title: Will I get a shock when I try to use my hair-dryer under water?

text: Occasionally people get killed in their bathtubs by having an electrical device such as a hair-dryer take the bath with them - in movies. It seems to be a common belief that this is realistic, even though it makes no sense to me. There are two scenarios:   1. The device short-circuits internally (that means entirely over either both poles of the energy supply having contact with water, or the pole under electric tension together with the earth conductor - that way, the current should not leave the devices chassis).   2. The device short-circuits over the pole under electric tension and the bathtub itself (earth eventually, but a different route). In the first case (which I thought would be common, since the earth conductor is often connected to prominent large metal parts for safety reasons) I can't see what should happen: Clearly a human being wouldn't be affected from that local a current that takes place entirely in the chassis of the device - or am I mistaken? In the second case, the question is whether the human body is more conductive (including the skin barrier) than the bathtub water. And even if it was, which I don't know, that would only make a difference if this circumstance would actually lead to a shortcut the current could take on its way to earth. All that sounds like a lot of "ifs" to me, so I thought I put the question out here.   * What do people think on the physics?   * Do people have links to statistics, that is: does this at all happen?


title: Direction of current flow

text: In one of my homework questions, I was given the following setup. I was asked to determine if the induced current flows from X to Y, or from Y to X. ![enter image description here](http://i.stack.imgur.com/Ie7uM.jpg) From Lenz's Law I know that the current in the tube flows in the direction opposite to R to oppose the change in flux due to the rotation of the tube in the direction R. However, I am completely lost as to how to determine the direction of current flow across XY. It seems that the charges on the tube along XY are always parallel to the flux field of the magnet. Because of this, no emf should be induced across XY by Faraday's Law.


title: Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

text: I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}-\mu+V\left(z\right) & \triangle(z)\\\ \triangle(z) & \frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\mu-V(z) \end{array}\right)\left(\begin{array}{c} u_{n}(z)\\\ v_{n}(z) \end{array}\right)= \epsilon_{n}\left(\begin{array}{c} u_{n}(z)\\\ v_{n}(z) \end{array}\right)$$ along with the equations for gap function $\triangle(z)$ and number density $n(z)$. $$\triangle(z)=U\sum_{n}\left(1-2f_{n,}\right)u_{n}(z)v_{n}^{\star}(z)$$ and $$n(z)=2\sum_{n}|{u_{n}(z)}|^{2}f_{n}+|{v_{n}(z)}|^{2}\left(1-f_{n}\right).$$ For the case of solving the BdG equations in Fourier space in Matlab for the case of a periodic potential and periodic gap function (assumed), we can take $$u_{n}(z)=\sum_{k}\exp\left[ikz\right]U_{n,k}, $$ $$\triangle(z)=\sum_{K}\exp(iKz)T_{K},$$ and $$ V(z)=\sum_{K}\exp(iKz)P_{K} $$ where the sum is over the reciprocal lattice vectors $K$ leading to the number equation $$N=2\sum_{n,k}\left[f_{n}|{U_{n,k}}|^{2}+\left(1-f_{n}\right)|{V_{n,k}}|^{2}\right]$$ with $ f_{n}$ as the Fermi distribution function. Solving the set of equations self-consistently for a fixed $N$, I am trying to get a value of chemical potential from the number equation each time after solving the eigenvector components $U_{n,k}$ and $V_{n,k}$, but due to the form of the exponentials in the number equation and sum over large number of them, I am unable to get a correct value of chemical potential out of them using Matlab routines as the root of the equation to put it back into the equations for eigenvector components. In most cases, I get random values of chemical potential since the equation is more or less insoluble. How can I avoid this error ? Is there a better way to numerically solve the BdG equations self-consistently ? I also want to do this assignment in real space avoiding finite size effects but started with the Fourier space case to avoid errors associated with discretizing the differential. Please guide and ask for any details you might need. Following is my MATLAB code to solve the equations in real space but the code does not work as fsolve does not find the mu value. http://postimg.org/image/v7amx5vd9/full/ ## http://postimg.org/image/do9pyyk7z/full/ **If you have solved BdG equations numerically, please tell about the method and steps you used such that the above problems are eliminated.**


title: How do I figure out the effects of wind on flight?

text: For a school project, I'm trying to make an automated flight planner, considering mainly the differences in flight paths according to wind. Now I've heard that flying with/against the wind affects airspeed. But I really don't know any specific(even empirical) laws on determining by how much it does so. What's more, I've also heard about gas savings through these effects. That I would have pretty much no idea of how to calculate but that's less important. Basically if anyone can point me in the right direction to figure out how to figure out solid speed gains, I'd be grateful, even moreso if I can find out the theoretical origins of such laws. (The only thing I found that I think is close to what I want is this, but I have no clue what the laws derive from)


title: Velocity in Motional EMF

text: To calulate motional $\epsilon$, we use the following formula: $\epsilon$ = $-vBL$ To calculate the velocity so the motional $\epsilon$ can be calculated, what is the proper formula from what is below? Assuming acceleration is constant. $$ v = \frac{\Delta x}{\Delta t} $$ or, $$ a = \frac{\Delta v}{\Delta t} $$ And what differs from each one of them? The displacement is given, and the acceleration is calculated from the force & mass, and the time is calculated via this formula: $$ s = \frac{1}{2}at^2 $$


title: Capacitance in a capacitor

text: This here is a question that I just don't know what to do with. I don't know what I'm doing wrong. " _A plate capacitor consists of two plates with area 2.5 cm$^2$ at a distance of 1.6 mm from each other._ _a) Calculate the capacitors capacitance_ _b) How large is the charge of the capacitor if the voltage between the plates is 1700V_ _c) How does the capacitance change if you place a 1.6mm thick glass pane between the plates?_ " Now this is how I tackle the problem. For a) I assume that since there is no other material mentioned, we're either dealing with a vacuum or air. Both have a relative permativity of around 1. This means that: $C = \epsilon\frac{A}{d} = 8.9 * 10^{-12} * 1 * 0.00025 \div 0.0016 = 1.4 pF$ That's correct. For b) I do the following: $C = \frac{Q}{U} <=> Q = CU$ $Q = 1.4 * 10^{-12} * 1700 = 2.4nC$ The answer in the book is 16nC. How? Finally for c), I use the same formula I did for a) but I change the relative permativity to that of glass, and again I get the correct answer. So it is only b) I'm confused about.


title: Thermal expansion of two bolts

text: ![Bolts](http://i.imgur.com/EpuQK5G.png) I have this question asking me about the thermal expansions of two bolts, a steel one, and a brass one. I have the equation: $\ (\delta L/L)/T = \alpha $ I don't understand how I can use this equation to manipulate the temperature for the two bolts simultaneously, as opposed to the temperature required to expand each individual bolt by 5 $\mu$m. Is this even the correct equation? Or is there another that I should be using. What I have done is rearranged for T: $\ (\delta L/L)/\alpha = T$ Then, using the individual values for $\delta$L = 5$\mu$m L= 0.01 m and the $\alpha$ for steel to get $T=45.5^\circ C$ and similarly, for Brass, to get $T=8.77^\circ C$. This obviously cannot be correct, considering, using this method, the $T_0=27^\circ C$ has not been taken into consideration. Any help would be good. Thanks.


title: "Skidding" to Brake on a Skateboard

text: When people are skateboarding, sometimes they kind of push out their back foot when they turn while carving, causing the board to skid a bit. I was wondering the physics behind this, any details on the subject. One thing in particular I was wondering was why it's harder to do this on smaller boards. Here's a video of carving on skies: https://www.youtube.com/watch?v=qhZmnHtgwec And here is a link to my previous, even more poorly phrased, question: Physics of Carving on a Skateboard


title: Class of scalar field actions invariant under conformal transformations

text: From the actions in $d$ dimensions given by $$S = \int d^dx \,\, \partial_{\mu}\phi \partial^{\mu} \phi + g \phi^k$$. What is the condition that needs to be $k$ so that the theory is invariant under conformal transformations? Initially, I have been trying to tackle the special case of pure scale transformations $x^{\prime}= \lambda x$. After putting in the transformed measure and fields as $d^d x^{\prime} = \lambda ^d d^dx$ and $\phi^{\prime}(\lambda x)= \lambda ^{-\Delta}\phi(x)$, I got the following equation $$\lambda^{-2-2\Delta} + \lambda ^{-k \Delta}=\lambda^{-d}$$ Can I solve this in general for k, in terms of $\Delta$ and $d$. How do I find the scaling dimension of a theory, or is it a parameter? And how do I solve the general case of any conformal transformation (including SCTs)?


title: exponential potential in physics

text: given the differential equation $$ -\hbar^{2}D^{2}y(x)+ae^{bx}y(x)=E_{n}y(x) $$ here $ D=d/dx $ derivative are there examples in physics where this potential appears ??, i know how to solve it but i do not know pratical examples where the exponential potential appears the solution is given by http://www.wolframalpha.com/input/?i=-y%27%27%28x%29%2Baexp%28bx%29y%28x%29%3Dcy%28x%29


title: Thermal Conductivity Graph

text: This is our first time (as an engineer) seeing this type of graph that we can't interpret. This is a rough comparision of thermal conductivity from the Wiki page. http://en.wikipedia.org/wiki/Thermal_conductivity **What we know** The more we go in the log x axis, the more conductive the material is. Say, _silver_ vs _insulation fiber_. **What we don't know** What the length of each bar presents (in terms of y axis). Say, why _silver_ bar is 3 times the _copper_ and what does it mean. ![enter image description here](http://i.stack.imgur.com/HsyLk.jpg)


title: Isotropy of Space

text: Weinberg writes in his Cosmology text "Likewise,isotropy requires the mean value of any three-tensor $t_{ij}$ at $x=0$ to be proportional to $\delta_{ij}$ and hence to $g_{ij}$, which equals $a^2\delta_{ij}$ at $x = 0$" May someone please illuminate the point.


title: Force acting on a simple rigid body in space

text: so this is the question that's been bothering me: Say you have a simple rigid body in space that is at rest or travelling with only translational motion at a constant speed. Say that the body is something like a rod and it's not rotating. So, at some point, an external force is acted on the rod, just for an instance and it is not acted on some axes that goes through the center of mass. What will happen?? My guess is that it will start rotating about the center of mass (because of torque) + it will get some translational motion towards the direction of the force. Is that correct? and if so, how much of the force becomes rotation and how much translational movement and why?? please forgive my english and thnx in advance!!


title: Is there a giant cloud of antimatter at centre of the Milky Way

text: Among others, this page says there is a giant cloud of antimatter at centre of the Milky Way, which was discovered in the 1970s. My brother doesn't believe there is any such cloud. I'm prepared to believe it does exist, but can anyone explain in simple terms _how_ the astronomers know it's there for sure? Also - is there any quick and easy way to explain why the _total_ amount of matter in the universe is thought to be more than the total antimatter (or confirm that we don't even know if that's true or not)?


title: Green function two solutions questions

text: I am having some trouble with Green functions in electrostatics What is the meaning of this trick: Given $$\vec{\nabla}^2 V(\vec{r}) = \frac{-1}{\varepsilon_0}\rho(\vec{r}) = \frac{-1}{\varepsilon_0} \int \delta ^3(\vec{r}-\vec{r}')\rho(\vec{r}') d^3 \vec{r}' = \frac{1}{4 \pi \varepsilon_0} \int \vec{\nabla}^2G(\vec{r},\vec{r}')\rho(\vec{r}') d^3 \vec{r}'.$$ I see $$\vec{\nabla}^2 V(\vec{r}) = \vec{\nabla}^2\left[\frac{1}{4 \pi \varepsilon_0} \int G(\vec{r},\vec{r}')\rho(\vec{r}') d^3 \vec{r}'\right]$$ and so $$V(\vec{r}) = \frac{1}{4 \pi \varepsilon_0} \int_V G(\vec{r},\vec{r}')\rho(\vec{r}') d^3 \vec{r}'$$ where $G$ is a greens function satisfying $$\vec{\nabla}^2 G(\vec{r},\vec{r}') = - 4 \pi \delta(\vec{r} - \vec{r}').$$ Why is this not a solution? It seems like it is, and further it is general (applies to elliptic, parabolic, hyperbolic), the problem is specifying boundary conditions. If this is a solution it should turn into the following in some obvious easy way: Using Greens identities I can show $$V(\vec{r}) = \frac{1}{4 \pi \varepsilon_0} \int_VG(\vec{r},\vec{r}')\rho(\vec{r}') d^3 \vec{r}' + \frac{1}{4 \pi}\int_{S}\left[G(\vec{r},\vec{r}')\frac{\partial V}{\partial n'} - V(\vec{r})\frac{\partial G}{\partial n'} \ \right] \ dS'$$ Why are the extra terms missing from the first solution I gave? It is said that this is not a solution because it over-specifies the boundary conditions, but once we specify Dirichlet or Neumann it does become one. What is the intuition for this statement though, would not over-specification only help us? Jackson does not make sense to me on this point.


title: de Rham Cohomology of Schwarzschild Manifold

text: Let $C^p(M)$ denote the group of closed $p$-forms on the manifold $M$, and $Z^p(M)$ the group of all exact $p$-forms on the manifold $M$. The de Rham cohomology is given by the quotient, $$H^p(M)=C^p(M) \, / \, Z^p(M)$$ I am interested in computing the de Rham cohomology of a Schwarzschild manifold, i.e. $$H^p\left(\mathbb{S}^2 \times \mathbb{R}^2\right)$$ Proceeding from the above definition may be arduous, so could one use a Mayer- Vietoris approach instead? If so, what is the Mayer-Vietoris sequence for cohomology (rather than homology), and what decomposition of the manifold, if any, can we apply to use Mayer-Vietoris? Otherwise I was hoping to utilize a theorem which expresses the cohomology of a Cartesian product of spaces, as $$H^p(\mathbb{S}^2)\quad H^p(\mathbb{R}^2)$$ are well-known cohomologies. Other creative/different approaches to computing the cohomology are certainly welcome and encouraged.


title: How to find Lepton Number?

text: is a Standard Model particle with (u, d, b) quark content. What are the electric charge, baryon number and lepton number of this particle? Is this the only particle expected to exist with this quark content? Justify your answer I know that the overall charge is 0, baryon number is 1. But what is the lepton number? ( The answer is 0) . Why is it 0? Why is it not the only expected particle with this quark content?


title: Why do we exclude the $(i,i)$ case when summing over internal forces?

text: In the majority of the literature and lectures I see when a system of particles is involved, I usually see the following expression (or similar) for the total force on particle $i$: $$\vec{F}_i = \vec{F}_{i_{ext}} + \sum_{i\neq j}\vec{F}_{ji}$$ Why is it necessary to include the condition $i\neq j$ in the internal force terms? We know that $\vec{F}_{ii} = 0$, and hence removing the constraint and summing over general $i,j$ surely won't change the total.


title: Yang-Mills existence and mass gap

text: In the Clay institute problem description of the Yang-Mills existence and mass gap problem it states that the quantum Yang Mills needs to be formulated in $\mathbb{R}^4$ space. I was wondering whether this meant it needed to be formulated in Euclidean space or Minkowski space? (It seems like Euclidean but the majority of QFTs are in Minkowski space, right?)


title: How do I calculate the necessary velocity of two reels of tape to maintain constant tension on the tape?

text: I have a real-world problem that I'm quite certain can be solved with a formula. Unfortunately I myself am not particularly skilled in the realm of physics or math. Any and all help is very much appreciated! I have a cassette tape. It's on a transport that does not use a capstan to drive the tape. As the tape travels from the first reel to the second, the first reels diameter decreases while the second reels diameter increases as the tape moves from one to the next. In this situation, both reels have independent speed control. At what rate does motor A need to increase/decrease in speed, in proportion to motor B, to maintain constant speed and tension on the tape between the two reels? I want to calculate the velocity from the radius. To know the radius, we have to know where we are on the tape. Any ideas on the best way to go about this?


title: Electric field and magnetic field question here?

text: Are the energy of the electric field and the energy of the magnetic field concentrated on their sources OR are they scattered in the environment where the fields arent zero? Can you base your answer on a formula so I can understand it better?


title: What are the AdS/CFT papers which study the stringy effects in the bulk?

text: I would like to know of a list of pedagogical/classic/nice papers that study stringy effects in the bulk. May be a sequence which a student follows to understand the stringy nature that is at play.


title: Why are roofs blown away by wind?

text: Whenever there are high winds, such as in storms, thin metal roofs on sheds as well as concave roofs on huts are sometimes blown away. One explanation provided to me said that the higher velocity of the air outside causes the air pressure above the roof to decrease and when it has decreased to a certain extent such that the air pressure above the roof is lesser than the air pressure beneath the roof and due to _some kind of osmosis_ , the air particles move from the area of higher pressure (beneath the roof) to the area of low pressure. In this process, the roof is blown away. Another explanation, specifically about the thin metal roofs, said that it was blown away due to the lift caused by the air and this is the same kind of lift you get when you blow on paper. Both these explanations puzzle me. What really bothers me is the basis of the first one, **how can an increase in velocity cause pressure to drop?** I can't seem to correlate that with the Force per unit area definition of pressure. Please, oh great physicists of the internet, help me and every other ordinary person to understand how and why roofs get blown away.


title: Work to pump water through a hole in a trapezoidal prism

text: So I don't want to give the full details of the problem I'm working on, since I want to solve it myself. But I'm not sure which physical principles I'm supposed to use, since this is a Calc 2 question, and I'm not that familiar with Physics. Basically, I need to pump water out of a tank, which is shaped like a trapezoidal prism through a hole at the top. (The question is poorly written and doesn't tell me which side is the top, but I'll assume it's the short side of the parallel sides of the trapezoid.) Certainly I'll need the work formula $W = \int F(x)dx$ but will I also need some kind of fluid flow formula (didn't Bernoulli have something relevant here?). Thank you in advance.


title: Magnetic declination

text: i couldnt just figure out when i got to know that declination can be zero also. How can true and magnetic north ever align themselves in a straight line in any place? Also if a compass aligns in the direction of horizontal component of MF at that place does this mean that at any place horizontal component is directed towards the magnetic north ?? Maybe i am misinterpreting this idea of direction. here is what i think : If u look at a bar magnet's field lines not every tangent to the curve will pass through the north pole. So the compass placed at a point will align with the field but it wont point at the north pole always . please explain


title: What exactly is a gauge anomaly?

text: In lots of papers I read about gauge anomalies. For example, avoiding gauge anamolies in the MSSM is the reason for introducing an extra Higgs doublet. Gauge anamolies in the Standard Model are cancelled due to accidental symmetries etc. Can someone please explain what a gauge anamoly exactly is and also how introducing an extra Higgs doublet helps avoid it in MSSM?


title: Mathematical formalism to include wave and particle perspectives of light

text: Does the exist any mathematical formalism (model) describing the behavior of light and incorporating its particle character (divisibility, quantization) and wave character? (i.e. quantized wave model)


title: Strongly coupled electromagnetic force

text: What would be defining about a strongly coupled electromagnetic force? Would it mean that separating two oppositely charged particles makes another particle-antiparticle pair, rather than continuing to separate the particles? Would it make the electromagnetic force "hadronic", in a sense?


title: Proof for the Mass gap of sine-Gordon action with $g \cos(\beta \Phi)$

text: This is the sine-Gordon action: $$ \frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi \+ g \cos(\beta_{}^{} \cdot\Phi_{}) $$ Here $\mathcal{M}^2$ is a 1+1 dimensional spacetime manifold, where 1D space is a $S^1$ circle of length $L$. At $g=0$ : it is a chiral boson theory with zero mass, gapless scalar boson $\Phi$. At large $g$ : It seems to be well-known that at large coupling $g$ of the sine-Gordon equation, the scalar boson $\Phi$ will have a mass gap. > Q1: What is the original Ref which states and **proves this statement about > the nonzero (or large) mass gap for large $g$**? - > Q2: What does the mass gap $m$ scale like in terms of other quantities (like > $L$, $g$, etc)? - **NOTE** : I find S Coleman has discussion in (1)" _Aspects of Symmetry_ : Selected Erice Lectures" by Sidney Coleman and this paper (2)Quantum sine-Gordon equation as the massive Thirring model - Phys. Rev. D 11, 2088 by Sidney Coleman But I am not convinced that Coleman shows it explicitly. I read these, but could someone point out explicitly and explain it, how does he(or someone else) **rigorously prove** this mass gap? Here Eq.(17) of this reference does a quadratic expansion to show the mass gap $m \simeq \sqrt{\Delta^2+\\#(\frac{g}{L})^2}$ with $\Delta \simeq \sqrt{ \\# g k^2 v}/(\\# k)$, perhaps there are even **more mathematical rigorous way to prove the mass gap with a full cosine term?**


title: Formation of black holes

text: If stars start with a finite density and light can escape from them, how can they be compacted to form a mass with infinite density which light cannot escape? The black hole will have the same mass as the original star (correct?) and therefore will act on the photons with the same force of gravity, right?


title: Why can you add moment vectors?

text: My book says the following: > If the body is acted upon by a system of forces, the resultant moment of the > forces about point O can be determined by vector addition of the moment of > each force. The resultant can be written symbolically > > $$(M_R)_O = \Sigma (r \times F)$$ I don't understand why you can add the vectors. Shouldn't you just calculate the magnitude of each moment vector, if its counterclockwise make the magnitude positive, if its clockwise leave it positive and add the magnitudes? For example if you have two moment vectors: $$\vec{M_1} = (a,b,c)$$ (CLockwise) $$\vec{M_2} = (c,d,e)$$ (Anticlockwise) So you know that there is a moment of magnitude $| \vec{M_1} |$ acting clockwise and a moment of magnitude $|\vec {M_2} |$ acting counterclockwise. So why can't you just do the following: $$ x = \pm | \vec{M_1} | \pm |\vec {M_2} |$$ $$\text{If } x > 0, \text {the moment is counterclockwise, if its negative its clockwise} $$ Where the sign of the moments depend on whether they are clockwise or anticlockwise. Why is the above method invalid? The methods are obviously not the same since adding two vectors isn't equal to adding the magnitude unless the vectors are collinear. Also, if you do add the vectors and get vector $M_3$, how do you know if $M_3$ is clockwise or counterclockwise?


title: Ice cream cone and loop-de-loop

text: Was siting in class thinking about this problem, did some rough sketches of a solution but never really managed to solve it. ![Ice cream cone and a loop-de-loop](http://i.imgur.com/D8XAh.png) > Assume a boy starts at the top of a circle with radius R as described in the > picture. It is a snowy day and the path can be considered without friction. > The boy enters a loop with radius r at the bottom of the hill. At the top of > the loop the boy loses his icecream cone in such a way that it starts > faling. The initial velocity of the icream is 0 m/s straight down. The problem is to find R expressed by r, such that the boy reaches the icrecream just as he reaches the bottom of the loop. The problem boiled down to finding out how much time the boy uses getting from the top of the loop to the bottom. Any help, solutions or inputs would be great. * * * My attempt, I know that this is most likely 90% wrong By using conservation of mechanical energy. The speed at the bottom of the hill equals $$ v_b^2 = Rmg $$ And the velocity at the top of the loop equals $$ v_t^2 = 2g\left( R - 2r \right) $$ Vi know that the aceleration is constant and equals $ g $ (Here is where I think I make my mistake, forgot to acount for the angular velocity) $$ s = \dfrac{v_1 - v_0}{2} t $$ We use this equation to find out how long it takes the boy to get from the top, to the bottom of the loop. $$ \large t \, = \, \dfrac{2s}{v_1 - v_0} \, = \, \dfrac{2\left( \dfrac{2\pi r}{2}\right)}{\sqrt{2gR} - \sqrt{2g(R - 2r)}} $$ Now we figure out how long it takes the icream to fall the distance of the diameter or $ 2r $ . $$ s = v_0 + \dfrac{1}{2}gt^2 $$ $$ t = \sqrt{\dfrac{2s}{g}} \, = \, \sqrt{\dfrac{4r}{g}} \, = \, 2 \sqrt{\dfrac{r}{g}} $$ By setting these two equations equal each other, and solving for $$ R $ , we obtain that $$ R = \dfrac{16+8 \pi^2+\pi^4) r}{8 \pi^2} \cdot r \approx 2.43 r $$


title: Why don't electric fish shock themselves?

text: Fish like electric eels and torpedoes have specially designed nerve cells that allow them to discharge hundreds of volts of electricity. Now, while pure water is usually nonconductive, the dissolved salts and other stuff in both sea and fresh water allow them to be conductive. If an electric fish is able to use its electricity to stun enemies or prey, how come the fish itself is unaffected?


title: Detailed logical steps to show experimentally that radioactivity ionizes air?

text: Suppose one knows almost nothing about the nature of radioactivity (like the discoverers of this phenomenon). What are the detailed/rigorous logical steps/arguments to show experimentally that radioactive radiation ionizes air?


title: Physics and Computer Science

text: Not sure if this is a 'real' question, but what is the relation between physics and computer science? A lot of physicists are also computer scientists and vice versa. My professor has a PhD in Physics but is a Computer Science professor. Whats the relation? Why is this so common?


title: The Heisenberg limit is not a limit?

text: This new Best-ever quantum measurement breaks Heisenberg limit > PHYSICISTS have made the most accurate quantum measurement yet, breaking a > theoretical limit named for Werner Heisenberg. Nature, DOI: 10.1038/nature09778 When an experiment breaks a theoretical limit we have to reassess what we are accustomed to know. Is it the case with this experiment? At what level ?


title: "Single-shot" Heat engine efficiency limits

text: The sun is 5778K and Earth is ~290K. Using the sun as the hot reservoir and earth as a cold reservoir we get 95% Carnot efficiency. However, the solar power efficiency limit is only 86%, see: http://www.energy.udel.edu/pdf/Honsberg_UDEI_Symposium.pdf This is not just because of our atmosphere or a non-ideal sun. There is a more fundamental constraint: Carnot heat engines don't care how quickly energy is transferred from the hot to the cold. In our case, however, we are force-fed energy and must accept it as fast as possible. If energy is lost back to the sun we lose efficiency. Thus the term "single-shot": we only have one chance to generate power. What is the single-shot efficiency limit as a function of temperature ratio? Assume you are surrounded with black body radiation from all directions at the cold temperature (otherwise you wouldn't even need a sun to get energy!) and an unlimited supply of coolant. The "sun" is a hot black body radiator that takes up a small angle of the sky. Efficiency is (useful power)/(intercepted radiation power). This is a theoretical calculation, there are no restrictions on the design (solar thermal, PV, hybrid, etc).


title: How does one calculate the polarization state of random light after total internal reflection

text: How does one calculate the polarization state of random light after having been totally reflected by a single dielectric interface? Please consider pure specular reflexions from a plane interface between two dielectric mediums of indexes $n_1,\,n_2$ when the angle of incidence $\theta_1$ is greater than the critical angle $\arcsin(n_2/n_1)$.


title: Are the the elongation the same when one end of a spring is attached to the wall and

text: Consider there are 2 identical springs.   * One end of the first spring is attached to the wall and the other end is pulled by a force $\vec{F}$. It is depicted as shown in the first figure below.   * Both ends of the second spring is pulled by a force $\vec{F}$. It is depicted as shown in the second figure below. ![enter image description here](http://i.stack.imgur.com/uY225.png) Is the elongation for the first case identical to the second case?


title: Magnetization of coin on a railway track

text: The rumor was you could make a magnet by leaving a piece of iron on a train track. The train going over it would magnetize it. Is it true?


title: How to read a lens spot diagram?

text: I would like to get an explanation on how to understand such a lens spot diagram: ![Spot diagram in Zemax](http://i.stack.imgur.com/ff8UF.png) Thanks


title: The Gunn diode and the two valley theory

text: In today lecture of microwave and radar my teacher explained about the Gunn diode.   He said it is made up of only one type of matrial e.g. $GaAS$ as shown in (a) part of the image.   ![image 1](http://britneyspears.ac/physics/highfields/images/Image93.gif)   He said that there is no depletion layer and no gate so this diode conducts in reverse bias. He explained its working by using two valley theory. I have mainly two questions which emerged from this lecture: >   1. Why a Gunn diode is called a diode as it conducts in both the > directions. > My teacher said that there are two valleys in the conduction band as shown. And the electron in the lower valley has lower effective mass as compared to that of in upper valley. ![image 2](http://britneyspears.ac/physics/highfields/images/Image79.gif) So my question is : >   1. Since electron in the lower valley is more near to the nucleus so its > velocity should be more so its effective mass should be more because > $m^*=\dfrac{m_0}{\sqrt{1-\dfrac{v^2}{c^2}}}$in the lower valley >


title: Moving towards a clock at .866C

text: If you set up a clock that sends out a light pulse every second, and move towards it at a speed of .866c, will the clock appear to run faster?


title: Why do chiral objects only come in pairs?

text: My question arise and is connected to the "strange" fact that many things seem to come in pair or in number of two similar "objects". Why are there chiral "pairs" and not groups of 3,4, or more? What happens in higher dimensions.


title: Can stress be observed directly?

text: Strain can be directly observed using e.g. a ruler. Can (internal) stress be directly observed?


title: Electromagnetic Waves

text: We all know that light is an electro magnetic wave. but is electricity a EM wave? If it is then why light does not requires a medium to travel and why on the other side electricity needs a conductor ( I mean a medium) to travel. WHY? Or HOW?


title: What happens to the atoms and their constituents when we break something ?

text: My query is: how does an atom stable itself. When we break something, what actually happens in the chemical bonding of its atoms, does it rupture or remain intact?


title: What was missing in Dirac's argument to come up with the modern interpretation of the positron?

text: When Dirac found his equation for the electron $(-i\gamma^\mu\partial_\mu+m)\psi=0$ he famously discovered that it had negative energy solutions. In order to solve the problem of the stability of the ground state of the electron he invoked Pauli's exclusion principle and postulated that negative energy states well already filled by a "sea" of electrons. This allowed him to predict the positron, viewed as a hole in the sea. This interpretation was ultimately discarded owing to its inapplicability to bosons and difficulties with explaining the invisibility of the infinite charge of the sea. According to my understanding, the modern argument goes something like this. There is a discrete symmetry of the lagrangian called charge conjugation $\psi \rightarrow \psi^c$ which allows the negative energy solutions to be interpreted as positive energy solutions for a second mode of excitation of the electron field with opposite charge, called positrons. The decay of electrons to positrons is then suppressed by the $U(1)$ gauge symmetry of the lagrangian forcing conservation of electrical charge. According to this interpretation What Dirac would have missed was the lagrangian formalism. Is this historically and physically correct?


title: If the k of a wave is negative, is the wavelength negative too?

text: My friend went to an interview for a reputed scholarship program and was asked this question. A wave has an equation $a\sin(\omega t-kx)$. Sometimes k surely can become -ve. We know that $k=\frac{2\pi}{\lambda}$. So $\lambda$ is -ve? How can this be? What he said was that we can write $k=\frac{\omega}{v}$. Since $\omega=\frac{2\pi}{t}$, and t can't be -ve, v should be -ve. So it implies that the wave is in -ve x direction. That is why wavelength has come -ve due to this sign convention. But they didn't agree to it. Even I think the above is correct. Where is the problem then?


title: Force experienced on two particles in a rotating system?

text: I've a system of two particles of the same mass who rotate in a circle about the centre of mass of the two particles. Is the force experienced by the particles $F=MV^{2}/r$ or should I use $Torque=$Moment of Inertia*angular acceleration?


title: Inertia and Rocket Propulsion

text: We were taught in school that the law of inertia indicates that an object tend to stay the way it is, so if you throw something in space it will tend to go on forever and ever. The reason an object falls down when you throw it on Earth is because of gravity and air resistance. If that's the case, why don't rockets and spaceships need just enough fuel to escape the atmosphere plus the single thrust to push the craft in the right direction and let inertia drift it away?


title: Do massless particles follow the curved spacetime or not?

text: I am assuming that zero (rest) mass particles don't interact gravitationally with each other and other particles. Does that mean they experience a "flat" spacetime instead of a curved one? I find it a little hard to imagine that. Also, does this mean massless particles can pass through an event horizon (not the singularity itself, I assume there would be some other way of interaction that would prohibit that).


title: How would you quantify and predict the internal friction and efficiency of a bungee cord?

text: I am in an introductory physics class and we have been working with Gravitational Potential Energy, Elastic Potential Energy, Kinetic Energy and the Law of Conservation of Energy in relation to bungee cords. Recently, we delved into the topic of efficiency and with it I came upon the following stumbling block. For a project, we need to design a bungee cord for an egg (Average mass: 57.3g +/- 3.0g) falling from a height of 10.0m, and try to get the egg's stopping point as close as possible to the ground. We also need to take efficiency into account. Now I completely understand the basics of the calculation. Pick a desired stretch, use that to determine cord length, use that to determine the spring constant of the cord, etc. However, when you bring efficiency into account things get more complicated. Energy definitely escapes the system as the egg falls and the cord is stretched. Energy escapes in the cord as a result of internal friction, and during the fall as a result of air resistance. I think air resistance should be negligible given the mass of the egg and the shortness of the drop. I have scoured the internet for a model to determine the energy loss of the system due to internal friction to no avail. **So...My question is, how can I quantify and predict the internal friction of the bungee cord, then use that to determine the % efficiency of my system?** Sorry if my question's a little long and/or misplaced and/or I'm making some kind of mistake in my thinking here. This is my first post on the site. **Edit:** Here is all the given information for this problem:   * Average mass of the group of eggs being used: 57.3g   * Standard Deviation: 3.0g   * Height: 10.0m   * Desired height at the egg's lowest point: 0.10m


title: Momentum acceleration in space?

text: I'm an engineering student and have a few ideas to bat at the scientific community. First premise is based upon common sense. I understand that if I am standing on a skateboard on a relatively smooth surface and a stone of significant mass is thrown to me and I catch it, the momentum of the projectile is transferred to me causing a forward acceleration. My question: Suppose that a system is designed to provided constant acceleration in space utilizing the aforementioned intuitive concept. In the simplest form I can idealize such a system as a basketball constantly striking a flat surface. Opposed to a ball consider an arbitrary mass striking a greater mass. I suppose that if creative means are applied to control the striking action (e.g. magnetism, mechanical means) then this action can be repeated to provide constant acceleration without the use of carrying fuel loads. Would it not be possible to reset the system to an initial state without canceling the resulting acceleration? Due to the length of this question I will post the next question later. Thx


title: How is the path integral for light explained, or how does it arise?

text: In a question titled How are classical optics phenomena explained in QED (Snell's law)? Marek talked about the probability amplitude for photons of a given path. He said that it was $\exp(iKL)$, and that "...this is very simplified picture but I don't want to get too technical so..." I want to know how it arises, even if it is technical. I find it very strange. If we compare it to the case of a particle obeying the Schrodinger equation, we have $\exp(iS/h)$ where $S$ is the action of a given path. $S$ is what we want to minimize(in the classical limit). In this case the path is a space- time path. But in the other case, of the photon, where $L$ is that we have to minimize(in the classical limit or if you want in the geometrical optics limit) the paths are only in space, and I can't find any temporal dependence. when I check any book about QED, I can read about the photon propagator (about space-time paths) but I never have found out about the expression $\exp(iKL)$. In general terms I find hard to relate what Feynman teaches in his book with what I have read in the "formal QED books" like Sokolov, Landau, Feynman or Greiner.


title: Entanglement: Is it possible to prepare and reset probabilities to send information?

text: I'm pretty certain that the answer to the question in the title is a no, but I don't understand why. I have some basic misunderstanding of quantum processes that I’d like clarified in the form of asking questions about a hypothetical scenario. So, let’s say we have a pair of entangled photons… 1) Is it possible to prepare an entangled pair such that it can be known that, for example, the photon going down a certain path will be measured 25% of the time to be horizontally polarized and 75% likely to be vertically polarized? I guess this would be some sort of quantum decoherence? Partial collapse? 2) If that is possible, then would it also be possible to measure that photon’s diagonal polarization in order to "reset" the horizontal-vertical probability back to 50-50? I've seen a trick done where you take some polarizing filters and stack them horizontal on top of vertical, so that no light gets through. But when you slide a diagonally oriented filter between them, some light does get through, because the horizontal/vertical polarization information gets "reset" when measured against the diagonal filter. 3) If these two things are possible, then wouldn’t it be possible to send information along the entangled pair? If you sent bursts of 1000 photons and were able to measure them all, and found that the first burst had ~750 vertically polarized photons but the second burst had ~500 vertically polarized photons, then wouldn’t you know that the second burst had their diagonal measurements taken? Or would that not work because the extra measurements "break" the entanglement..? 4) Along with that, how many times can the photon pairs be measured before there are no longer entangled? Just once? Or maybe just once per state/qubit/aspect (such as polarization angle)? I understand that measuring the photon would necessarily change it (like with the polarization filter trick), but then how do scientists measure the polarization angles of two photons like in experiments of Bell’s inequality? I know that somewhere along the line, what I've described cannot be possible. If it were, then you could easily send information faster than light. E.g., say you had a photon-entanglement-generator-and-probability-fixer station in between two planets, 1 light year from the planet Foo and .99 light years from the planet Bar. After a year's time, after the photon stream has propagated to both planets, scientists on Bar could measure diagonally polarization of 1000 photons to encode a 1 or not measure to encode a 0. Then scientists on the planet Foo could measure vertically polarity and decode the 1s and 0s based on the statistical readings. The Bar scientists could encode that such a message and the Foo scientists would "instantly" receive the message. Except it would actually be from the past, since Foo is 1.99 years outside the Bar light cone. So since this is impossible, what am I misunderstanding? Thanks for answering, and thanks for putting up with yet another clueless but curious layman.


title: Lattice QCD and the 5th dimension

text: I was digging into Nielson-Ninomiya Theorem and doubler fermions, as well as solutions to these problems using Domain Wall Fermions and overlap lattice fermions, both of which make effective use of a 5th dimension. Does this imply that our universe is either a continuous 3+1 dimensional space, or a space that is 4+1 dimensions on a lattice?


title: Selection rule used in singlet/triplet recombination in LEDs

text: In organic light emitting diodes, only singlet excitons contribute to the light emission (this is flouresence). Everything I read, say that triplet excitons cannot recombine on the same timescale as the singlets because spin selection rules forbid it. Can anyone expand on how the spin selection rules allow for singlet and not triplet emission?


title: Conservation of energy

text: > I have given one-dimensional motion of the particle directed horizontally. A > problem says: " _...Show that for this given motion Conservation of Energy > Law holds._ ". Since Energy can intuitively be thought of an operation that changes something over time, energy being conserved essentially means that the motion is not a function of time, but position only? I.e. does energy conservation mean that a process is time-independent?


title: Solution of 1-D Schrodinger equation for the potential $V(x) = -\frac{1}{|x|}$

text: May be this question might have already been asked but i couldn't find it, so let me know if its already there. Consider a potential, $V(x) = -\frac{1}{|x|}$ and if we apply this to a one dimensional Schrodinger's equation, I'd like to know the solution for the wave function in 1-D. Does it have a simple analytical solution? Does it have any oscillatory behavior like $$\psi(x,t) = P(x) e^{ikx}e^{i\omega t}$$ I mean will there be a factor like $e^{ikx}$ ? From the internet search, looking at one-dimensional hydrogen atom, first of all i am not sure whether there is any analytical solution, but I guess it was suggested that an exponential decay, something like $$P(x) = e^{-\alpha x}$$ is present. But I am not sure about presence of oscillations like $e^{ikx}$. Hence I'd appreciate some suggestions and clarification. PS : I am not interested in Hydrogen atom, but in this specific 1-D potential.


title: Heat Sink Design-Choice of Material

text: I am currently designing a heat sink for OPA 549. Among the many considerations, for example, the choice of material, the geometry of heat sink, the design of fins and all the parameters that come into play during the modelling, I am most curious about the simple choice of material. Copper has more conductivity than Aluminium while the heat capacity of Aluminium is more than twice of copper. So naturally there has to be a trade off between the two. And I have no constraint on weight. I cannot use the combination of the two as there is bonding problem. My question is simple- Which one to use and why? Relevant details: Max Power 90W; Forced Convection with 21 cfm; Overall thermal resistance is around 0.5 SI units. thanks in advance


title: Spontaneous symmetry breaking by axions?

text: I am just reading at the beginnin of this nice article, that axions could be responsible for spontaneously breaking of a symmetry in the early universe. Does anybody know which symmetry is alluded to and how the mechanism of spontaneous symmetry breaking exactly works in this particular case? I'd like to learn in some more detail about this.


title: Cutoff regularization: Why not cutoff exactly at the momentum reached in an experiment?

text: So far I have only actually calculated dimensional regularization and I just know about the idea of cutoff regularization. From what I understand, as the name suggests, you just ignore momentum as from some high value and integrate the virtual momenta until this arbitrary chosen value. Depending on which value you chose, and thereby to what order you consider the Feynman diagrams, you get a (little bit) different result. Now what I was wondering is, why don't people just cutoff exactly at the value that corresponds to the momentum of the process you want to consider, if there is some specific experiment you want to calculate. E.g. if someone wants to calculate some cross section of an experiment that will be/has been done at CERN, why don't they just consider exactly the momentum that the virtual particle must (maximally) have (due to momentum conservation of the particles that are smashed together)? Intuitively it seems (to me) that this must give the best result. And let us ignore of course, that physicists that calculate cross sections for CERN probably do not use cutoff regularization.


title: Why doesn't light kill me?

text: I was attending my philosophy class and in the middle of student presentations, I found myself mentally wondering off and thinking about light. After a few minutes of trying to piece together how the sun works I came to ask a question I could not answer myself. Why does each individual photon have such a low amount of energy? I am hit by photons all day and I find it amazing that I am not vaporized. Am I simply too physically big for the photons to harm me much, or perhaps the Earth's magnetic field filters out enough harmful causes such as gammy rays?


title: simple MHD simulation code for (self) education and play with

text: I would like some **super simple computational code for solving magnetohydrodynamics problems**. High accuracy nor performance is not my concern. I wan't it just to visually explore qualitative behavior of plasma. Important for me is:   * **Generality** \- it should not be specialised on any particular subproblem of MHD    * **Easy to get it work** \- does not require any libraries difficult to instal. Input is strightforward and well documented by some examples   * **Easy to read and modify** \- you can read the code and learn about MHD solution from it. You can use this code as starting point for your own MHD code development  Something as simple as this Navier stokes solver would be best best would be something in python-numpy or java, but C++ or Fortran is not a big problem for me. **Up to now I found:** some libraries ( MHD-Hermes and python-mhd ) which are in python, but doesn't seem to have any documantation or examples how to use it. and this _A Free, Fast, Simple and Efficient TVD MHD Code_ which is in frotran but has just 400 lines I was thinking about writing something by myself but I wan't to be sure there is nothing similar already avaible.


title: Does water turn solid under deep ocean because of high pressure?

text: I know that we can make water solid with high pressure, so I think water will be solid in the deep ocean? If that is true, the depth of the ocean would be limited because water will become ice? Anyone know that maximum depth?


title: Actual meaning of "Gravitational Potential"?

text: In a gravitational field, the gravitational force acting on a body (of mass m) at a point x metres away from the attracting body (of mass M) is $\frac{GMm}{x^2}$. Integrating this force from a point at infinity to x gives $-\frac{GMm}{x}$, or the work done by the gravitational field on the mass in moving the mass from a point at infinity to x. Then, the gravitational potential at point x is $-\frac{GM}{x}$. However, the definition that my school gives is : "Gravitational potential at a point in a gravitational field is the amount of work done by an **external agent** in moving one unit of mass from a point at infinity to the point in the gravitational field, without any acceleration". The lecturers explained that as a body moves closer to the attracting body, it accelerates and gains kinetic energy. In order to maintain a constant velocity, negative work must be done by an external agent to remove this extra kinetic energy. Now I am very confused, because both seem valid to me. What does "gravitational potential" actually mean?


title: Would a projectile keep going forever in empty space?

text: Would a projectile fired in space and assuming there were no stars or planets in the way, would the projectile continue on to infinity, since the x-component of the projectile's velocity never changes from it's original?


title: Landau & Lifshitz - Euler's equation for one-dimensional flow

text: One page 5 in Landau & Lifshitz _Fluid Mechanics_ (2nd edition), the authors pose the following problem: > Write down the equations for one-dimensional motion of an ideal fluid in > terms > of the variables $a$, $t$, where $a$ (called a _Lagrangian variable_ > ) is the $x$ coordinate of a fluid particle at some instant $t=t_0$. The authors then go on to give their solutions and assumptions. Here are the important parts: > The coordinate $x$ of a fluid particle at an instant $t$ is regarded as a > function of $t$ and its coordinate $a$ at the initial instant: $x=x(a,t)$. For the condition of mass conversation the authors arrive at (where $\rho_0 = \rho(a)$ the given initial density distribution): > $$ \rho\,\mathrm{d}x = \rho_0 \mathrm{d}a $$ or alternatively: > $$ \rho\left(\frac{\partial x}{\partial a}\right)_t = \rho_0 $$ Now the authors go on to write out Euler's equation, where I start to miss something. With the velocity of the fluid particle $v=\left(\frac{\partial x}{\partial t}\right)_a$ and $\left(\frac{\partial v}{\partial t}\right)_a$ the rate of change of the velocity of the particle during its motion, they write: > $$ \left(\frac{\partial v}{\partial t}\right)_a = -\frac{1}{\rho_0} > \left(\frac{\partial p}{\partial a}\right)_t $$ **How are the authors arriving at that equation?** In particular, when looking at Euler's equation: $$ \frac{\partial\mathbb{v}}{\partial t} + \left( \mathbf{v} \cdot \textbf{grad} \right) \mathbf{v} = - \frac{1}{\rho} \textbf{grad}\, p $$ what happens with the second term on the LHS $\left( \mathbf{v} \cdot \textbf{grad} \right) \mathbf{v}$? Why does it not appear in the authors' solution?


title: Accelerometer Orientation Conversion

text: Got two accelerometers that are measuring accelerations oriented at +/- 45 deg from horizontal. I am looking to determine the conversion of the accelerometer measured data to accelerations in the vertical and horizontal direction. Can I use coordinate system conversion below ? $$F_{Vertical} = (F_1 + F_2) \cos(\frac{\pi}{4})$$ $$F_{Horizontal} = (F_1 - F_2) \cos (\frac{\pi}{4})$$ ![enter image description here](http://i.stack.imgur.com/KKydJ.jpg) I don't know phase relationship, but I can assume they are out of phase since I know the vertical acceleration is high and the horizontal acceleration is small. Are the conversions above correct ?


title: On the definition of work

text: Work is defined as $$W = \vec{F}\cdot\vec{s}$$ But what what exactly is $\vec{s}$? Is it the displacement of the body on which the force is being applied? Or is it the displacement of the point of application of the force? If you look at the derivation for the definition of work from kinetic energy (the way many textbooks do it), it would seem to be the former, but I'm not sure since I can think of many examples that contradict the fact. Or is it something else entirely?


title: How to turn water opaque by pouring the smallest quantity of matter into it?

text: Consider a glass of water and a glass of coffee. Their contents differ by no more than a few grams of particles coming from the roasted and ground coffee, yet the former lets almost all visible light pass through, and the latter blocks most of it. I am wondering **what are the most efficient ways to turn water opaque by pouring matter in it** , under normal temperature and pressure. By efficient I mean minimising the mass of added matter. By opaque, let's say 99% of daylight is blocked by two inches of liquid. There is no other reason for my asking than sheer curiosity from the many hours I spend gazing fixedly through the coffee pot.


title: Can particle physics be represented as an algebra?

text: Possibly the most useful thing anyone could tell me about particle physics: Naively, one could try and make an algebra by enumerating all the types of particles and defining equivalence relationships (some rules), for example Objects: object type 1: photon object type 2: electron object type 3 ... object type n Rules: rule 1: a photon is equivalent to an electron and a positron rule 2: a proton is equivalent to three quarks rule .... rule n Then one could study the properties of these relationships as a mathematical structure containing objects that represent particles and rules that define equivalence - i.e. as an algebra. I assume such an algebra would be, if formulated correctly, represented by Feynman diagrams (for some particles at least). Does such an algebra have a name? Is there more than one? Is this at all connected to the idea behind stating that the standard model is U(1) x SU(2) x SU(3)? By an algebra I understand a closed and consistent collection of mathematical objects and relationships. * * * Thanks for trying to understand what I'm asking, with your input I can aim to make this more comprehensible. So I guess I'm looking for a formal structure which reflects particle reactions which is abstracted away from spatial, temporal and energetic considerations as far as is possible (is it at all possible?).


title: How broad is the term "String Theory"?

text: How broad is the term "String theory"? Typical brief descriptions of string theory focus on the fact that it describes fundamental particles as being string-like rather than point-like, or, more generally, being at least 1-dimensional. So is any model in which the fundamental particles are at least 1-dimensional a form of string theory? If not, what are the other requirements? To put it another way, given a specific model, what factors would you consider when deciding whether that model was a string theory model or not?


title: Can we apply de Broglie's relations to sound waves?

text: Can we apply the de Broglie relations to a sound waves ? Is it possible? if yes how do you do that? what would be the mass(m) in the equation?


How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum? I used the Gordon Decomposition to split the Probability Current of the Dirac Field into its orbital current and its spin current. I multiplied the currents by $mc$ to covert them into momentum and then crossed the momentum with position to obtain the orbital angular moment and the spin angular momentum. However the spin angular momentum was twice as large as the accepted value of spin angular momentum. I am stuck on how to get rid of the extra factor of two. The Gordon Decomposition splits the probability current into two terms \begin{align} mc\langle \gamma^{0n} \rangle = \langle \gamma^{0} i\hbar \partial^{n} \rangle \+ \tfrac{\hbar}{2}\partial_{j}\langle i\gamma^{0nj} \rangle_{n\neq j} , \end{align} where $\langle \gamma^{0} i\hbar \partial^{n} \rangle$ looks like a orbital momentum current and $\tfrac{\hbar}{2}\partial_{j}\langle i\gamma^{0nj} \rangle_{n\neq j}$ looks like a spin momentum current? The angular moments of $mc\langle \gamma^{0n} \rangle$ can be computed by crossing then with position to obtain the following: \begin{align} mc \left( x^m\langle \gamma^{0n} \rangle \- x^n\langle \gamma^{0m} \rangle \right) = \langle \gamma^{0} i\hbar (x^m\partial^{n}-x^n\partial^{m}) \rangle \+ \tfrac{\hbar}{2}\partial_{j} \left( x^m\langle i\gamma^{0nj} \rangle_{n\neq j} \- x^m\langle i\gamma^{0nj} \rangle_{n\neq j} \right) , \end{align}


title: Calculate the distance between two points from iPhone Camera

text: I want to calculate the distance between two objects using an iPhone camera. Suppose I'm standing with my iPhone 10 feet away from the objects. Now, I want to calculate the distance between those two objects. Suppose these two objects are on a straight horizontal line. So, how can I calculate the distance between those two points? I have only the one predefine value like 10 feet or 5 feet/meter which is the distance between camera and the object. From the above information how can I calculate the distance between two point OR distance of maximum width of screen ? Reference Android App: Speed Gun


title: Quantum Field Theory and Hilbert space dimensionality

text: Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis.   How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is countable, or does it “need” to use an uncountable, continuous space (e.g. rigged Hilbert space) for mathematical consistency, or some other reason?


title: Wedge and Sphere problem

text: > A sphere of radius $R$ is in contact with a wedge. The point of contact is > $\frac{R}{5}$ from the ground as shown in figure. Wedge is moving with > velocity $20~\text{m/s}$ towards left then the velocity of the sphere at > this instant will be > > ![enter image description here](http://i.stack.imgur.com/8Qubm.png) http://www.artofproblemsolving.com/Forum/viewtopic.php?f=513&t=530952 I have attempted a solution there , however , unable to make any progress . Kindly advice if that is the right path to the solution , if something is there that I am not considering.


title: Clarification on measurement in QM

text: Supppose we are given a quantum state that isn't pure state, such that it is a linear combination of the eigenstates of a Hermitian operator $\hat O$. $$|\psi\rangle=N\sum \alpha_i |i\rangle$$ where $N$ is just a normalization constant. I just want to make something clear about measuring. If we measure the corresponding eigenvalue of $\hat O$ and find it to be in the $|1\rangle$ state then immediately measure again, would I be right in thinking that the probability of getting the $|2\rangle$ state is $0$? I think that because I believe the wavefunction collapses to the $|1\rangle$ state upon the first measurement...


title: interference pattern when two sources are not coherent

text: How would the interference pattern look if one source emits blue light and the other source emits red light in Young's double slit experiment?


title: Orthogonality in curved space/spacetime

text: When are two vectors orthogonal in curved spacetime? From wikipedia: _"In 2-D or higher-dimensional Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90°, or π/2 radians. Hence orthogonality of vectors is an extension of the concept of perpendicular vectors into higher-dimensional spaces."_ [http://en.wikipedia.org/wiki/Orthogonality] How does this generalize for non-Euclidean space? Is the following true? Two vectors, $V_1$ and $V_2$, are orthogonal if and only if: $$G_{MN} V_1^M V_2^N = 0$$ Where $G_{MN}$ is the metric of the space. P.S.: I used Einstein notation: Summation over $M$,$N$ implied and $M$,$N$ $\in$ $\left\\{1, 2, ..., d\right\\}$.


title: Question on entropy

text: All of my textbooks mention, that entropy-change of all spontaneous physical, and chemical processes is positive, and that such processes need another condition to fulfill- decrease in the net internal-energy of the system, taking part in the process. I just want to know that what is the reason behind this **tendency** of a system to increase its entropy, and to lose its internal-energy.


title: Extrinsic Photoconductor Charge Carriers

text: I'm studying some materials on semiconductors, and a section on photoconductivity has left me somewhat confused. In an extrinsic material, is photoconductivity the result of electrons moving from the valence band to the conduction band, or is it the result of dopant atom ionization? If it is the latter, is the complete ionization assumption invalid for photoconducting devices?


title: Building free energy directly from Lagrangian

text: Energy can be built from Lagrangian when considering the symmetry of time $(\frac{\partial L}{\partial t}=0)$. Free energy is a generalization of energy when the system exchanges heat with the environment. I can't find any sources that building free energy directly from Lagrangian. Is there any way to do that? If it is, what symmetry is it based on?


title: Accelerating cavity in synchotron- how does it actually work?

text: I wanted to know how a radio frequency accelerating cavity actually works. I know that an electric field is used to accelerate the charged particles. However, is this done by using metal plates with opposite polarities or are there tubes (like in the linac) within the accelerating cavity which have fields in between the gaps?


title: Does red shift evidence necessarily imply that the universe started from a singularity?

text: We are taught that the universe began as a singularity - an infinitely small and infinitely dense point. At the beginning of time there was a 'Big Bang' or, more accurately, 'Inflation'. The main evidence for this is the observation of the red shift of all of the galaxies. This shows us that as time increases, the universe becomes bigger. A logical outcome of this is that going back in time, the universe shrinks. This is then extrapolated back to the beginning of time, where the universe was infinitely small. However, the only thing that I can see that we know for sure is that the universe used to be smaller. This does not necessarily imply that it used to be infinitely small. How do we know, for example, that the universe doesn't oscillate and that we are in a time where the universe is expanding (and accelerating) and will eventually contract again? What other evidence is there that suggests we started from an singularity?


title: Equation of the saddle-like surface with constant negative curvature?

text: What is the equation for the saddle-like 2d surface (embeded in 3d Euclidean space with cartesian coordinates x, y and z) with constant negative curvature frequently used to illustrate open universe (for example in the following image is taken from Wikipedia)? ![enter image description here](http://i.stack.imgur.com/WNUNI.jpg) Flat universe (zero curvature) is illustrated by a plane, with equation say $z = 0$ Closed universe (constant positive curvature) is illustrated by a surface of sphere, say $x^2 + y^2 + z^2 = r$


title: Quantum Gravity and Calculations of Mercury's Perihelion

text: In an astronomy forum that I frequent, I have been having a discussion where the state of quantum gravity research came up. I claimed that Loop Quantum Gravity theories couldn't prove GR in the continuum limit, nor could they compute Mercury's perihelion because they didn't have any matter, at this point. Another poster claimed that one of the first things that any gravity scientist checks for the theory is the theory's prediction for the precession of Mercury's perihelion. Now for cosmological extensions to GR like, MOND, TeVeS or STVG, I can see where this might make sense. But I can't see how this poster's claim holds for quantum-gravity theories that haven't been able to establish that they reproduce GR in the continuum limit and that don't have matter at all. So I feel like I'm either missing something important about quantum gravity theories, in general, or the poster's comment only applies to cosmological- scale gravity modifications designed as an alternative to dark matter and not quantum gravity theories. Or perhaps a little of each. How, for instance, would one compute the precession of Mercury's perihelion using CDT, or Rovelli et al.'s spin-foam version of LQG? It may be that the dynamics of any object are implied in the spacetime microstructure, I don't understand the math well enough yet to follow the implications to know if this is true. But how can you compute the orbit of a planet when you require mass and fermions in order to even have the Sun and a planet like Mercury? I note the very very recent paper of this week, Dec. 21, http://arxiv.org/abs/1012.4719, where the Marseille LQG group run by Carlo Rovelli claims they can now incorporate Fermions, so my question applies to research prior to this event, not that going forward. I'm not even close to an expert, so I'm looking for enough information that I'll be able to respond intelligently to the other poster. I'll point them to the answer I received here so perhaps this will help the marketing for this excellent resource.


title: EM irradiament and multipoles

text: Why in the irradiament mulipoles of Lienard-Wiechert's potential we say that electric quadrupole give a contribute of the same order of the magnetic dipole? How can we see it from their equations? And is there a physical reason for this? Sorry for my trivial question.


title: How much friction is caused by a 10x10 cm window on the side of an airplane?

text: Say that the airplane is going in 1000 km/h. On the side of the airplane, there is a 10x10 cm window. How much friction would this window cause. For the sake of the calculation, imagine that the airplane is infinitely long. The window is also perfectly level with the rest of the wall, and there is no turbulence on the side of the plane. The outside air is also standing perfectly still. The airplane is travelling at sea level. I know it is neglectable compared to the turbulence etc. caused by the form of the airplane, but I really need the answer to the question.


title: Why can we not reduce the size of a system below the correlation length without qualitatively changing its properties?

text: This question is posed in the context of thermodynamics/statistical mechanics. Suppose we define the correlation length as the $\xi$ in the exponential factor $e^{-r/\xi}$ that appears in the correlation function $$C(r) = \langle m(0)m(r) \rangle - \langle m \rangle^2$$ (where $m$ is some relevant order parameter). Then my question is: how can we, from this mathematical definition, argue the following two physical properties. **Suppose we have our thermodynamic system and we take a chunk out of it with side-length L.**   1. If $L > \xi$, the sample has the **same** qualitative behavior as the original sample;   2. If $L < \xi$, the qualitative behavior is **different**. If one can add extra conditions for these statements to be true, that would be nice/welcome.


title: Conservation of Energy in a Capacitor

text: Consider a parallel-plate capacitor in free space. A negatively charged point particle with initial velocity $v$ passes through the space between the pair of parallel plates (with an initial path perpendicular to the normal vector of the plates). The point particle accelerates towards the positively charged plate but passes beyond the edge of the plate. How is energy conserved, given that the capacitor does work on the particle by accelerating it in the direction towards the negatively charged plate? EDIT: Was reminded by Art Brown that a negatively charged particle accelerates towards the positive plate.


title: The Four-Clock Special Relativity Conundrum

text: Two open-car trains approach each other at fixed velocities. Each has a radar to see how quickly the other train is approaching, but apart from that the trains have no _a priori_ knowledge of each other. Each train has engineers on its first and last cars. Each engineer has an atomic clock and a laser for communicating with their partner on the same train. Long before the trains meet, the engineers on each train use their lasers to adjust their relative separations to exactly one kilometer. Using the synchronization procedure first defined by Einstein, the engineers also exchange time data and use it to adjust their atomic clocks until they are precisely synchronized within their shared frame. The trains meet. The clocks are positioned so that they almost touch as they pass. At the moment of nearest contact, they exchange and record each other's values (timestamps). Some time later, the clocks on the trailing cars meet and perform the same procedure. The delay between the leading and trailing data events can now be measured in two ways. If the two timestamps taken from the first train are compared, the result is the time between the events as measured from the first train. This value is meaningful because the engineers on that train previously synchronized their clocks and stayed within the same frame of reference at all times. If the timestamps from the second train are used, a similar but distinct measurement of the time between the two events can be obtained. Now, three questions:   1. Is there anything wrong or impossible with this experimental setup? If so, what is it?   2. If you accept the experiment as realistic and meaningful, will the delays calculated from the perspective of each of the two trains be the same, or different?   3. If you answered "different," what is the correct procedure for predicting in advance what the ratio of the two delays will be? * * * **2013-01-10 - The Answer(s!)** I awarded the bounty to @FrankH for pages of excellent and educational work worth of reading by anyone who wants to understand special relativity better. However, I've also taken the unusual step of re-allocating the _answer_ designation to @MatthewMcIrvin. There are two reasons: (1) Matthew McIrvin was the first one to spot the importance of the symmetric-velocities frame, which others ended up gravitating (heh!) to; and (2) Matthew's answer is _short_ , which is great for readers in a hurry. FrankH, sorry about the switch, but I didn't realize I could split them before. So: If you are not overly familiar with special relativity and want to understand the full range of issues, I definitely recommend FrankH's answer. But if you already know SR pretty well and want the key insights quickly, please look at Matthew McIrvin's answer. I will have more "proximate data exchange" SR questions sometime in the near future. Two frames turns out to be a very special case, but I had to start somewhere. * * * For folks with strong minds, stout hearts, and plenty of time to kill, a much more precise version of the above question is provided below. It requires new notations, alas. To reduce the growing size of this question, I have deleted all earlier versions of it. You can still find them in the change history. * * * **Precise version of the 4-clock conundrum** Please see the first three figures below. They define two new operators, the frame view and clock synchronization operators, that make the problem easier to state precisely: * * * ![Setup of the four-clock conundrum using the frame operators](http://i.stack.imgur.com/JTWkQ.png) * * * ![Event T1: Leading edge clocks A1 and B1 pass very closely](http://i.stack.imgur.com/347QJ.png) * * * ![Event T2: Trailing edge clocks A2 and B2 pass very closely](http://i.stack.imgur.com/EVZtI.png) * * * Note that the four timestamps $\\{T_{A1}, T_{B1}, T_{A2}, T_{B2}\\}:>\\{A,B\\}$. That is, the four timestamps are shared and agreed to (with an accuracy of about 1 nanosecond in this case) by observers from _both_ of the interacting frames A or B. Since T1 and T2 are historically recorded local events, this assertion can be further generalized to $\\{T1,T2\\}:>*$, where $*$ represents all possible frames. (And yes, $:>$ is two eyes looking left, while $<:$ is two eyes looking to the right.) Using the four shared time stamps, define: > $T_{\Delta{A}} = T_{A2} - T_{A1}$ > > $T_{\Delta{B}} = T_{B2} - T_{B1}$ My main question is this: * * * > Assuming that $T_{\Delta{A}} = f(T_{\Delta{B}})$ exists, what is $f(x)$? * * * **Analysis** (why this problem is difficult) Based purely on symmetry in the setup, the most obvious answer is $f(x)=x$, that is: > $T_{\Delta{A}} = T_{\Delta{B}}$ There are some interesting reasons to be troubled by that seemingly straightforward and even obvious conclusion, not the least of which is that it violates the whole concept of special relativity (the Dingle heresy). That is, if you assume $f(x)=x$ and follow that line of logic through to its logical conclusion, you quickly end up with time that flows the _same_ for all frames -- that is, no relativity. Such a conclusion is in flat violation of over a century of very detailed experimental evidence, and so is just not supportable. The following four figures show why it's so hard to assert that $T_{\Delta{A}} = T_{\Delta{B}}$ without violating special relativity. * * * ![View of Event T1 from Frame A](http://i.stack.imgur.com/G59Bl.png) * * * ![View of Event T2 from Frame A](http://i.stack.imgur.com/j2K87.png) * * * ![View of Event T1 from Frame B](http://i.stack.imgur.com/IFj5Q.png) * * * ![View of Event T2 from Frame B](http://i.stack.imgur.com/jmoYk.png) * * * While the above figures accurately capture the reality of relativistic contraction of both distance and time, the problem in this case is simple: How do you decide which frame to select? The experiment as described can only give one outcome. Which one will it be?


title: What were the immediate consequences Yang-Lee work on Weak Interaction?

text: I am studying the history of Modern Physics and Yang-Lee earned their Nobel the next year after the Cobalt experiments. I am familiar with the chronology, but am not clear what those findings meant to the physics community to warrant such recognition for two relatively' unknown physicists. Other household names had to wait decades for more seemingly significant work. So can someone clarify what their work meant to the eventual development of the Standard Model?


title: How is wavefunction probability redistributed after partial wavefunction collapse?

text: Suppose I set up the double-slit experiment using photons as my particle. Behind the left slit I place a beam splitter that points some of the light off in the direction of a camera (represented as `C` in the diagram below). We'll say that the beam splitter splits a light beam passing through it into two equal beams. The light that passes through the beam splitter unaffected and the light that passes through the right slit continue on to another camera (represented as `CCC` in the diagram below). We'll say that camera `C` is closer to the beam splitter than camera `CCC` is.                    CCC          | |          | |        C-\ |          | |     -----|-|-----           |           |         Laser      If I fire a single photon through this apparatus, there's about a $1/4$ chance that it will be detected by camera `C` and about a $3/4$ chance that it will be detected by camera `CCC`. When the wavefunction reaches camera `C`, the photon is forced to either be detected by camera `C` or have the part of the wavefunction leading to camera `C` disappear. **Question:** In the case that the photon is not detected by camera `C`, how is the $1/4$ probability from that branch of the wavefunction redistributed to the remaining two branches of the wavefunction, the branch went through the left slit and straight through the beam splitter and the branch that went through the right slit? The first starts with about $1/4$ probability and the second starts with about $1/2$ probability. Does the first get a new probability of $1/3$ and the second a new probability of $2/3$? Does the first get a new probability of $1/2$ while the second keeps its old probability of $1/2$?


title: Is there analysis library for stress-strain data?

text: I have three column data that has time-displacement-force from 1D tensile/compression test. Now I would like to get the standard mechanical properties of the material, like Young modulus, yield stress/strain, strain hardening/softening exponent, Fracture toughness, work done... Is there algorithms/libraries available that will do it for me or do I have to code them myself?


title: Is singularity at the exact centre of a black hole?

text: I've read that all paths inside the EH lead to singularity. ALL paths. Even the ones pointing away from it, right? Because there's NO pointing away from singularity, since ALL paths point to it. So how could it be at the exact center? Or am I misunderstanding "center" here?


title: Does light really "travel"?

text: From what I've so far understood about light, a photon is emitted somewhere and after some time it's absorbed somewhere else. Have we had experiments that confirm the path taken or something akin to verifying that photon really do "travel"? If so what are they..


title: On the optics of high-resolution surveillance drones

text: In this youtube video (which is an except from a documentation I believe) a DARPA development for a high-resolution surveillance camera is presented. This question is regarding the optics that are likely to be required to make it work. ## Summary of the specifications given:   * $1.8\times10^9$ pixel   * covering $35\,km^2$   * from an altitude of $5\,km$   * using $368$ cellphone camera chips ## Some back of the hand calculations:   * pixel-equivalent area: $\frac{35\times10^6\,m^2}{1.8\times10^9\,px^2} = 1.94\times10^{-2}\,\frac{m^2}{px^2}$   * edge length of pixel-equivalent area: $\sqrt{1.94\times10^{-2}\,\frac{m^2}{px^2}}=1.39\times10^{-1}\,\frac{m}{px}\approx14\,\frac{cm}{px}$   * pixel count per chip: $\frac{1.8\times10^9\,px}{368\,chips}\approx5\times10^6\,\frac{px}{chip}$ ## Optics question Cellphone chips have pixel pitches of the order of a few microns. Say they use a typical, decent quality 5 megapixel chip with $2.25\,µm$ pitch. How are the optics likely to look like to image 15 cm at 5 km distance onto 2.25 µm on the chip within a camera that is at best a meter in diameter? I am looking for answers beyond "they use a telephoto lens"... Lens focal lengths, combinations and setup for producing the required image is what I am struggling to work out.


title: Potential due to a spherical surface charge

text: The potential at the surface of an insulating sphere (radius R) is given by   $$V(R,\theta) = k \cos(3\theta)$$ where $k$ is a constant. Use separation of variables to find the potential inside the sphere (r $\leq$ R) and outside the sphere (r $\geq$ R), and then use your answer to determine the surface charge density $\sigma(\theta)$ on the sphere. Assume there is no charge inside or outside the sphere. My approach: I will set my reference point at infinity, therefore the potential at infinity is 0, to set that as a boundary condition. Essentially, the approach in finding the surface charge density would be to find the potential function outside the sphere, then integrate that with the surface area. I am following Griffiths for E&M, but he doesn't include a specific example I can refer to for the separation of variables, and how to apply it. I can follow his examples for following potentials pretty easily, but cannot understand the first steps to set up this problem with SOV.


title: What is the initial velocity of a projectile so that it passes through a target point in its trajectory?

text: Let's say I have a projectile being thrown by a player in my 2-D game. I want to work backwards and find the initial velocity to apply to the projectile such that it passes through a target point in space given that the launch point might not be at $y=0$. Some applications of this would be a basketball shot simulator or a pub darts simulation. Given:   * initial or launch angle: $\theta_o$   * initial or launch height: $y_o$   * target point: ($x_f$, $y_f$)   * constant acceleration due to gravity ($g$)   * air resistance ignored I need to find:   * initial launch velocity: $v_o$ Here's an image of what I'm talking about. ![enter image description here](http://i.stack.imgur.com/uRRkX.png) I am interested in learning the derivation of the answer not just a formula that I plug-and-chug. Thanks!


title: Where might hertz per dioptre actually be useful?

text: I once came across the strange, artificial unit "hertz per dioptre", which is dimensionally equivalent to "metres per second". Could this unit, by some stretch of the imagination, be used in some artificial situation where the usage implications of both "hertz" and "dioptre" (frequency of periodic events and refractive power, respectively) would make for the ratio to actually be useful?


title: Is it really possible for water to be held in a "cone shape" for a brief period of time?

text: I just saw this "trick" where a cup of water is turned over onto a table without spilling (using a piece of cardboard. After removing the cardboard from underneath the cup, the person then removes the cup in a particular way (lifts straight up and twists) and lo and behold, the water stays in it's position as if the cup were still there!? (watch the video to fully understand) Is this really possible? If so, and the real question I'm looking to have answered is, how? After further research it appears that deionized water is needed as well.


title: Quantum computing records (entangled qubits)

text: What is the current **record** number of entagled qubits and how has this number been increased? The latest result on stack exchange, which is 3 years old, reports 14 via this post: How many stabilised qubits have been achieved in Quantum Computing? in accord with this paper: http://arxiv.org/abs/1009.6126? For the purposes of this post, I'd prefer to leave the D-Wave computers out of the answers.


title: Help with vacuums?

text: Okay, here is my understanding. Please correct me if anything here is incorrect. Suppose I have a cube with a side length of ten inches. It has a surface area of 600 square inches, and at an atmospheric pressure of 14.7 pounds per square inch, we can approximate 8800 pounds of air are applied on the cube by the atmosphere. The cube has a volume of 1000 cubic inches of air. But since there is air on the inside of the cube, and the pressure is equal, there pressure is cancelled out. Now suppose we were to have a bunch of cubes with ten inch sides. We remove 1/2 of the air from the inside of one, and 1/4 of the air from another, and 1/10 from another. How can we calculate the actual pressure of the atmosphere on the cube?


title: How do you make a collision more elastic?

text: Currently, as described in this question, collisions cannot be elastic. However, is there a way to make a collision more elastic? **Background:** We're working on a project right now involving high speed energy transfer to an exercise ball. One of the issues right now is that the exercise ball is going far slower than what basic (e.g. AP Physics AB) calculations say they should be. I know that this is most likely due to the less-than-perfect elasticity of the collision between the ram and the ball. Is there any way to make the collision more elastic?


title: From representations to field theories

text: The one-particle states as well as the fields in quantum field theory are regarded as representations of Poincare group, e.g. scalar, spinor, and vector representations. Is there any systematical procedure that one starts from the Dynkin label for a given representation, to construct a Lagrangian of that field theory? If yes, where can I find that procedure? I don't care adding interaction by gauge invariance from these Lagrangians will cause non-renormalizability or not. I can live with effective theories.


title: Why are differential equations for fields in physics of order two?

text: What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations? * * * If someone on the street would flat out ask me that question, then I'd probably mumble something about physicists wanting to be able to use the Lagrangian approach. And to allow a positive rotation and translation invariant energy term, which allows for local propagation, you need something like $-\phi\Delta\phi$. I assume the answer goes in this direction, but I can't really justify why more complex terms in the Lagrangian are not allowed or why higher orders are a physical problem. Even if these require more initial data, I don't see the a priori problem. Furthermore you could come up with quantities in the spirit of $F\wedge F$ and $F \wedge *F$ and okay yes... maybe any made up scalar just doesn't describe physics or misses valuable symmetries. On there other hand in the whole renormalization business, they seem to be allowed to use lots and lots of terms in their Lagrangians. And if I understand correctly, supersymmetry theory is basically a method of introducing new Lagrangian densities too. Do we know the limit for making up these objects? What is the fundamental justification for order two?


title: Why there is the requirement for derivatives no higher than second order in free quantum field equations?

text: Why there is the requirement for derivatives no higher than second order in free quantum fields equations? We can get the equations for the free fields of an arbitrary spin by using the requirements of linearity of the equations, derivatives no higher than second order. But why there is the second requirement? Is it connect with initial conditions $A_{\mu}(0), \partial^{\mu}A_{\nu}(0)$ for the field? For example, Schrodinger equation is first-order time-derivative equation, because we have the postulate that if we know the $\psi (\mathbf r , t)$ in the present, we know it in the future.


title: Why do fundamental physical laws involve the second derivative?

text: The title says it all. This is a question that has been nagging at me for some time. Mathematically, the first derivative is not really any different from the second derivative, or the $k$-th. So I ask, what is so special about the second derivative?


title: Commuting momentum and position operators?

text: I think this is a question about the mathematical axioms of quantum mechanics... Consider the following operators $\tilde{x}$ and $\tilde{p}$ on Hilbert space $L^2(R)$, defined for fixed $\delta>0$: $$ (\tilde{x}\psi)(x) = (n+1/2) \delta\ \psi(x) $$ when $n\delta \leq x <(n+1)\delta$ for some integer $n$; and $$ (\tilde{p}\psi)(x) = -i \hbar \frac{d\psi}{dx}(x) $$ when $n\delta < x < (n+1) \delta$, and $(\tilde{p}\psi)(x) = 0$ when $x=n\delta$. Both these operators are self-adjoint and they commute. Further, $\tilde{p}$ is identical to the usual momentum operator $\hat{p} = -i\hbar \frac{d}{dx}$ on the subspace of $L^2(R)$ on which $\hat{p}$ is defined, and thus has identical spectrum. Finally, by taking $\delta$ small we can make $\tilde{x}$ as close as we like to the usual position operator, $\hat{x}$. Thus naively it looks like $\tilde{x}$ and $\tilde{p}$ represent compatible observables which can be made arbitrarily close to $\hat{x}$ and $\hat{p}$. I'm pretty sure that I've cheated somewhere, but I can't find anything in the axioms of quantum mechanics that rules out defining observables $\tilde{x}$ and $\tilde{p}$ as above (or at least, the axioms as they are usually presented in under/graduate physics texts). Is there some requirement that observable operators should map $C^\infty$ functions to $C^\infty$ functions? In any case, I'd be grateful if someone could tell me why the above is ruled out. (As background, I am teaching an undergraduate class on quantum mechanics next semester and I wanted to explain to students that while it's not possible to make exact simultaneous measurement of position and momentum; it is possible to make an approximate simultaneous measurement. In other words, I wanted to find operators which approximate $\hat{x}$ and $\hat{p}$ on 'macroscopic' scales and which commute. This was before I looked in the literature and realised how technical constructing such approximate operators is.)


title: Time Dilation in Orbits in the Schwarzschild Metric

text: I am wondering if there exist closed form-expressions for the time dilation experienced by an observer in different orbits around a Schwarzschild black hole, outside the event horizon, relative to some distant observer sitting fixed relative to the black hole. I am no expert in GR, but I know these quickly turn into some complicated integrals. Any point in the right direction, even toward an approximate answer, would be much appreciated.


title: Why aren't four-vectors used in the definition of a Klein-Gordon quantum field?

text: I am a beginner who is learning QFT. When I was going through the quantisation of Klein-Gordon real-field. I got confused about something: The solution to Klein-Gordon equations are of the form $ \psi(x^\mu) \sim e^{ik_\mu x^\mu} $. Now the solutions in Peskin and Schroeder have no time dependence. It gives a Fourier transform of this kind: $$ \psi(\vec x) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2\omega_p}} \Bigl[a(\vec p) e^{i\vec k. \vec x} + a^\dagger(\vec p) e^{-i\vec k. \vec x} \Bigr] $$ My problem here is, why is the solution is a superposition of $ e^{i\vec k. \vec x} $ and not $ e^{ik_\mu x^\mu} $ ? [EDIT] For example in these notes in equations 90 and 113 the solutions are superposition of $ e^{ik_\mu x^\mu} $ and I don't where these two things disagree.


title: What makes water boil?

text: Basically how boiling takes place? _**Also like to know..._**   What makes boiling point alter at various altitudes?   Why bubbles rise through boiling water?


title: Local degrees of freedom in QUGRA lead to black holes

text: I am reading Jan Boer's review of the AdS/CFT correspondence and I quote from end of page 1, where he is talking about equivalence of (d+1)-dim gravity to d-dim field theory “If true, it implies [...]. If the degrees of freedom in gravity would be local, one would imagine that one can have arbitrarily large volumes with fixed energy density.[...]” I don't quite understand that. What does it mean for “degrees of freedom to be local”? And how does that lead to fixed energy-density?


title: Find the minimum value of velocity

text: Find the **minimum value of the initial velocity** $u$ of the particle such that the particle crosses the wheel of radius $R$.   ![enter image description here](http://i.stack.imgur.com/hN0F9.jpg) **Details and assumptions**   $R=2m$   $g=9.8m/s^2$   Neglect air resistance.   All surfaces are frictionless.   The value of $\theta$ (angle the projectile makes either with vertical or horizontal), range and $u$ is not known.   Consider the motion in 2-D space only. > I tried setting the maximum height equal to $2R$ and then finding the > corresponding minimum value of $u$, but my answer was incorrect.   >  Then I tried to set the latus rectum of the parabola (equation of > trajectory) equal to $2R$ but that too didn't work.   >  Can anybody suggest a way to do this question?   >  Thanks in advance!


title: Electrostatic potential and charge

text: Say we have a balloon, negatively charged, the voltage on it is 500 V. Can I measure the charge on it or in other words, the number of excess electrons?


title: Energy of unmixing

text: Mixing of two different fluids is associated with an increase of entropy. Conversely, separation of two gases must be associated with a decrease of the entropy of the two fluids. Is there a minimum requirement imposed by this thermodynamic constraint on the minimum energy needed to separate two fluids?


title: Do the laws of physics work everywhere in the universe?

text: Do the laws of physics change anywhere in the universe?Or will they change from place to place in the universe?


title: Fermi Walker vs. Fermi transport

text: A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu v^\mu) f_\nu,$$ where $v^\mu$ is the tangent vector $\gamma$ and $a^\mu$ is its derivative. The uppercase D denotes the covariant derivative. This is the usual transport law for nonrotating tetrads. However, in "Introduction to General Relativity" Lewis Ryder mentions the Fermi transport for which $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = v^\mu a^\nu f_\nu.$$ What is the significance of this transport? Are there any applications of it?


title: Basic questions in Majorana fermions

text: Why any fermion can be written as a combination of two Majorana fermions? Is there any physical meaning in it? Why Majorana fermion can be used for topological quantum computation?


title: Summing up magnetic fields

text: In the case of a complex shape filiform distribution of current, are we allowed to determine the magnetic field created by sections of the distribution and then summing them up, like we do with a discrete distribution of charge when calculating the electric field? Thank you


title: How can something finite become infinite?

text: How can the universe become infinite in spatial extent if it started as a singularity, wouldn't it take infinite time to expand into an infinite universe?


title: Fermionic interaction potentials

text: Are there any examples of fermionic particles or quasiparticles for which the interaction potential is a globally smooth function? i.e. no singularities or branch points. As an example, in Flügge's Practical Quantum Mechanics, problem 148 has two repulsive particles on a circle. This is supposed to model the two helium electrons in the ground state. The equation he gives is $$ -\frac{\hbar^2}{2mr^2}\left(\frac{\partial^2 \psi}{\partial x_1^2}+\frac{\partial^2 \psi}{\partial x_2^2}\right)+V_0\cos(x_1-x_2)\psi=E\psi$$ I don't quite follow why this potential does not have a singularity when $x_2\rightarrow x_1$. Are there other such examples?


title: Mass of a galaxy via Luminosity

text: Is there a way of calculating the mass of a galaxy, or even a nebula from the luminosity? EDIT I'm deleting this, and moving the question to Astronomy Stack Exchange - thanks david


My text shows (sections 0.2 and 0.3) that the joint "state space" of a system composed of two subsystems with $k$ and $l$ "bits of information", respectively, requires $kl$ bits to fully describe it. A critical consequence of this is that the $k+l$ bits in each of the individual subsystems are not sufficient to "span" their joint space, so that there must be states that are "entangled" (formally, cannot be expressed by the tensor product of the states of the subsystems). That much I ( _think_ ) I understand. But the text then seems to argue that this is a property that is exclusive to quantum systems. Is that true? Certainly there are classical systems where the state of one subsystem depends on the state of another. Doesn't any joint system that requires conditional probabilities to describe need "extra bits" beyond those necessary to describe the individual subsystems? Perhaps I'm missing some subtlety about what constitutes a "sub system" or some unstated assumption about how systems are broken into parts. Perhaps a classical system that is "entangled" by conditional probabilities isn't thought of as consisting of valid "subsystems" in the same way that quantum system is. Is "entanglement" unique to quantum systems? Are conditional probabilities just a kind of "classical entanglement"? * * * Please be pedagogical. This is not meant to be a deep or advanced mathematical question, just a simple conceptual and definitional one. Just imagine I'm having basic probability explained to me (without reference to quantum vs. classical, or even physics). If one struck out all occurrences of the word "quantum" from the linked text (sections 0.2. and 0.3), wouldn't that be a perfectly valid part of such an explanation?