number of loops   * $C$ is circumference But I dont understand why is there an $L$ * * * I did it by: $$B = \mu_0 n I$$ Then length of wire needed is just $nC$ whats wrong?


title: A question about how light hits a surface

text: my question is about how photons travel from a light source and hit an object. When you look at an object being hit by light the whole surface becomes brighter. What i'm trying to understand is why the entire surface lights up. When the photons leave the light source they scatter out to hit objects, this makes me logicically imaging that a surface will light up based on where those light packets hit. And not all parts of a surface will light up because the surface area of the light source is too small to match up with each corresponding part of a surface. Here is a quick text example of what im saying. LightSource = * Photons = / or | or \ Surface = _ Expected bright surfaces = %                             *                 / | \               _________                %  %  %      So because the light source's surface area was only big enough able to put out 3 streams of light i expect there to be areas not being hit by light. So what i want someone to explain to me is why in real life, the entire surface lights up. Sorry for such a stupid question, i usually keep these kinds of questions to myself but i decided to reach out.


title: Hawking Radiation: how does a particle ever cross the event horizon?

text: The heuristic argument for Hawking Radiation is, that a virtual pair- production happens just at the event horizon. One particle goes into the black hole, while the other can be observed as radiation. I never quite understood this explanation. Say, a virtual pair is created. From the point of view of the "radiation particle" the other particle will need an infinite amount of time in order to reach the event horizon. But the virtual pair production violates energy conservation, so the particles can only exist for a finite amount of time (Heisenberg uncertainty principle). Then, they must annihilate each other again, without emitting any radiation. I often heard the "explanation" that one particle "tunnels" through the event horizon. But isn't this again a flawed argument? Tunnelling is an effect known from flat spacetime and it makes particles cross potentials that they could not cross classically. How could this help to "jump over" an infinite time interval? For me it seems like superimposing ideas from flat spacetime on curved spacetime without any justification. While I understand, that the original derivation from Hawking follows a different argument, one should, in principle, be able to attach his results to a physical process. I worked through his derivation and while I must admit that I didn't understand every step, it seems to me that a lot of assumptions have to be made along the way in order to produce the results. Also the whole derivation is based on Quantum Field Theory in curved spacetime, which stands on shaky grounds, since nobody can say, where it is valid and where not - we don't have a complete theory of Quantum Gravity and we simply can't say in which situations QFT in curved spacetime is a good approximation. As you can see, I am really confused about this issue. Every sort of help is appreciated!


title: Using Electrostatic Force to Repel Dust From an Object

text: I have two 4,000V, 2.5mA, DC power supplies and am attempting to use them in such a way to cause a 6x4x1-inch ABS plastic object to repel dust from the ambient air and prevent this dust from settling on the object. I understand that two points that have opposite electrical charges will attract each other and that two points that have like electrical charges will repel each other. Using one or both of my power supplies and the plastic object described above, I am looking to somehow charge any potential dust particles that are in a small room and apply the opposite charge to the plastic object. First Question: Assuming all potential dust particles in the small room can be charged and the plastic object can be given an opposite charge, it should repel the dust particles and prevent them from settling on it. Is this correct? Second Question: How can I apply a charge to all potential dust particles in the small room? Third Question: Is it possible to apply a charge to a plastic object of this size? Does the ABS plastic present too high resistance for an object this size? Fourth Question: If the answer to the third question is yes, what ways can be used to enhance the conductivity of the plastic part. Perhaps a process such as dipping the plastic part in a liquid suspension of copper powder. Any other ideas?


title: Chemical Potential in AdS/CFT

text: In AdS/CFT a charged Black hole is probably someway equivalent to introducing a chemical potential (Chemical potential) at the boundary theory. Is there a quick way to see how it is or how does this correspondence work? I am sure it's well argued, but I haven't found a satisfactory explanation in any paper. Specially I will like to understand by connecting it with the thermodynamic case. In addition, it will be very helpful, if you can suggest me any introductory references or something with a nice explanation. Thanks!


title: Hall conductivity and edge response

text: The hall conductivity $\sigma_{xy}$ seems to reflect to some extent the response of a system in direction $\hat{y}$ to certain perturbation (electric field for example) restricted in $\hat{x}$ direction. My question is, does a nonzero $\sigma_{xy}$ imply anything about the the physics of edge response, i.e. if given a half infinite system with an edge at $x=0$, what would be the effect on y direction? Would there be a current in y direction along the edge? Thanks!


title: Ball rolling without slipping inside a hollow cylinder

text: A small ball of radius $r$ performes small oscillations within a hollow cylinder of radius $R$. What would be the angular frequency of the oscillations given that the rolling is without slipping? The angle between the radius connecting the center of the hollow cylinder to the ground (my $y$ axis) and the line connecting that center to the point of contact between the ball and the cylinder is $\phi$. The positive $x$ axis is to the right. The position of the ball may be written thus: $$y = R - (R-r)\cos\phi \\\ x = (R-r)\sin\phi$$ The ball has translational as well as rotational kinetic energy, hence, the total kinetic energy, $T$, should be: $$T=\frac12m(\dot{x}^2 + \dot{y}^2) + \frac12I\dot{\phi}^2$$ where $I$ is the moment of inertia of the small ball. Hence, $T$ is equal to $$T=\frac12m[(R-r)^2\dot{\phi}^2] + \frac12I\dot{\phi}^2$$ The potential energy, $V$, should be $mgy$. Now, the Lagrangian, $L$, should be $T-V$, hence $$L=\frac12m[(R-r)^2\dot{\phi}^2] + \frac12I\dot{\phi}^2 - \frac12mg(R-r)\phi^2$$ (under small oscillations approximation). Now, from the Lagrangian, using the Euler-Lagrange formalism, the angular frequency could be easily determined. Is that correct? I believe it isn't yet am not really sure why. I'd be grateful for some comments on this solution.


title: Will density of a metal increases during forging?

text: This question is metallurgical engineering, but I had a similar doubt regarding density of liquids and what causing it. Forged parts refines defects, dislocations will be moved strengthening the metal. But will the density of forged metal change? My earlier question was, what causes liquids to have different densities?


title: Atomic layer deposition applications?

text: What unexplored areas (known unknowns) are there in atomic layer deposition (ALD)? What unexplored applications of ALD are there? It seems like people use it a lot for coatings of either insulators or sometimes transparent conducting contacts. What else could you do with it?


title: Do Maxwell equeations change somehow after Higg's boson finding?

text: When I was in some physics -lesson, probably something to do with Quantum Physics -- the teacher said that certain Maxwell equations would change if the Higg's boson is found. It is also possible that I have mixed something, he may have meant magnetic monotones. Anyway does there exist any change to Maxwell equations after the Higg's boson?


title: Reference for stellar figures

text: Could anybody suggest a reference for the present stellar models? _In particular_ , I would appreciate references containing the core temperatures and pressures of neutron stars...


title: If quantum mechanics is ultimately deterministic, would Shor's factorization algorithm still work for large integers?

text: Victor Stenger argues that the apparent randomness in quantum mechanics is a result of the randomness in the macroscopic detectors (similar to the randomness in the laws of thermodynamics) and is not something that is inherent to quantum mechanics (this is my interpretation of Stenger). This would imply that QM is ultimately deterministic. See http://www.colorado.edu/philosophy/vstenger/Timeless/08-timeless.pdf If this is true, then would Shor's factorization algorithm still work for large integers? More generally, how would scalable quantum computing be affected?


title: Time reversal effect on time derivative in Quantum Mechanics

text: I am reading Zee's _Quantum field theory in a nutshell._ On time reversal he has > Consider the transformation $t\rightarrow t'= -t$. We want to find > $\Psi'(t')$ such that $i(\partial/\partial t′)\Psi′( t′) = H\Psi'(t′)$. > Write $\Psi′(t′) = T\Psi(t)$, where $T$ is some operator to be determined > (up to some arbitrary phase factor $\eta$). Plugging in, we have $i[ > \partial/ \partial( − t)] T\Psi( t) = HT\Psi( t)$. Multiply by $T^{-1}$, and > we obtain $T^{ − 1}( − i) T( \partial/ \partial t)\Psi( t) = T^{−1}HT( > t)\Psi(t)$. My question is: Has he assumed that $T$ and $\partial/\partial t$ commute and if so why is it valid to do that?


title: Which angle causes an object to land quickest?

text: Say a canon is where the circle is, and it shoots two different canonballs at different angles, but at the same speed, which angle would make the cannonball hit the ground first? ![enter image description here](http://i.stack.imgur.com/6LZic.png) Intuitively I'd think they'd hit at the same time, however, I remember a formula describing the second coordinate $y$: $y = - 1/2 \cdot g \cdot t^2 + v_{0y} \cdot t$ Where $t$ is the time, and $v_{0y}$ is the starting velocity. Thus a high $v_{0y}$, would lead to a greater total time $t$, thus it would hit A first. This seems to be missing something though.


title: Does unitarity apply in between measurements?

text: Sorry if this is a silly question (engineer here), but I was wondering if the math in particle physics assumes that unitarity applies even between measurements. In other words, I take it that the evolution of quantum states is governed by an operator that ensures the probability of all possible events adds up to 1 _at all times_. What I'm wondering -- is there an operator for which this does not apply _at all times_ but still gives measurement results with probability between 0 and 1?


title: SR time dilation

text: Two clocks are located at either end of a two light-hour long pole and motionless relative to the pole. Each clock transmits its time and notes that the other clock shows a reading two hours behind its own. That is, the clocks can be considered synchronised with each other. There is a flashbulb at the midpoint of both clocks. It goes off, and when each clock sees it (one hour later), it starts accelerating toward the other and each at the same rate (applying the same amount of thrust for the same local time). They do this for a short time until reaching a steady speed of 0.4c, relative to the flashbulb. Now according to the most recent generation of relativity experts, each clock should observe the other running more slowly. This needs to be the case because time dilation is based on the square of velocity so direction of travel is unimportant.   As they approach each other, the observed time difference will reduce because it takes less time for the transmitted signal to arrive. But the observed clock rate (after adjusting for doppler shift) will be slower at all times. By logical extension then, when they finally pass alongside or stop adjacent to each other, each clock should observe the timestamp of the other clock to be less than its own. Now obviously that outcome can’t be acceptable. Therefore we must conclude that any time dilation observed during their passage is nothing other than an illusion, and certainly not ‘real’ according to any experimental measurement, since only the final side-by-side comparison counts. It goes without saying then that if the clocks were instead moving apart from each other then any observed time dilation must also be an illusion. Am I correct?


title: Rotatory motion of uniform disk

text: Consider a uniform disk rolling without slipping with a certain constant angular velocity.Firstly it is moving in sufficiently rough surface.What will happen if it crosses the rough surface and just enters the smooth frictionless surface in its way?Will it be in the state of pure rotation or attains translatory motion or remains in pure rolling state.Please explain.


title: Why do the RGB gamut vertexes not intersect the edges of human vision on the CIExy plot?

text: As I understand, the CIExy graphic maps "greenness", or rather middle- wavelengthness, to the Y axis and "redness", or rather long-wavelengtsness, to the X axis. The trapping used to reduce the 3d gamut of the human eye to 2d is that the gamut is specified for a certain constant luminosity, and long- wavelength + middle-wavelength + short-wavelength equals the said luminosity, thus the third coordinate can be extrapolated from the first two. An example of this plot can be seen here, on wikipedia. The curved edge of the human vision gamut gives the single wavelength spectrum. If this is the case, how come the RGB gamut (triangular) does not intersect the curved edge of the human vision gamut? The light coming off the 3 LED categories in the display should be of a nigh-single wavelength (as LEDs have a single, very sharp emission peak).


What is the difference between stress and pressure? Are there any intuitive examples that explain the difference between the two? How about an example of when pressure and stress are not equal?


title: When a pole of magnet comes near another pole possessing the same charge does it generate electricity?

text: That's all there is to it. Well... I was daydreaming about making gloves that had the ability to shock people when you punched them. I thought how it would be better if they didn't need a battery and I thought I wonder if you could put two repelling magnets on the knuckle that when forced to come together (by a punch for example) would generate the electricity that shocked your opponent. Problem is I don't know if that's even possible and Google didn't seem to be able to answer my question. Also, not really capable of making these gloves but I don't like daydreaming about fantastical situations that don't make sense.


title: Uncertainty Principle and Bohmian mechanics

text: The Uncertainty Principle is a relationship between measurements of pairs of attributes, position and momentum, as well as energy and time. Perfect precision of one attribute's measurement leads to a full lack of knowledge about the other attribute (most likely, because there is no solid quantity for the other attribute). This appears to be a fundamental attribute of the world at large. Bohmian mechanics posits hidden variables, and makes the claim that particles (ordinary objects) have attributes at all times. Bertrand Russell developed an argument against Zeno's paradoxes which he called the "at-at theory of motion." > Bertrand Russell offered what is known as the "at-at theory of motion". It > agrees that there can be no motion "during" a durationless instant, and > contends that all that is required for motion is that the arrow be at one > point at one time, at another point another time, and at appropriate points > between those two points for intervening times. In this view motion is a > function of position with respect to time. In order to measure anything's position, you would need to have a single precise instant of measurement. The same would apply to energy, which comes in discrete units. To measure momentum (mass times velocity) with the at-at theory, you need to take at least two measurements. To take a time measurement, such as comparing elapsed time as measured by two different timepieces, you would also necessarily need at least two measurements. The Uncertainty Principle gives a precise mathematical formulation of an apparent fact of nature, which is unlikely to be something that a thought experiment could derive. However, the nature of the relationships appear to follow as natural consequences of Russell's response to Zeno. (And if space is quantized, it may be a fact of nature.) Does the Uncertainty Principle actually follow from Bohmian mechanics and the at-at theory of motion? If not, what am I missing?


title: How is Special Relativity (SR) shown to NOT be an artifact of perception or measurement

text: Special Relativity (SR) paradoxes are old-hat. But as I read explanations, they tend to resolve issues of simultaneity by applying the appropriate math... but that seems to me to be proving the theory by positing the theory. Just because the math is valid doesn't mean an argument is sound. All I have to do is believe warping space and time against curves and yes... it all works out. For instance... A space ship is traveling toward an asteroid and away from a stationary body at 60 percent the speed of light while at the same time an asteroid is traveling directly toward the space ship and toward the stationary body at 60 percent the speed of light. So the typical question is, "when does the space ship meet its demise?... distance / (1.2*c)?" _My question is distinctly different._ Why is it we are confident that the conclusion matches reality... i.e. how do we know the space ship doesn't just blow up before it thought it should based on only the perception and measurements available to it which seem to be governed by SR?


title: Study of Black-body Radiation

text: Why did scientists study black body radiations from something as complicated as a hollow container rather than the radiation from something simple like a thin solid cylinder?


title: Water pump with a tap connected at its opening not pumping water when water is drawn from the pump before starting the pump

text: Please give your explanation in layman terms, without throwing any complex equations at me. We have a 5000 liter tank dug in ground and a water pump connected to this tank that draws water from it and fills a overhead tank. We also have a tap at the opening of the pump. (A T joint is connected to the output of the pump, one goes to overhead tank and the other has a tap attached to it). Now, people draw water from this tap without turning on the pump (We try a lot to prevent this, yet people stubbornly do it). Nowadays when we turn on the pump, unless we pour water into the tap (About a liter of water) after turning on the pump we are not getting water output from the pump. A plumber suggested to us that it is because of Air lock and said to turn the tap upside down, like its a fountain :| Because of some physical constraints we cannot do this and it will be freaking expensive to do it. I am somehow not convinced that it is a solution to the problem. Could someone tell me what is happening here and how to solve this problem ?


title: Properties of the Scalar Field in Scalar-Tensor Theories

text: I've been reading about scalar-tensor theories of gravity, such as Brans-Dicke theory, and I started thinking about the scalar field. Now, I know that the Higgs field is a scalar field, and of course has a quanta, the Higgs boson. According to Wikipedia, the quanta of a scalar field will always be a spin-0 boson. What would the general properties of a boson arising from the scalar field in scalar-tensor theories? How would it interact with other particles (if at all)?


title: Reference Frame and Angular Speed Related?

text: I am given the following problem: > If an airplane propeller rotates at 2000 rev/min while the airplane flies at > a speed of 480 km/h relative to the ground, what is the linear speed of a > point on the tip of the propeller, at radius 1.5m, as seen by (a) the pilot > and (b) an observer on the ground? The plane’s velocity is parallel to the > propeller’s axis of rotation. I was able to solve part a pretty easily by just using the formulas that relate linear speed with angular speed, but I didn’t get part b correct. I thought that the answers would be the same from both perspectives because the speed of the plane does not contribute to the rotation of the propeller, but I’m assuming that is the wrong way to think about it (because that produces the wrong answer). Can someone explain why this is the wrong approach? The solution to this problem involved noting that "The plane’s velocity $v_p$ and the velocity of the tip $v_t$ (found in the plane’s frame of reference), in any of the tip’s positions, must be perpendicular to each other." How is this relevant to the problem?


title: Electric field strength at the center of an equilateral triangle

text: **Questions:** Three $x$ m long rods form an equilateral triangle. Two of the rods are charged to $+q$ C and the third to $-q$ C. What is the electric field strength at the center of an equilateral triangle? **Attempt:** I know how to find the electric field strength due to one rod, I just divide the rod into pieces, each of length $dx$ and charge $dq$ then integrate from 0 to x. After I find the electric field at the center due to each rod, how do I find the resultant electric field?


title: Does acceleration at an angle to velocity change the direction?

text: > During an interval of time, a tennis ball is moved so that the angle between > the velocity and the acceleration of the ball is kept at a constant 120º. > Which statement is true about the tennis ball during this interval of time? > Choose one answer. > > a. Its speed decreases and it is changing its direction of travel.   >  b. Its speed remains constant, but it is changing its direction of travel.   >  c. Its speed decreases and it is not changing its direction of travel.   >  d. Its speed increases and it is changing its direction of travel.   >  e. Its speed remains constant and it is not changing its direction of > travel In my mind the ball is travelling with a negative velocity, south, all in the y component. At the time it is being accelerated at 120 degrees, thus it is slowing down in the negative Y direction. "Its speed decreases and it is not changing direction of travel." That is, it will eventually change its direction of travel, but just because it is accelerating in the opposite direction of the current vector does not mean that it has changed direction; yet. The answer is given as "a." But couldn't "a." or "c." be true?


title: Approximation of a summation by an integral

text: Is it valid to approximate the function $$ Z(t)=\sum_{n}e^{-tE_{n}} ,\ t\ge 0$$ by the integral over phase space: $$ \frac{ 1}{2\sqrt \pi}\int_{0}^{\infty}dxe^{-tV(x)}?$$ For example, in order to evaluate the zeta function over eigenvalues $ \Gamma (s) \zeta _{H} (s,q) = \int_{0}^{\infty}dtZ(t)\exp(-qt)Z(t)$ with 'q' a positive number, and $ \zeta _{H} (s,q)= \sum_{n}(q+E_{n})^{-s} $ Is this approximation faithful and reliable?


title: How do you calculate instantaneous velocity in projectile motion?

text: > An object is thrown horizontally with a velocity of 30 m/s from the top of a > tower. It undergoes a constant downward acceleration of 10 m/s2. The > magnitude of its instantaneous velocity after 4.0 sec, in meters per second, > is: To approach this question I first thought to myself that the velocity in the y-component after 4s is going to equal 10+2(10)+3(10)+4(10); 100m/s. The x velocity will remain constant. Thus the velocity at t=4 would be the resultant vector of 100m/s in the y and 30m/s in the x, which equals 104.4m/s. I am wondering where I am going wrong with my reasoning here?


title: Phonon vectors and characteristic length interpretation

text: Basically I have a set of vectors of unit length, $\\{\nu_i\\}$, describing the movement of phonons (all orthogonal to each other), $\\{\omega_i\\}$. Lets say I only have two atoms, $m_1$ and $m_2$. In this case with only two atoms I have $N=3\times2=6$ modes. In the following it really doesn't matter how many modes I have. The displacement of a single atomic mode would then be $\nu_i\times \sqrt{\frac{\hbar}{m_1\omega}}=r$, from the harmonic oscillators characteristic length, $l_i=\sqrt{\frac{\hbar}{m_i\omega}}$, see Quantum Harmonic oscillator, if it were a single mode. Thus I have a matrix of orthogonal mode vectors, $V=\\{\nu_i\times l_i\\}$, which can be used to create a displacement in cartesian coordinates, $R=\\{r_i\\}$ by knowing the vector of phonon displacements, $U=\\{u_i\\}$. This means that solving the linear equation: \begin{equation} V\cdot U=R \end{equation} I can find the displaced coordinates by knowing the phonon displacement $U$. For same mass $m_1=m_2$, I have suspected that I can use the reduced mass for both atoms, thus yielding $l_i=\sqrt{\frac{\hbar}{m_i\omega_i/\sqrt2}}$.   But what about $m_1\neq m_2$? I suspected I could use the reduced mass again: \begin{equation} \mu=\frac{m_1m_2}{m_1+m_2}, \end{equation} however, how to apply it for two different mass objects? If you have a general application $N$ particles I would be much obliged.


title: Why do single particle states furnish a rep. of the inhomogeneous Lorentz group?

text: Following up on this question: Weinberg says > In general, it may be possible by using suitable linear combinations of the > $\psi_{p,\sigma}$ to choose the $\sigma$ labels in such a way that > $C_{\sigma'\sigma}(\Lambda, p)$ is block-diagonal; in other words, so that > the $\psi_{p,\sigma}$ with $\sigma$ within any one block by themselves > furnish a representation of the **inhomogenous** Lorentz group. But why inhomogeneous Lorentz group if, in the first place, we performed a homogeneous Lorentz transformation on the states, via $U(\Lambda)$? I also want to be clear what is meant by the states "furnishing" a representation. Regarding the above confusion, the same scenario again shows up during the discussion on the little group. Here's a little background: $k$ is a "standard" 4-momentum, so that we can express any arbitrary 4-momentum $p$ as $p^{\mu} = L^{\mu}_{\nu}(p) k^{\nu}$, where $L$ is a Lorentz transformation dependent on $p$. We consider the subgroup of Lorentz transformations $W$ that leave $k$ invariant (little group), and find that: $U(W)\psi_{k \sigma} = \sum_{\sigma'} D_{\sigma' \sigma}(W)\psi_{k \sigma'}$. Then he says: > The **coefficients $D(W)$** furnish a representation of the little group; > i.e., for any elements $W$ and $W'$ , we get $D_{\sigma' \sigma}(W'W) = > \sum_{\sigma''}D_{\sigma' \sigma''}(W)D_{\sigma''\sigma}(W')$. So is it that even in the first part about the Lorentz group, $C$ matrices furnish the representation and not $\psi$? Also, for the very simplified case if $C_{\sigma'\sigma}(\Lambda, p)$ is completely diagonal, would I be correct in saying the following in such a case, for any $\sigma$? $$U(\Lambda)\psi_{p,\sigma} = k_{\sigma}(\Lambda, p)\psi_{\Lambda p, \sigma}$$ Only in this case it is clear to me that $U(\Lambda)$ forms a representation of Lorentz group, since $\psi_{p,\sigma}$ are mapped to $\psi_{\Lambda p, \sigma}$.


title: Physical Interpretation of Lorentz-transformed Single Particle states being linear

text: As in this question, let $\psi_{p,\sigma}$ be a single-particle 4-momentum eigenstate, with $\sigma$ being a discrete label of other degrees of freedom. Weinberg discusses the effect of a homogenous Lorentz transformation $U(\Lambda, 0)$ or $U(\Lambda)$ on these states, and concludes that $U(\Lambda)\psi_{p,\sigma}$ is a linear combination of $\psi_{\Lambda p,\sigma'}$. $$U(\Lambda)\psi_{p,\sigma} = \sum_{\sigma'} C_{\sigma'\sigma}(\Lambda, p)\psi_{\Lambda p,\sigma'}$$ Again, is there any physical information that we can extract from this? (I realize that $\psi_{\Lambda p,\sigma'}$ represent physical states after Lorentz transformation).


title: Kähler potential vs full effective potential

text: In evaluating the vacuum structure of quantum field theories you need to find the minima of the effective potential including perturbative and nonperturbative corrections where possible. In supersymmetric theories, you often see the claim that the Kähler potential is the suitable quantity of interest (as the superpotential does not receive quantum corrections). For simplicity, let's consider just the case of a single chiral superfield: $\Phi(x,\theta)=\phi(x)+\theta^\alpha\psi_\alpha(x) + \theta^2 f(x)$ and its complex conjugate. The low-energy action functional that includes the Kähler and superpotential is $$ S[\bar\Phi,\Phi] = \int\\!\\!\\!\mathrm{d}^8z\;K(\bar\Phi,\Phi) \+ \int\\!\\!\\!\mathrm{d}^6z\;W(\Phi) + \int\\!\\!\\!\mathrm{d}^6\bar{z}\;\bar{W}(\bar\Phi) $$ Keeping only the scalar fields and no spacetime derivatives, the components are $$\begin{align} S[\bar\Phi,\Phi]\big|_{\text{eff.pot.}} = &\int\\!\\!\\!\mathrm{d}^4x\Big(\bar{f}f\,\frac{\partial^2K(\bar\phi,\phi)}{\partial\phi\partial{\bar\phi}} + f\,W'(\phi) + \bar{f}\, W(\phi)\Big) \\\ \xrightarrow{f\to f(\phi)} -\\!&\int\\!\\!\\!\mathrm{d}^4x\Big(\frac{\partial^2K(\bar\phi,\phi)}{\partial\phi\partial{\bar\phi}}\Big)^{-1}|W'(\phi)|^2 =: -\\!\int\\!\\!\\!\mathrm{d}^4x \ V(\bar\phi,\phi) \end{align}$$ where in the second line we solve the (simple) equations of motion for the auxiliary field. The vacua are then the minuma of the effective potential $V(\bar\phi,\phi)$. **However** , if you read the old (up to mid 80s) literature on supersymmetry they calculate the effective potential using all of the scalars in the theory, i.e. the Coleman-Weinberg type effective potential using the background/external fields $\Phi(x,\theta)=\phi(x) + \theta^2 f(x)$. This leads to an effective potential $U(\bar\phi,\phi,\bar{f},f)$ which is more than quadratic in the auxiliary fields, so clearly not equivalent to calculating just the Kähler potential. The equivalent superfield object is the _Kähler potential + auxiliary fields' potential_ , as defined in "Supersymmetric effective potential: Superfield approach" (or here). It can be written as $$ S[\bar\Phi,\Phi] = \int\\!\\!\\!\mathrm{d}^8z\;\big(K(\bar\Phi,\Phi) + F(\bar\Phi,\Phi,D^2\Phi,\bar{D}^2\bar{\Phi})\big) \+ \int\\!\\!\\!\mathrm{d}^6z\;W(\Phi) + \int\\!\\!\\!\mathrm{d}^6\bar{z}\;\bar{W}(\bar\Phi) $$ where $F(\bar\Phi,\Phi,D^2\Phi,\bar{D}^2\bar{\Phi})$ is at least cubic in $D^2\Phi,\bar{D}^2\bar{\Phi}$. The projection to low-energy scalar components of the above gives the effective potential $U(\bar\phi,\phi,\bar{f},f)$ that is in general non-polynomial in the auxiliary fields and so clearly harder to calculate and work with than the quadratic result given above. * * * **So my question is** : when did this shift to calculating only the Kähler potential happen and is there a good reason you can ignore the corrections of higher order in the auxiliary fields?


title: What is energy in $z \neq 1 $ theories?

text: In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in general $\omega$ and $E(\vec{k})$ can have different scaling dimensions. Some clarification would be very appreciated.


title: "gauge fixed world-sheet action"

text: My question is in reference to the action in equation 4.130 of Becker, Becker and Schwartz. It reads as, $S_{matter}= \frac{1}{2\pi}\int (2\partial X^\mu \bar{\partial}X_\mu + \frac{1}{2}\psi^\mu \bar{\partial} \psi_\mu + \frac{1}{2}\tilde{\psi}^\mu \partial \tilde{\psi}_\mu)d^2z$   * Its not clear to me as to why this should be the same as the Gervais-Sakita (GS) action as it seems to be claimed to be. Firstly what is the definition of $\tilde{\psi}$? (..no where before in that book do I see that to have been defined..) Their comment just below the action is that this is related to the $\psi_+$ and $\psi_-$ defined earlier but then it doesn't reduce to the GS action.    * What is the definition of the "bosonic energy momentum tensor" ($T_B(z)$) and the "fermionic energy momentum tensor" ($T_F(z)$)? I don't see that defined earlier in that book either.  I am not able to derive from the above action the following claimed expressions for the tensors as in equation 4.131 and 4.133, $T_B(z) = -2\partial X^\mu(z)\partial X_\mu (z) - \frac{1}{2}\psi^\mu(z)\partial \psi _\mu (z) = \sum _{n=-\infty} ^{\infty} \frac{L_n}{z^{n+2}}$ and $T_F(z) = 2i\psi^{\mu} (z) \partial X_{\mu} (z) = \sum _{r=-\infty}^{\infty} \frac{G_r}{z^{r+\frac{3}{2}}}$   * It would be helpful if someone can motivate the particular definition of $L_n$ and $G_r$ as above and especially as to why this $T_B(z)$ and $T_F(z)$ are said to be holomorphic when apparently in the summation expression it seems that arbitrarily large negative powers of $z$ will occur - though I guess unitarity would constraint that.    * Why is this action called "gauge-fixed"? In what sense is it so?


title: Why are non-momentum DoFs of single-particle states discretely labeled?

text: Following the treatment of Weinberg, chapter 2, we consider $\psi_{p,\sigma}$ as single-particle eigenstates of the 4-momentum. Weinberg says that $\sigma$ labels all other degrees of freedom and we take this label to be discrete for one-particle states. So what exactly is the physical implication of discrete and continuous labeling of other degrees of freedom? And why is discrete labeling physically pertinent to single-particle states?


title: At what temperature does water become a liquid on Mars? On the asteroids? And in a vacuum?

text: I know that I can just read off the phase diagram for water (for the surface atmospheric pressure on each object). But could there possibly be some nuances that someone might miss just from viewing the diagram?


title: Will the James Webb Space Telescope be able to capture something similar to, or better than, the Hubble Ultra Deep Field?

text: Will the James Webb Space Telescope (JWST) be able to capture, or ever be used for, anything similar to the Hubble Ultra Deep Field (HUDF)?


title: How will the luminosity of the current very near supernova Ia "PTF 11kly" develop in the next weeks and why?

text: Currently there is a unique chance for amateur astronomers to observe a very near type Ia supernova, named PTF 11kly. As standard candles are very important to measure distances in the universe, can you give a brief overview of how the luminosity of "PTF 11kly" will probably develop according to current star models? Where do our current models lack accuracy? Is this single supernova so special, that it can fill some gaps in our knowledge?


title: Areas of computer science required for quantum computing

text: What knowledge of computer science should I have, to be able to pursue research in quantum computing. I am a Physics undergrad and would take three core courses in QM, before the completion of my degree. SO I guess necessary QM would be done. What about computer science?


title: Introduction to differential forms in thermodynamics

text: I've studied differential geometry just enough to be confident with differential forms. Now I want to see application of this formalism in thermodynamics. I'm looking for a small reference, to learn familiar concepts of (equilibrium ?) thermodynamics formulated through differential forms. Once again, it shouldn't be a complete book, a chapter at max, or an article. **UPD** Although I've accepted David's answer, have a look at the Nick's one and my comment on it.


title: Apparent contradiction between calculations and intuition?

text: I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with. We have a potential step described by $$V(x)=\begin{cases}0& x\le0\\\V_0 & x>0\end{cases}$$ and a wavefunction $\psi(x)$ that satisfies the equation $${\hbar^2\over 2m}{\partial^2 \over \partial x^2}\psi(x)+V(x)\psi(x)=E\psi(x)$$ I wish to find the probability of reflection. By continuity constraints at $x=0$ I have arrived at the reflection amplitude being $$R={k-q\over k+q}$$ where $k=\sqrt{2mE\over \hbar^2}$ and $q=\sqrt{2m(E-V_0)\over \hbar^2}$ then we let $V_0\to -\infty$ giving $q\to \infty$, so $R\to -1$ $\implies |R|^2\to 1$ But I would have guessed that $|R|^2$ should vanish at the limit so that the incident wave is totally transmitted! Could someone please explain?


title: What controls whether a ball will skid or roll?

text: A billard ball is struck with a cue. The line of action of the applied impulse is horizontal and passes through the center of the ball. The initial velocity $v_0$ of the ball, its radius $R$, its mass $M$ and coefficient of friction $\mu_k$ between the ball and the table are all known. How far will the ball move before it ceases to slip on the table?


title: How to learn physics effectively and efficiently

text: How do you effectively study physics? How does one read a physics book instead or just staring at it for hours? (Apologies in advance if the question is ill-posed or too subjective in its current form to meet the requirements of the FAQ; I'd certainly appreciate any suggestions for its modification if need be.)


title: How to study physics as a first year student?

text: I firstly apologise if this question is off the topic. I am a first year undergraduate student and the required textbook for the course Advanced Physics is Fundemental of physics by Halliday. This textbook is huge and to be honest I was scared when I saw the size of the textbook. There are too much text to read and there are many exercises at the end of each chapter and I do not think that I would have time to do every single problem at the end of each chapter. So with this information, what is the effective way of studying physics? what to read and what not to read? what exercises should I do? should I try to do all exercises? any other advice that I should do to be successful in physics is also appreciated. If you need also some information about my background: I am a first year combined bachelor of electrical engineering and bachelor of mathematics and I have good knowledge of math but did not do any physics in highschool.


title: What is an effective and efficient way to read research papers?

text: I will be a grad student in condensed matter theory starting this fall. As an undergrad, I did the basic physics and math courses as well as a few grad classes (qft, analysis, solid state physics etc.) When I start reading research papers, I often feel overwhelmed because there is so much that I don't know and I find it hard to decide which points to gloss over and which points to spend time on and understand more thoroughly (which in my case, would probably require supplementary reading of textbooks or related papers) What are some things to keep in mind while reading a paper so that:   1. I get a general overview of the paper and I more useful insights into parts   2. I can do the above reasonably fast (say, finish reading at least 1 paper a week for a start) You don't have to be specific to condensed matter theory papers when you answer.


title: Good ways for learning and cramming formulas?

text: I got an exam coming up and its numerical based (its pre-university level exam) but really tough. I want to know about various ways and methods to learn formulas. I know how can I derive them but its time consuming. I want to know how you people learnt these formulas?


title: Slow thermal equilibrium

text: I have a question which is inspired by considering the light field coming off an incandescent lightbulb. As a blackbody radiation field, the light is in thermal equilibrium at temperature $T$, which implies that each normal mode has a _mean_ energy given by Planck's law, and a random phase. Thus, if I were to look, microscopically, at the electric field, I would see a fairly complicated random function that can only really be considered constant at timescales $\tau\ll \hbar/k_B T$ (at which the corresponding modes have next to no amplitude and therefore do not affect the electric field's time dependence). This illustrates a general aspect of thermal and thermodynamic equilibrium: they are only relevant concepts when the systems involved are looked at on timescales far longer than their relevant dynamics. My question, then, is this: are examples of slowly-varying systems (where by "slowly" I mean on the timescales of seconds, or preferably longer) that can be considered to be in thermal equilibrium on timescales longer than that known?


title: Why do joined massless springs, act like a rope under tension?

text: In an oscillations exercise there is a spring attached to another spring, attached to a block. Long story short: I have to find the global $k$. In the solutions it says: "Because the springs are massless, they act similar to a rope under tension, and the same force $F$ is exerted by each spring." I don't really understand how the springs being massless, is an argument for saying that they exert the same force (being the global force) upon the block. Anyone care to elaborate?


title: Apparatus for recieving Radiant Energy by Nikola Tesla

text: http://www.keelynet.com/tesla/00685958.pdf An elevated, insulated copper plate, a patented Tesla Condenser, and a voltage inverter, we've got free electricity right? admittedly small, but as a proportion to potential difference in the height of the mast and possibly the depth of the ground pole. Anyone really know what's going on here and why it's not implemented?


title: Derive Schwinger-Dyson equations in Srednicki

text: On page 135 in Srednicki he defines the functional integral $$Z(J) = \int\mathcal{D}\phi\,\exp\Big[\mathrm{i}\big(S+\int\mathrm{d^4}y \,J_a\phi_a\big)\Big], \tag{A}$$ where $S$ and $J_a$ are the action and sources respectively (sum over $a$). What I don't seem to get is that when he cosiders a small variation $\delta Z$ he get the variation of the action inside an integral as follows (I get it without the integral): $$0=\delta Z(J) = \mathrm{i}Z(J) \times \Bigg[\int \mathrm{d^4}x\Big(\,\frac{\delta S}{\delta \phi_a(x)}+J_a(x)\Big)\delta \phi_a(x)\Bigg]\tag{B}$$ My attempt: $$0=\delta Z(J) = \frac{\delta Z}{\delta\phi_b(x)}\delta\phi_b(x)\\\\[10mm]=\int \mathcal{D}\phi\,\delta\phi_b(x)\Bigg[\frac{\delta}{\delta\phi_b(x)}\mathrm{e}^{\mathrm{i}(S+\int\mathrm{d^4}y\,J_a(y)\phi_a(y))}\Bigg].\tag{C}$$ The box becomes: $$\Bigg[\frac{\delta}{\delta\phi_b(x)}\mathrm{e}^{\mathrm{i}(S+\int\mathrm{d^4}y\,J_a(y)\phi_a(y))}\Bigg] = \frac{\delta}{\delta\phi_a(y)}\mathrm{e}^{\mathrm{i}(S+\int\mathrm{d^4}y\,J_a(y)\phi_a(y))}\frac{\delta\phi_a(y)}{\delta\phi_b(x)}\\\\[10mm]=\delta_{ab}\delta^4(x-y)\mathrm{e}^{\mathrm{i}(S+\int\mathrm{d^4}y\,J_a(y)\phi_a(y))}\times\mathrm{i}\underbrace{\frac{\delta}{\delta\phi_a(y)}\Big(S+\int\mathrm{d^4}y\,J_a(y)\phi_a(y)\Big)}_{\Lambda}. \tag{D}$$ Lambda becomes (?) $$\Lambda = \frac{\delta S}{\delta \phi_a(y)}+\int\mathrm{d^4}y J_a(y). \tag{E}$$ What I'm I doing wrong here?


title: Kaon spontaneously splits into two pions (just need an confirmation)

text: I just need a confirmation on a problem that I am dealing. In my problem I have a statioary kaon which spontaenously splits into two pions which are headed in different directions. Is it possible to write the energy conservation like this: \begin{align} E_1 &= E_2\\\ \sqrt{{E_{01}}^2 + (p_1c)^2} &= 2\sqrt{{E_{02}}^2 + (p_2c)^2}\longleftarrow \substack{\text{since $p_1 =0$}}\\\ {E_{01}} &= 2\sqrt{{E_{02}}^2 + (p_2c)^2}\\\ \end{align} I am especialy interested in a factor of 2 before the square root. * * * **EDIT:** What about if Kaon would split into 2 diferent particles A and B? \begin{align} E_1 &= E_2\\\ \sqrt{{E_{01}}^2 + (p_1c)^2} &= \sqrt{{E_{0A}}^2 + (p_Ac)^2} + \sqrt{{E_{0B}}^2 + (p_Bc)^2} \end{align} where $p_A = p_B$?


title: Use Equations 1 and 2 to eliminate $T$ and show the expression for $f$ is given by

text: I am not quite understanding what needs to be done but I am assuming that I must combine the two equations and get rid of the variable $T$ in order to make this equation of $f$ below: (Note:These formulas are in the regards to inclined planes) **Equation of $f$:** $$f=g(m-M\sin(\theta))-(m+M)a$$ **Equation #1:** $$T-Mg\sin(\theta)-f=Ma$$ **Equation #2:** $$mg-T=ma$$ Here is the work I have done so far: $$T-Mg\sin(\theta)-f-Ma=mg-T-ma$$ (I add and subtract the variables to one side where I get) $$f=2T-g(m-M\sin(\theta))-(m+M)a$$ The only part that is confusing me is, how do I get rid of the variable $T$ in this equation? (NOTE: I am not looking for the answer but only how to deal with this type of problem so that I may know what to do in the future if this problem comes around. Also please edit this post for the sake of the quality of the content of this stack exchange site) I thank everyone in advance for the contribution to answering this question


title: Is the newton's second law for a body experiencing a frictional force, relative to the surface in contact?

text: Let us consider a routine mechanics problem.A block of $ 10kg $ rests on another block of $ 2kg $ on a frictionless table.Let $ \mu = 0.2 $ be the coefficient of friction(let's neglect the difference between coefficients of static and kinetic friction here)between the surfaces of the two blocks. ![image](http://i.stack.imgur.com/Iwfb3.png) A horizontal force of $ 10N $ is applied on the lower block.Now,the maximum force of friction( $F_\mu $)that can be applied on either block by the other surface is equal to $$ F_\mu\,_\max = \mu R $$ where $R$ is the normal contact force between the two blocks.As the blocks don't accelerate vertically, $$ R= 10g \approx 100N $$ Therefore, $$ F_\mu\,_\max = 0.2 \times 100 = 20N $$ The newton's 2nd law for the lower block in the horizontal direction would be $$ 10 - Friction = 2kg \times a_2 $$ and that for the upper block would be $$ Friction = 10kg \times a_1 $$ Clearly,the maximum force of friction is more than the force applied($10N$).So,frictional force will ensure that none of the blocks have any acceleration. But,if you look at both the blocks as a single system,the only net external force is $F=10N$ and hence the acceleration of the centre of mass of the system is $ a= \frac{10}{10+2} = \frac{5}{6} m/s^2 .$ Since both of the the above results contradict each other,(unless the blocks accelerate in the opposite directions with same magnitudes of acceleration,which is not the case),I assume that its fairly wrong to say that the blocks have zero individual accelerations(with respect to ground).I seriously suspect that the acceleration of either block in my equation is of the frame of reference of the other block,rather than ground;but I fail to see how.I think my question is mostly a confusion in writing newton's 2nd law for different reference frames when friction is involved.


title: Effects of a very large magnetic field on the human body

text: Ever since reading about the NHMFL I have always wondered about this and asked several people without getting a good satisfactory answer. My question is, considering the simplest case let's say a uniform magnetic field with a very high magnitude constant both in time and space permeating a large room, what would happen to my body in such a field like if I was to just walk through it? How large would the magnitude need to be before I "feel" anything? One tesla is fairly large, would I feel anything? I imagine as we crank up the magnitude, I would feel queasy and sick. What if I crank it up to fifty teslas or a hundred teslas? Would it hurt? Would it mess up my synaptic potentials? Would I go crazy with a dysfunctional brain? Would I pass out or go into a coma? At what point will the damage become irreversible? What magnitude will cause death? With a high enough magnitude would molecules in my body start falling apart? What happens at hundreds of teslas? Thousands of teslas or millions of teslas? The closest thing here I found was here in the accepted answer "a magnetar that would be 1000 miles away would kill us due to diamagnetism of water in our cells". This is the kind of stuff I am looking for, the magnitude of the B-field and then its effect on a human body. Like "at 100T, your body would **___ _** because **_ _**and at 1000T, your body would **___ ___ __** because **___ ___**" and so on. ~~If we allow changes in the magnetic field in time, does the induced electric field "hasten" the effects somehow? Would a strong enough E-field cause a shock within us burning our organs and killing us even if the average B-field is small but the db/dt is "large" for example?~~ I don't know if any experiments on biological samples have been done because artificially creating magnetic fields beyond a 100T or so hasn't been quite done yet much less sustaining them and observing the effects on a biological tissue. But if there are any cool references even if they are on theoretical grounds, that would be interesting. Thanks. * * * Edit: Just to make the question more answerable, I'll focus only on static fields. Anyone know of any references/experiments regarding the effects of large magnetic fields on biological tissues?


title: Decay of particle (for example $\pi^+$); Find energy

text: I don't understand how to solve this: A $\pi^+$ decays into a muon and neutrino. Find the pion's energy if   * max $E_\nu$ / min $E_\nu$ = 100/1;   * $m_\nu = 0$   * $m_\pi*c^2 = 140\text{ peta-eV}$


title: Why is there a $\pi$ phase difference when light goes from a rarer medium to a denser medium?

text: I want the basic reason. I want the description of answer graphically also.


title: Why is a $\pi$ phase added on reflection and why do things change with absorption?

text: 1. Mathematically, how does a $\pi$ phase shift appear upon reflection of light off a optically denser medium?   2. Why is it always $\pi$?   3. If the medium is absorptive it is no longer $\pi$?


title: Why does the echo for soundwaves hitting a vacuum come back out of phase?

text: > **Possible Duplicate:**   >  Phase shift of 180 degrees on reflection from optically denser medium I've read in a physics book for musicians that, when a soundwave hits a near- solid object, it generates an almost completely in-phase echo. However, when the wave hits a near-vacuum, the echo generated is almost completely out of phase echo. Can someone explain, in detail, why this happens (or point me at a detailed explanation)? (My math-fu is fairly strong, but my physics-fu is not).


title: why does the phase change when wave reflects from rigid boundary

text: when the wave is reflected from open end there is no phase change but when it reflects from the rigid surface its phase changes. in open surface its phase change is 0 and in rigid surface its phase change is pi. How is it possible. Is is possible to reflect from open end.