title: Confused about the electric field at the surface of a conductor

text: We know that the electric field at the surface of a conductor only have a normal component equal to $\rho/\varepsilon$ (finite number). But let’s consider the point $\text{P}$ (at the surface of a conductor). Assume that there is a charge at an infinitesimal distance from the point $\text{p}$. We can obtain the field at the $\text{P}$ by the formula $E=Kq/r$. Obviously, $E\sim1/r$. So the normal component of the field is infinite. Now if we add the field due to other charges, it will remain infinite. So where could I be possibly wrong?


title: Ultra Deep Field 3D camera speed

text: I guess most of you saw Ultra Deep Field 3D video. In the end it shows camera moving in 3D perspective through all the galaxies. My question is, how fast is the camera moving in that video? I couldn't find this answer anywhere.


title: Uncertainty in approximated relation

text: I'll give directly an example to fix the ideas. Suppose that you're studying the acceleration of a system of masses that depends from the number $n$ of masses $m$ by the following relation: $$a=a_0+n\dfrac{m}{\mu}g.$$ Here $[a_0]=[L][T^{-2}]$ and $[\mu]=[M]$ are two costants independent from $n$. Suppose also that, in the case where the $n$ masses are different, the relation becomes:$$a=a_0 +\dfrac{\sum _{i=1}^{n} m_i}{\mu}g,$$ with the same constants. In an experiment, I had to use a relation of this kind and, to get a linear relation, it was needed to use the first approximation, where $n\cdot m$ replaces the sum. Clearly all masses weren't equal and I had a weighing scale enough sensible to see that. My question is, what would be the best value $m$ to be used in the first relation and what its uncertainty? In my specific case I had a quite symmetric distribution of values, so I took:$$m=\dfrac{m_{\text {max}}+m_{\text{min}}}{2}\pm\dfrac{m_{\text {max}}-m_{\text{min}}}{2},$$ where the uncertainty is took to include all values possible. Is there a more precise way to do this? **Note** : I'm not looking for the approximation of $m$ for a fixed value of $n$. I'm looking for the best approximation of $m$ that fits for all the cases $n=1,2,...,N$, where $N$ is the total number of masses.


title: M(atrix) theory and things other than D0-branes? And is it non-peturbative M-theory or non-peturbative Type IIA theory?

text: When I first read the BFSS Paper on M(atrix)-theory, I was under the impression that it was a non-peturbative formulation of M-theory. But recently, upon reading this paper of Nathan Seiberg's, I realised it only describes a non-peturbative formulation of M-theory compactified on a circle. But since M-theory compactified on a circle is simply the S-dual of Type IIA string theory, does that mean that M(atrix) theory is really a non-peturbative formulation of Type IIA string theory, rather than 11-dimensional M-theory? But I've heard that Matrix String theory does both a non-peturbative formulation of Type IIA string theory and a non-peturbative Type HE string theory? So, is BFSS Matrix theory a type of Matrix String theory? Another closely related quesiton. Sometimes, I have often read statements like > M(atrix) theory describes D0 branes. This suggests that M(atrix) theory describes D0 branes only? But doesn't the AdS/CFT correspondence mean that it thus also describes 2-branes, 4-branes, 6-branes and 8-branes, since the Type IIA string theory is a string theory which contains odd-numbered Ramond-Ramond Potentials $C_1, C_3, C_5, C_7$ and thus even-numbered D-branes $D0,D2, D4, D6, D8 $? So, to summarise, my questions are   1. Is BFSS Matrix theory a non-peturbative treatment of 11 dimensional M-theory or 10 dimensional Type IIA string theory, or something else?   2. Other than D0 branes, what are the other branes that BFSS Matrix theory describes? I am presuming they are $D2, D4, D6, D8$ and that they are certainly not $D1, D3, D5, D7$.


title: Time travel and entropy

text: I saw a post on reddit regarding immortality and how it would never be possible due to entropy. That said, assuming time travel was possible, would it not be possible to never reach this state of entropy if you could keep traveling back in time? Say for instance that you couldn't travel back in time within your own time curve, but you could travel to other time curves. You would merely jump to another curve when your current universe was about to reach its end. Is it too big of an assumption to think that your own initial entropy (by this I mean your entropy from your first timeline) would not 'follow you' to other time curves? I may be totally off-base in my assumptions, as I know next to nothing about physics. Any feedback/criticism is welcomed. Here is the link to the post in reddit.


title: rope wrapped around a pole

text: I would like to solve this question without using conservation of angular momentum(because of some reason I'll elaborate later). So imagine that we have a pole with radius $r$ and a ball attached to a rope of length $R$. Initially the distance between the ball and the attach point is $R$(which means the rope is tight). The initial velocity of the ball is perpendicular to the rope. Now we know $R>r$. At a later time $t$, what is the direction and magnitude of the velocity of the ball? The reason we cannot use conservation of angular momentum is because I don't assume that the ground is not moving. Instead I assume that the ground is the Earth. So if the rope applies a torque on the Earth, the Earth's angular momentum will increase. I always see people use conservation of angular momentum to solve such a question but **not conservation of energy**. And if we assume that the ground is not moving, there must be one of them that is not conserved! And I would like to know if the common way of doing it is right or wrong. However I got stuck at the very beginning... Once I figured out the initial and final energy and momentum, I should be able to solve it. Any help would be much appreciated! **The pole is vertical. And we can assume no gravity. Also I guess friction is important, otherwise the rope can't be wrapped around the pole. However let's assume there is no loss of energy thru friction. There is of course tension on the rope.** **IMPORTANT REMARKS: It might look really simple to you at first. But it's actually not that as straightforward as it seems. When we solve this kind of problem in the standard first year physics text, we always assume conservation of angular momentum. However this would imply the violation of conservation of energy if we assume the ground does not move. If we do assume that the ground moves, both angular momentum and energy will not be conserved for the pole(because the system gives angular momentum and energy to the earth). In that case, if we take the limit as mass of the earth goes to infinity, which one is more conserved(It has to be angular momentum, otherwise we would have used conservation of energy to solve this kind of problem in first year physics textbooks. But now I just want to justify it)?** **THIS IS NOT A FIRST YEAR PHYSICS TEXTBOOK PROBLEM!** **Also although I added the homework tag to this question, it's not an actual homework problem(as you can see from the date I posted it). So please feel free to write down any detail that you think might help explaining your solution. Thanks!**


title: Electric Potential of Conductors

text: I understand that charges in a conductor reside on the surface of a conductor. So why is it that the neutral inside of a conductor and the charged surface are at the same potential?


title: Who invented the perfume bottle thought experiment?

text: A common thought experiment used to explain the second law of thermodynamics, the "arrow of time", etc. is perfume escaping from an opened perfume bottle; the perfume is likely to diffuse into the environment, but the escaped perfume is unlikely to all return to the bottle. Hence, the entropy of the system increases. This thought experiment shows up in many textbooks and web pages, but I have not seen any reference to its originator. Who originated it or a similar thought experiment (e.g. some other volatile substance diffusing into the environment)? If you're not certain of the answer, what is the earliest mention you know of?


title: why are the square of the components of velocity equal?

text: In Principles of Physics by Resnick,Halliday,Walker, when evaluating the $v_{rms}$ ,they first found $p = \frac{nM(v_x)^2}{V}$ & then substiuted $(v_{avg})^2 = \frac{1}{3} .v^2$ where $v^2 = (v_x)^2 + (v_y)^2 + (v_z)^2 $ saying that there are many molecules and all are moving in random directions hence average values of the square of the velocity components are equal and wrote $v^2= \frac{1}{3} (v_x)^2$. But i couldn't understand their reasoning. How have they came to this conclusion that the square of the components of the velocity are equal? Can anyone explain me their reasoning why they have taken the square of the components of velocity be equal? Help.


title: First experiment which was used to prove existence of Electromagnetic waves

text: When I was in high school I heard from my physics teacher in the last year of high school when he was starting the chapter of electromagnetic waves that the first person who proved existence of Electromagnetic waves (perhaps Faraday, Hertz, Maxwell, ..., I don't remember who) made a transmitter and a receiver and put one on a mount and the other on the other mount. Then he sent waves, and at the other side received light (or something like this). I can't remember who, either. Please excuse me, my field of study is not physics and I didn't do anything on it after high school except calculating some equations which my friends needed in physics. My question has two parts:   1. Who was the person I am mentioning in my above story exactly? I would like to know who it is to avoid making mistakes in the future.   2. (The main part) What was his experiment exactly? I'm interested to know what he did at that time and of course what his experimental apparatus was. Think of me as your student in high school, and you want to show me that experiment again and our high school has all necessary instruments and lets you do that experiment in lab for your students to learn better.


title: How do we decode the image formed by a gravitational lens?

text: Using our own sun as a gravitational lens, we can scrutinise planetary surfaces in distant solar systems with a good deal of accuracy: http://www.amazon.com/Mathematical-SETI-Statistics-Processing- Astronomy/dp/3642274366/ref=la_B009WTAMOO_1_1 How do we translate this smeared out and curved image into a normal photo style image? Related: The Sun as a gravitational lens


Why the hydrogen radial wave function is real? Is it a coincidence?


title: Autocorrelation of noise - negative correlation

text: I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an 8-bit AtoD from a noise generator (whose description was not provided). I first sampled the noise directly, then I sampled it after passing it through a low-pass filter. I imported the data into MATLAB and used the `autocorr` function to autocorrelate it. The no-filter data autocorrelated as expected, being just 1 at t=0 (as in Fig 1 in paper); however, the filtered data decays initially as expected but then dips below 0 before coming back up and staying around 0 as in the image below. ![Negative autocorrelation](http://i.stack.imgur.com/igIUk.jpg) My three issues are:   1. I am not really sure what this means physically (is the correlation 'direction' changed so-to-speak?),   2. Why might this be occurring? I know that a description of the noise generator may be important here but I do not have that information myself.   3. Is there any way to correct this issue, and if not, what would be the best compromise? EDIT: Here are snapshots of the noise without and with the filter (RC=0.5ms) respectively: ![Noise without filter](http://i.stack.imgur.com/kEGrs.png) ![Noise after going through RC=0.5ms low-pass filter](http://i.stack.imgur.com/4vU9q.png)


title: Can we think of gravity as space itself moving?

text: So if you move through space with a constant acceleration you experience longer time dilation than when you're at rest, but you also experience the same time dilation when you're under the effect of gravity like on earth, so is it possible that by standing on earth, space itself is moving relative to you at a constant acceleration, which causes the same time dilation as when you move in space with same acceleration of earth's gravity $9.8\tfrac{m}{s^2}$? Maybe that's why under free fall you don't sense the acceleration and feel weightless, because you are moving along with space itself that is attracted to earth, neither you are moving relative to space, nor space is moving relative to you. By moving I mean accelerating and - constant speed of course. Sorry if this question is silly or something that is maybe already suggested before.. I'm not a specialist here.


title: What decides the trajectory of shrapnel upon explosion?

text: What are the factors that govern over the path that shrapnel and/or other particles follow upon explosion of explosives(the ones that are planted i.e. stationary ones) etc. Is it possible to predict the path of all the particles ? Also is it possible to make the particles move in desired directions ?


title: Pure State Non-zero Entropy Paradox

text: Entropy measures the number of microscopic states of a given system. For a pure state, the count is one. Thus, entropy ~ log(1) = zero. However, on the other hand, if we calculate the entropy of finding a particle in real space. It will not be zero. ![pure state entropy paradox](http://i.stack.imgur.com/yEaZd.png) My question is, what is the entropy of such pure state? Is it zero or not? Then what about my idea to calculate it in real space distribution?


title: Weird resistor patterns

text: I came up with the following question: > The vertices of tetrahedron ABCD are all connected by 1-ohm resistors. What > is the total resistance between A and B? I haven't the faintest idea how to solve it. Does it involve infinite path summations at some point? [edit: how about from A to C?]


title: What's the electric field with a point charge not in the center of the sphere?

text: That's a hollow conducting sphere link My charge is at P (10uC). R = 0.15m. PS = 0.05m. DS = 0.35m. What's the electric field at point D? ![enter image description here](http://i.stack.imgur.com/UkYgu.png)


title: Projectile Motion with Drag

text: The overall goal is to write a Mathematica program that will compute the launch angle that will yield the greatest range with using [RandomInt] function, but I was having trouble with the physics. In 2D Trajection with no friction, the greatest range came at angle $45^\circ$. But using the quadratic model of friction, $$F_{drag} = -kv^2, k = \frac{1}{2}C_D\rho A$$ where $\rho$ is the density of air, $A$ is the cross sectional area of the moving object (circle in this case), and $C_D$ is the drag coefficient. $$v^2 = v_x^2 + v_y^2$$ At this point, I'm not sure on how to set up the problem, as $v$ is dependent on both $v_x$ and $v_y$, and cannot be modeled as linearly independent of each other. Some given parameters of the sphere projectile: (I'm assuming these values can be easily plugged into the general equation when writing the program) Intial Velocity = Between $30-40 \frac{m}{s}$ Mass = 0.145 $kg$ Radius = 0.0367 $m $ Air density = $1.2 kg/m^3$ Drag Coefficient = 0.46 * * * How would I incorporate both velocities in an equation? For simple kinematics, it is simply: $$Total Range = v_xt$$ and we solved for $v_x$ by using trig properties from $v_0$. But is it correct to model this drag force with the same trig properties? $$v_y = vsin\theta, v_x = vcos\theta $$ $$\sum F = ma = kv^2 - mg = (\frac{1}{2}C_D\rho A({vsin\theta}^2+{vcos\theta}^2) - mg$$


title: Calculating the acceleration of a car

text: I'm trying to calculate the maximum acceleration a car can achieve with the current gear ratio. I am ignoring drag forces and friction to keep it simple. I'm doing this by:   * calculating the torque on the wheels: $T_e/G$ (engine torque / Gear ratio)   * Calculate the Force exerted on the ground: `T_w/r` (wheel torque / wheel radius)   * then finding the acceleration using $F=ma$ However acceleration values are too small. Is there something wrong with my reasoning? My car's engine Torque is 500Nm, gear ratios: [2.97,2.08,1,0.86,0.56], car's mass = 2500Kg


title: Is the movement of electrons truly random?

text: The result of rolling dice is considered pseudo-random because it depends on an almost endless list of factors (how you roll it, the terrain it lands on, etc.), but it is not TRULY random. Is the movement of electrons TRULY random or just pseudo-random? If it is just pseudo-random, what factors would typically effect it (gravity, temperature, etc.)?


title: Non-vanishing commutator of potential and mass matrices for Majorana fermions interaction theory

text: Consider 2 different Majorana fermions $\Psi_{L}, \Psi_{R}$ (physically, neutrinos). In general case I can write the massive part of lagrangian of these fermions in the form $$ L_{m} = (\bar {\Psi}_{1} \bar {\Psi}_{2})\begin{pmatrix} m_{11} & m_{12} \\\ m_{21} & m_{22} \end{pmatrix}\begin{pmatrix} \Psi_{1} \\\ \Psi_{2} \end{pmatrix} = \bar {\Psi}^{a}\hat {m}_{ab}\Psi^{b}. \qquad (1) $$ Then let's introduce matrix of some gauge interaction $$ \hat {A}_{\mu}^{ab} = A_{\mu} = \begin{pmatrix} A^{11}_{\mu} & A^{12}_{\mu} \\\ A^{21}_{\mu} & A^{22}_{\mu} \end{pmatrix}_{ab}. \qquad (2) $$ and corresponding fermion's charge $g$. The full lagrangian with interaction and mass term takes the form $$ L = \bar {\Psi}(i\gamma^{\mu}\partial_{\mu} + g\gamma^{\mu}\hat {A}_{\mu})\Psi - \bar {\Psi}\hat {m}\Psi . $$ I want to represent the lagrangian in terms of states with definite masses. Let's call them $\Psi_{L}, \Psi_{R}$. So by introducing mixing unitary matrix $$ \begin{pmatrix} \Psi_{L} \\\ \Psi_{R} \end{pmatrix} = \begin{pmatrix} cos(\theta ) & -sin (\theta ) \\\ sin(\theta ) & cos(\theta ) \end{pmatrix}\begin{pmatrix} \Psi_{1} \\\ \Psi_{2} \end{pmatrix} $$ I can rewrite the mass term in a form of $$ L_{m} = (\bar {\Psi}_{L} \bar {\Psi}_{R})\begin{pmatrix} m_{1} & 0 \\\ 0 & m_{2} \end{pmatrix}\begin{pmatrix} \Psi_{L} \\\ \Psi_{R} \end{pmatrix}. $$ But I can't diagonalize the $A$-matrix in general case in this basis. So the $A$-matrix and $m$-matrix don't commute with each other. So there is the question: what is the physical meaning of this result in the case of Majorana fermions?


title: emergent phenomena from microscopic equations of motion

text: Is an emergent phenomenon like "superfluidity" or "quantum Hall effect" derivable from microscopic equations of motion? If No, why?


title: Animating an Acceleration Vector - Acceleration of object on a crested path in gravitational field

text: So I was reading in Chapter 3 of my textbook, _Sears & Zemanksky's University Physics with Modern Physics_ by Young and Freedman, 13th Edition, and the discussion took us to a definition of the acceleration vector. (Please note that all pictures - which aren't obviously hand-drawn with with a pencil - do originate from this text.) Not so hard to swallow. But, one of the questions has me stumped - at least a little. Let's say we have sled sliding over perfectly flat terrain on perfectly super-slippery friction-less ice. Ignore air resistance - (the sled won't have much anyway, of course.) However, respect gravity. I know that this sled will have a 0-vector for acceleration when it is traveling along a perfectly flat surface, because there are _no external forces acting_ on the sled other than the normal force! (3rd sled From right) ![enter image description here](http://i.stack.imgur.com/egx7O.jpg) But in my physics book, we have this image, and by my 8th grade science teacher's Beard, the trough is fairly analogous to the crest. And here, we have a trough... and it's a trough with an acceleration vector on a similarly behaving object. ![enter image description here](http://i.stack.imgur.com/PyL6a.jpg) This suggests that the answer to the question using the diagram below - which vector is the acceleration vector? - is number 7 - despite the fact it seems as if normally there would be no acceleration there since the point of the crest qualifies as flat. ![enter image description here](http://i.stack.imgur.com/rj47H.jpg) First off, which vector in the above image (1-8, or 9 for zero vector) describes the acceleration vector of the sled going over that crest? Now let's say I know how to program my computer with 2D graphics. If I were to animate that sled going over the crest as shown in the book with the acceleration vector at every point right next to it, _but the crest then becomes flattened as in my hand-drawn image_ what would the vectors look like? If the vector is zero, why does the skier in the trough have an acceleration vector? If it is not zero, at what point in my animation does the acceleration vector magically disappear? Does it so disappear? If I were to make the similar animation for the skier going down the hill, would there be any differences in the acceleration vector, other than the obvious mirroring?


title: The reason(s) of seasons on earth

text: This maybe simple and usual question, although there is a lot of confusion about it over internet and even in some books, so I want from an astronomer / astrophysicist to fill the gaps for me accurately. Fixed axis tilt is the reason, this is the most common explanation, but with some research, you will find that it is not the only reason! Actually, earth distance from the sun playing its role: considering that the received energy from sun is inverse proportional to the square of earth distance, one can calculate that it's contribute to a change by 5-7% of the received energy. Moreover, it's effect is opposite, in senses that because we have summer when we are at the furthest point from sun, this actually reduces summer temperature due to axis tilt. Also I read a claim that mentions a third reason, that most of the texts ignores, it is the angle of earth orbit to the suns equator, anyway, I found no quantitative analysis. Your comments please.


title: Why is it so hard to accelerate macroscopic objects?

text: It seems all we're capable of accelerating currently are atomic particles. Why can't we, say, accelerate a clock to relativistic speeds?


title: Numerical Tools to find Braiding Statistics of Quasiparticles

text: While certain classes of systems that exhibit topological order can be solved exactly (such as the Toric Code, Abelian FQH Edges, etc.) there also exist systems (think of perturbed versions of the Toric Code or Abelian FQH Edges) that cannot be solved exactly. What are the common numerical tools that are used to extract the (not necessarily abelian) braiding statistics of quasiparticles from these models? What is the main idea of these techniques? For which systems do they work well and for which systems do they fail? Can one access the braiding statistics also from numerical exact diagonalization of a small system? (For say a perturbed Toric code I would guess so because at least in the unperturbed case the abelian braiding statistics do not depend on the system size) I would be very happy if someone could provide a brief overview. I am looking forward to your responses!


title: Rate of change of magnetic flux and the speed of the magnet

text: ![enter image description here](http://i.stack.imgur.com/69zno.png) The faradays law is $-N*A* \frac{\Delta B} {\Delta T}$ which is the rate of change of magnetic flux times area. How to find out the voltage induced when the magnet moves through the coil and exits from the other side with speed V? Someone suggested the formula should be $-\frac {2 N A B V} {l}$ ( where $V$ is speed of the magnet and $l$ is its length ) i need to know if it's true , how did he get it ?


title: Characteristic polynomial of a Matrix

text: In fact, this problem is more likely to be a math problem. When I read a paper(http://arxiv.org/abs/0707.2875), the author includes the characteristic polynomial for a type of matrix $A_k$ with eigenvalues $E_k$. The characteristic polynomial is expressed as \begin{equation} \rho(E_k) = E_k^4 - (\text{Tr}\\{A_k\\})E_k^3 \+ \\{\frac{1}{2}[|A_k-I| + |A_k+I|] - 1 - \text{det}A_k\\}E_k^2 \notag\\\ \+ \frac{1}{2}[|A_k-I| - |A_k+I|]E_k + \text{det}A_k = 0, \end{equation} while the matrix $A_k$ related here is \begin{equation} A_k= \left( \begin{array}{cc} \xi_k - \vec{\sigma}*(\vec{V}-\vec{g}_k) & i*(d_0+\vec{d}*\vec{\sigma})*\sigma_y\\\ [i*(d_0+\vec{d}*\vec{\sigma})*\sigma_y]^\dagger &-\xi_k + \vec{\sigma}^T*(\vec{V}+\vec{g}_k) \end{array} \right). \end{equation} Here, $\vec{\sigma}=(\sigma_x,\sigma_y,\sigma_z)$, $\xi_k=\frac{k^2}{2m}-\mu$, $\sigma_i$ are Pauli matrix. $\vec{g}_k$ is a vector satisfy $\vec{g}_k=-\vec{g}_{-k}$. Sometime $A_k$ is also called the Bogoliubov-de Gennes(BdG) Hamiltonian. My question here is how can we deduce the characteristic polynomial $\rho(E_k)$.


title: Calculate energy from vacuum electromagnetic-field action

text: I'm reading Rubakov's "Classical Theory of Gauge Fields", and I'm having a little bit of trouble with problem 7, p 15: > Using an expression of the type $E = \int d^{3} x \frac{\delta L}{\delta > \dot{\varphi} (x)} \dot{\varphi} (x) - L$, find the energy of an > electromagnetic field with action $S = -\frac{1}{4} \int d^{4}x F_{\mu \nu} > F_{\mu \nu}$ and dynamical coordinates $A_{\mu} (x,t)$. Show that when the > field equations $\partial_{\mu} F_{\mu \nu} = 0$ are satisfied, the energy > thus found agrees with $E =\frac{1}{2} \int d^{3}x (\vec{E}^2 + \vec{H}^2)$. I used the expression $E = \int d^{3}x \frac{\delta L}{\delta (\partial_{0} A_{\nu})} \partial_{0}A_{\nu} - L$, where $L = \int d^{3}x (-\frac{1}{4} F_{\mu \nu} F_{\mu \nu})$. First though, $\frac{\delta }{\delta (\partial_{0} A_{\nu})} (\int d^{3} x (\partial_{\alpha} A_{\beta} - \partial_{\beta} A_{\alpha})^2) = (?) 2F_{\alpha \beta} (\delta_{0 \alpha} \delta_{\nu \beta} - \delta_{0 \beta} \delta_{\nu \alpha}) = 4F_{0 \nu} $. Substituting, I got $E = \int d^{3}x (-F_{0 \nu} \partial_{0}A_{\nu} + \frac{1}{4} F_{\mu \nu} F_{\mu \nu}) $, which is where I'm now stuck; I'm suspicious of the first term. Any hints/ help would be much appreciated.


title: Two-point correlation function for planar Potts model

text: Fastest known method for computing Potts model partition function (Bedini and Jacobsen's "A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings") uses a "tree decomposition" of the square lattice. How can this method be extended to computing two-point correlation function? An obvious approach is to re-run it for every pair of vertices fixed to a particular value, but that ends up with a lot of redundant computation, is there a more efficient way? Example splitting scheme for grid ![](http://yaroslavvb.com/upload/grid- decompose.png)


title: Equilibrium and movement of a cylinder with asymmetric mass centre on an inclined plane

text: A cylinder whose cross section is represented below is placed on an inclined plane. I would like to determine the maximum slope of the inclined plane so that the cylinder does not roll. The mass centre (CM) of the cylinder is at a distance r from the central axis. The cylinder consists of a cylindrical shell with mass $m_1$ and a smaller cylinder with mass $m_2$ placed away from the axis and rigidly attached to the larger cylinder. What is the influence of friction? Is it possible to establish the law of the movement? I think that the piece may roll upwards until it stops. The figure was copied from _Projecto Ciência na Bagagem_ \-- _Cilindro desobediente_ ![alt text](http://i.stack.imgur.com/1ih2z.jpg) * * * EDIT: Depending on the initial conditions is it possible to find the highest point the cylinder rolls to, before stopping? EDIT2: From Institute and Museum of the History of Science -- _Cylinder on inclined plane_ [another cylinder] > "When placed on the inclined plane, [another] cylinder tends to roll upward, > coming to a halt at a well-determined position."


title: Where do atoms go after collision?

text: [I edited the question according to Mark's and Grisha's answers.] Consider two point-like particles of equal mass colliding centrally in 2D. The final directions of the momenta of the two particles are not determined by conservation of energy and momentum: they can go anywhere. > Under which circumstances the direction of the two particles _is_ > determined?


title: Is it possible to make glasses that make everything brighter, but do not magnify or focus?

text: Corrective glasses are usually intended to help focus light on your retina. Supposing I had good vision already, but simply wanted more light, could I make glasses that would send more light into my eye without magnifying, focusing, or distorting the image? (Ignore chromatic aberration.)


title: A charged sphere with pulsing radius

text: ![enter image description here](http://i.stack.imgur.com/D0854.png) Radius increases and decreases periodically (as a pulse).And so does the charges on the surface of sphere. ![enter image description here](http://i.stack.imgur.com/SqSv2.gif) I can't get what is gonna happen.the EM waves are produced perpendicularly to motion of the charges,but here where is the perpendicular ? Will the EM waves get produced into the space of sphere? Also, can two EM waves intersect each other or not? [as Electric fields lines can't intersect.]


title: Standing sound waves phase difference

text: This is a basic question but I don't fully understand what is going on. When we have a pipe in resonance we get standing waves, where displacement antinodes are at pressure nodes and vise versa. So we have a situation where pressure and displacement are 90 degrees out of phase, this means you can differentiate the displacement wave to recover the pressure wave. Does anyone have a nice explanation of this 90 degree phase difference?


title: What happens when a compact fluorescent lamp implodes?

text: When a incandescent lamp implodes, the filament burns up and the current is interrupted. Yesterday, a compact fluorescent lamp imploded and blew all the switches / fuses. I'm not sure if the same would happen with ordinary fluorescent lamps. Can it be that the charge stored in the capacitor is released backwards? Is something else going on?


title: Bound states for sech-squared potential

text: I'm working on an introductory qm project, hope somebody has the time to help me (despite the length of this post), it will be highly appreciated. My goal is to determine the bound states and their energies for the potential $V_j(x) = -\frac{\hslash^2a^2}{2m}\frac{j(j+1)}{\cosh^2(ax)}$ for any positive value of j (I think I'm supposed to show that j has to be integer at some point, but I don't know). By a change of variable, $ax\rightarrow y$, I have rewritten the Schrödinger equation for this potential to: $-u''(y)-\frac{j(j+1)}{\cosh^2(y)}u(y) = Eu(y).$ I will denote the corresponding Hamiltonian $H_j$. I have shown that the ground state for $V_j(x)$ is $\psi_0(x) = A\cosh(ax)^{-j}$ (this is all correct, has been verified). Now here is where serious problems begin. I am given these ladder operators: $a_{j+} = p + ij\tanh(y)$ $a_{j-} = p - ij\tanh(y)$ where $p = -i\frac{d}{dy}$ (no h-bar). I have shown that $H_j = a_{j+}a_{j-} - j^2$ and $H_{j-1} = a_{j-}a_{j+} - j^2$ and I have used this to show that if $|\psi>$ is an eigenstate for $H_j$ then $a_{j-}|\psi>$ is an eigenstate for $H_(j-1)$ and $a_{(j+1)+}|\psi>$ is an eigenstate for $H_(j+1)$, both with the same eigenvalue (energy). Thus the purpose of the a-operators is to carry an eigenfunction for the potential characterized by the value$ j (H_j)$ over to an eigenfunction for the potential characterized by the value j-1 or $j+1 (H_(j-1), H_(j+1)).$ Now I should be able to find all bound states and their energies (I have been told that there is only one bound state for every (integer?) value of j, so this amounts to showing that the ground state I found earlier is the only bound state there is). I'm clueless on this last step.


title: Frequency and wavelength of photons

text: I try to better understand how electromagnetic radiation works. So I have some questions. If an antenna emits at 100MHz (the charges on the antenna oscillate at 100MHz) what frequency will have the emitted photons? Will they have the same 100 MHz? In the case of the photons what will this frequency represent in fact? Also what does the wavelength of the photons represent? I mean in the case of an electromagnetic wave , the wave represents the variation in intensity of the magnetic and the electric fields, and the wave-length is the distance between two crests of this variations (correct me if I am wrong). How about in the case of the photon wave-length?


title: First integral of an equation of motion: $\mu\ddot r=-\frac{k}{r^2}$

text: I've got an equation of motion (EOM), which is $ \mu\ddot r=-\frac{k}{r^2} $ How do I find the first integral of this EOM? I'd appreciate it if someone could show me the steps involved. I should get $ \frac{1}{2}\mu\dot r^2=-k \left( \frac{1}{R}-\frac{1}{r} \right) $ but I'm not sure how to proceed.


Do materials cool down in the vacuum of space? If yes, how does it really work?


title: Why porcelain Insulators are brown in colour?

text: The porcelain insulators are brown in colour. Why?


title: The force exerted by a ~10 Tesla magnet on a C13 isotope?

text: How much force would a ~10 Tesla magnet exert on a weakly magnetic C13 isotope? If I made a molecule of diamond with $N$ C13 atoms, how large would $N$ need to be for me to pull on it with something like a ~1 pico-newton force?


title: Moons of the planets

text: What is the phenomena behind gas giants like Jupiter and Saturn having a large number of moons as compared to other planets. Were the present state moons a part of their parent planet long time ago ?


title: Random Walk Randomly Reflected

text: Hi I am not specialist in probability so I will not be surprised if the answer for this question is just a simple consequence of well known results from the random walk theory. In this case, I will be happy if you can tell me the "magic words" to find the material related to this problem. Let $\sum_{i=1}^n X_i$ a random walk in $\mathbb{Z}^d$ defined in the following way: In each step, the walker look at your current position and as long as its distance to the origin does not belong to the set $\\{d_1,d_2,\ldots\\}$ ( we assume that $d_n\in\mathbb{N}$ and $d_i<d_{i+1}$ ) it jumps for one of its nearest neighbor with probability $1/2d$. For the other hand if $\|\sum_{i=1}^n X_i\|\in \\{d_1,d_2,\ldots\\}$ then the walker toss a biased coin if the result is head, which occurs with probability $p$, it goes back to the previous position, that is, $\sum_{i=1}^{n-1} X_i$. If the result is tails it chose randomly one of its neighbors with probability $1/2d$. I would like to know if there exist a non-trivial $p_c$ such that this random walk is transient for $p<p_c$ in dimension $d=3$. Of course, for this question to be well posed we have to define the sequence $(d_n)$. I would like to chose it randomly but I have no idea for what kind of distribution this problem is tractable. So at this time we can assume that $d_n$ is deterministic sequence and, for example, has a polynomial growth as $d_n=n^2$. Any references or comments are very welcome. PS: Could an user with more rep. place random walk tag for this question ?


title: Does 4D N = 3 supersymmetry exist?

text: Steven Weinberg's book "The Quantum Theory of Fields", volume 3, page 46 gives the following argument against N = 3 supersymmetry: "For global N = 4 supersymmetry there is just one supermultiplet ... This is equivalent to the global supersymmetry theory with N = 3, which has two supermultiplets: 1 supermultiplet... and the other the CPT conjugate supermultiplet... Adding the numbers of particles of each helicity in these two N = 3 supermultiplets gives the same particle content as for N = 4 global supersymmetry" However, this doesn't directly imply (as far as I can tell) that there is no N = 3 QFT. Such a QFT would have the particle content of N = 4 super-Yang-Mills but it wouldn't have the same symmetry. Is such a QFT known? If not, is it possible to prove it doesn't exist? I guess it might be possible to examine all possible Lagrangians that would give this particle content and show none of them has N = 3 (but not N = 4) supersymmetry. However, is it possible to give a more fundumental argument, relying only on general principles such as Lorentz invariance, cluster decomposition etc. that would rule out such a model?


title: How do I calculate electric fields due to currents of magnetic dipoles?

text: **Short version of my question:** Do dipole currents cause fields? I think currents of aligned magnetic dipoles cause an electric field, but I don't know how to calculate this field except in the simplest of cases. I'd like to know how! **Full version of my question:** Suppose I have a wire (or pipe) that carries a steady current of particles, and the wire is shaped like a sine curve in the $X$-$Y$ plane with spatial period $P$ and amplitude $A$. I want to calculate the electric and magnetic fields produced by the current in the wire.   1. If the flowing particles are charged, I can use the Biot-Savart law to write an integral and (at least numerically) calculate the resulting magnetic field. In the limit where $A=0$, I can check my results against a Lorentz-boost calculation, and see that the two methods agree.   2. If the flowing particles are electric dipoles pointing in the $Z$-direction, things are more complicated, but I can still use the Biot-Savart law, adding up the magnetic fields from two equal, opposite, displaced sinusoidal electric currents to get a net magnetic field, albeit one that falls off much more quickly than in the previous case. I can still check my results against the Lorentz boost in the $A=0$ limit, and find that the two methods agree.   3. However, if the flowing particles are magnetic dipoles pointing in the $Z$-direction, **I don't know how to calculate their electric fields** except in the $A=0$ limit. In this limit, I can use a Lorentz boost argument to show that an electric field exists, but I don't know of any equivalent to the Biot-Savart law for currents of magnetic dipoles. I would be very surprised if the electric field vanished in the $A>0$ case. **How do I proceed?** Is this covered in elementary textbooks, and I've missed it somehow? I'm tempted to model this third case in a similar fashion to case 2, as a fictitious pair of equal and opposite "magnetic currents", and use an electric version of Biot-Savart. This produces the correct result in the $A=0$ case, and seems reasonable in the $A>0$ case, but seems to have no basis in any textbook or reference I can find. What am I missing? **Caveats:**   1. If at all possible, please **base your answer on credible textbooks or peer-reviewed papers**. For example, if you think Maxwell's equations is missing a $\vec{v} \times \vec{M}$ term, I'd very much like to see an external link to back it up.   2. This may be obvious from the 'spirit' of the question, but I'm not particularly attached to the sinusoidal shape of the current-carrying wire. Any nontrivial shape of the wire that precludes a Lorentz boost is equally interesting to me, so go ahead and change the wire's shape if it makes the math easier.


title: Does string/M-theory address higher-dimensional membrane vibration modes?

text: A loop is a 1-sphere that can vibrate in increasingly complex ways as it is embedded in higher dimensional spaces.   1. Does string theory assume that 1-spheres are the only possible vibrating structures, or does it also look at the vibrations of higher spheres, e.g. (2,3,...,8)-spheres? If only 1-spheres are assumed, what is the reason for that constraint?   2. Whether for 1-spheres or $n$-spheres, are the vibration modes of string theory assumed always to be in 9-space, or are more restricted modes in lower-dimensional subspaces also explored?


title: How to prolong life of liquid nitrogen in hosehold vacuum flask?

text: I need to do some work with liquid nitrogen at home. The main question is how to store it without buying huge vacuum flask specifically for liquid nitrogen. I've tried to use usual steel household vacuum bottles, added ~1 cm of extra insulation (some foamy material, multiple layers), wrapped in plastic to protect from condensation. Cap is also made from this foamy material (I remember that I should not seal the flask) . The problem is that liquid nitrogen evaporates in ~30 hours. I suppose the main issue is cap construction, sides of the flasks are warm, while cap is cold. Also, it seems heat loses are maximum near cap because hot and cold steel sides are touching there. Any known tricks on how to improve heat insulation and prolong lifetime of liquid nitrogen? Is that correct that I should be wrapping it all in aluminum foil on the "hot" side of insulation? My goal is 3 days evaporation, 7 is just perfect. ![enter image description here](http://i.stack.imgur.com/mzPJr.jpg) ![enter image description here](http://i.stack.imgur.com/ukzTg.jpg)


title: Quasiparticles in Bohmian mechanics

text: My questions are about de Broglie-Bohm "pilot wave" interpretation of quantum mechanics (a.k.a. Bohmian mechanics).   1. Do quasiparticles have any meaning in Bohmian mechanics, or not? Specifically, is it possible to trace the motion of a quasiparticle (e.g. a phonon, or a hole) by watching Bohmian trajectories?   2. Bohmian mechanics provides some explanation of difficulties related to quantum measurement process. But imagine that, in some kind of "theory of everything", all known elementary particles (leptons, quarks, gluons etc.) are actually quasiparticles (real particles are always confined). Would the explanation, provided by Bohmian mechanics, survive in this case?


title: What is the shielding in nuclear reactors mainly against?

text: I have a little knowledge about ionizing radiation and I have been confused over why nuclear reactors need these massive shields. So, if I am not mistaken, Alpha and Beta radiation are not that dangerous since they can be shielded with relatively light materials, the main problem is because Gamma and Neutron radiation. So now, which one requires that heavy shielding ? Also, if the reactor released either Gamma rays only or Neutrons only, which one of them would need less massive material to be reduced to a non-harmful level ? Any numbers on the density of radiation this shield has to stop will greatly help here too.


title: kinetic and potential energy

text: I have 2 cubes where one mass is greater than the other. $M$ and $m$, where $M>m$, and there is a hill that is symmetrical on both sides, and has a friction factor of $k$ between the object and the surface. If we place both objects on one side of the hill, point 1, that has no slope, so it is flat, and give both of the masses the same velocities in the direction of the top of the hill so they finally land on the other side, on the flat area, point 2 (symmetrical to the point 1). How can I prove that the speed of the heavier cube is smaller than the lighter one in the point 2? (If I'm correct) I tried equating $E_{kinetic}$ and $E_{potential}$... I see there is work from the friction, but whenever I try anything I cross out the mass. Heres a diagram: http://www.wolframalpha.com/input/?i=sin%5E2(x)%2C+0%3Cx%3Cpi&x=0&y=0 Where point 1 is at (0, 0), and point 2 at (pi, 0). What I have so far: where $g$ is constant of gravity and $k$ friction factor, and $d$ distance. $E_{kinetic.start} - W_{friction} = E_{kinetic.end}$ $M(\frac{v_0^2}{2}-gkd)=M(\frac{v_1^2}{2})$ I could change $M$ with $m$ and nothing would change, they'd both have same speeds... So it's obvious that the masses cancel out and the energy is proportionally lower at both masses, the distance for friction is the same and starting velocities are the same, therefore the velocity should be the same for both bodies at the end. This confuses me as I believe the smaller body should be faster. (Cant noone help me with this? Im now doubting the solution i've provided first is right. I cannot prove otherwise.)


title: Stationary state of time-independent Schroedinger equation is always real valued function?

text: I am reflecting on the solution of the time-independent Schroedinger equation. My reasoning is that the stationary state of the time-independent Schroedinger equation must be a real valued function because of their stationary condition they must not carry any flux. Is my reasoning correct?


title: What are the consequences of a body of mass moving at speed of light?

text: What would happen to someone who could move at the speed of light? I know that at the speed of light bodies gain mass and decrease in size. But what would happen to a body gaining mass tending to infinity? **EDIT:** It is a hypothetical question, I know that an object can't move at the speed of light.


title: Definitions in thermodynamics: temperature, thermal equilibrium, heat

text: I'm currently reading Fermi's "Thermodynamics" and I'm trying to grasp the (possibly different) right definitions for _temperature_ , _thermal equilibrium_ , _heat_. To clarify, I'm looking for definitions from a purely thermodynamical point of view, which is also the line followed by the book. * * * Let's start with the latter. We can define _heat_ through the 1° principle of Thermodynamics:$$Q=\Delta U + L ,$$that is, “Heat is the quantity of energy that a system absorbs from the ambient in a form that's not mechanical work.”. OK, I see no problem with this, apart from the fact that we need to define the energy $U$ of a thermodynamical system. Let's ignore it. * * * Now _thermal equilibrium_. This is the one I'm finding more troubles with, because in all definitions I've come across (maybe not very good ones, or maybe it's my interpretation) there's some reference to _temperature_ , while in the definition of the latter there's reference to the concept of _thermal equilibrium_ , but one has to start somewhere. For example, from (IT) Wikipedia, I read: > Thermal equilibrium: there is no flux of heat, temperature is constant in > time and is the same in every point of the system. * * * The way that _temperature_ is defined in the book is, first of all, the empirical (operational) one: > Temperature can be measured by putting a thermometer in contact with the > system, for a sufficient time interval so that **thermal equilibrium** is > established. Some pages later there's also mention to the gas-thermometer. Finally, in the “Second principle of Thermodynamics” chapter, it's said: > Until now, we've only made use of an empirical scale of temperature. [...]If > we put in thermal contact two bodies at a different temperature, heat will > flow spontaneously by conduction from one body to the other. Now, by > definition, we will say that the body from which the heat flows is the one > with the higher temperature. Now, clearly the definition in the first blockquote requires _thermal equilibrium_ (beetween a body itself and beetween to bodies, I suppose) to be independently defined. Regarding the second, how can one tell what's the direction of the heat flux? Also, the second definition doesn't give a method to measure temperature, but only a way to tell which body is the hotter, right? * * * * * * As I put them above, those definitions seem to me random pieces of a puzzle, I need to get a clearer picture. So any help is appreciated.


title: How to recognize broken candies from whole ones

text: Let's say I have a bag full of sugar candy. Some will be whole, some will be dent, some will be broken (in part, or half, etc). Let's say I have a device with an input box where I empty the bag, and the device has two output boxes where it start placing the whole candies in one box, and all the dented/broken one in the other box. What principle of the physic could use the device, to be able to tell the whole candies from the dented/broken ones?


title: Coherency matrix of partially polarized light doesn't contain all information on polarization state?

text: The electric field of quasi-monochromatic, partially polarized light can be expressed by the following random process (Goodman, Statistical optics) $$\bar{E}(t,\bar{x})=u_{x}(t,\bar{x})\bar{e}_{x}+u_{y}(t,\bar{y})\bar{e}_{y}$$ $$u_{x}(t,\bar{x})=\Psi_{x} e^{i(\bar{k}\cdot\bar{x}-\omega t)}$$ $$u_{y}(t,\bar{x})=\Psi_{y} e^{i(\bar{k}\cdot\bar{x}-\omega t)}$$ where $\Psi_{x}$ and $\Psi_{y}$ are radom phasor sums (which are circular complex Gaussian random variables). The joint statistics of $u_{x}=a+bi$ and $u_{y}=c+di$ describe the polarization state. Knowing that $E(u_{x})=E(u_{y})=0$, the covariance matrix of these two complex is given by $$C=\begin{bmatrix} E(aa)&E(ac)&E(ab)&E(ad)\\\ E(ca)&E(cc)&E(cb)&E(cd)\\\ E(ba)&E(bc)&E(bb)&E(bd)\\\ E(da)&E(dc)&E(db)&E(dd) \end{bmatrix}=\begin{bmatrix} E(aa)&E(ac)&0&E(ad)\\\ E(ac)&E(cc)&E(bc)&0\\\ 0&E(bc)&E(aa)&E(bd)\\\ E(ad)&0&E(bd)&E(cc) \end{bmatrix}$$ This matrix has 6 free parameters. However, one often states that the polarization is determined by the coherency matrix $$J=\begin{bmatrix} E(u_{x}u_{x}^{\ast})&E(u_{x}u_{y}^{\ast})\\\ E(u_{y}u_{x}^{\ast})&E(u_{y}u_{y}^{\ast}) \end{bmatrix}=\begin{bmatrix} 2E(aa)&E(ac)+E(bd)+i(E(bc)-E(ad))\\\ E(ac)+E(bd)-i(E(bc)-E(ad))&2E(cc) \end{bmatrix} $$ which has only $4$ free parameters because two pairs of free parameters of $C$ are combined in two free parameters in $J$. So we lost 2 degrees of freedom. Does this mean that $E(ac)=E(bd)$ and $E(bc)=-E(ad)$ or does this mean that the coherency matrix doesn't contain all information on the polarization state?


title: Internal moment in the hull of a pressure vessel

text: This question is related to the course structural analysis. As part of our exam grade every student has been given different multiple homework assignments which we have to solve. One of the problems I have been given is the following; > Given a cylinder with radius $R$ and internal pressure $p$, find the maximum > bending moment in the cross section. Provide a free body diagram to support > your answer. The bending moment which is meant is the internal moment created in the hull of the cylinder when you take a cut out of cross section which is a circle obviously. At this point I have only been able to proof that the internal shear force $V = 0$ and that the internal normal force $N$ must be equal to $N = p \cdot R$. Which can be proven as follows using the free body diagrams below. $$2 \cdot N = R\cdot \int_0^\pi p \cdot sin(\theta) d\theta $$ $$Pd\theta = 2 \cdot N \cdot sin(0.5 \cdot d\theta) + 2\cdot V \cdot cos(0.5 \cdot d\theta)$$ Another way I have been looking at this problem is by making use of strains $\epsilon$ and stresses $\sigma$. If you assume the strain $\epsilon$ on the outside and inside of the cylinder are equal the stress $\sigma$ distribution over the thickness must be constant thus the moment $M$ must be 0. However the assumption of the strains being equal on the in and outside is something I am not sure about. So what I'm looking for is a solution for the internal moment $M$ in the hull of the cylinder and if it is zero, a proof for this. ![hand drawing](http://i.stack.imgur.com/PaO3o.jpg)


title: Is it possible to transfer classical bits of information faster than light speed?

text: Is there any known, verifiable way to transfer classical information faster than light, using quantum entanglement or other phenomenon? Does quantum teleportation, or other known phenomenon, allow FTL transfer of information (not "quantum state", but true classical information)? A friend and I have a few $$$ riding on this ... I know I'm right, and I need some answer he will accept as irrefutable evidence one way or the other. (The evidence would be not that it's physically impossible, but that the general consensus in the physics community is that it's impossible) I saw some duplicate questions, but nothing that asks this simple, generic question. **Edit** \- I need a straight "Yes" or "No" answer, and so far I haven't seen it.


title: Is it best to look at light as a particle when trying to understand special relativity?

text: So my course about special relativity explains time dilation using a moving train, where one sends up (i.e. perpendicular to the direction of movement) a light pulse which gets reflected etc. (a similar example is to be found here so you guys know what I'm talking about) Let's say the source of the light pulse is a flash light. In the moving frame of reference, it is pointed upwards, and thus only has an upward component. Everything fine so far. The thing is, that when you look at it from the outside ("the train station"), I picture the flash light to still be pointed directly upward, but somehow when the pulse leaves the flash light, it gets a horizontal component. This does not make sense if you think of it in terms of some stationary ether (which is also wrong as Michelson & Morley showed). The problem is that I can't seem to get my mind around the fact that it somehow seems that the flash light is pointed at an angle in the outside frame of reference. Except if I think of light as photons (particles), then it seems intuitively correct that they get a horizontal component (compare it to a skater throwing up a tennis ball). So, when trying to understand SR, do you have to think of light as particles? My course states this nowhere explicitly so I'm not sure. _I might have answered my own question again by formulating it in a more or less ordered fashion, as happens so often when I post it here :P_


title: Definitions: 'locality' vs 'causality'

text: I'm having trouble unambiguously interpreting many answers here due to the fact that the terms locality and causality are sometimes used interchangeably, while other times seem to mean very different things to the author. My current understanding is that 'a-causality' is "obviously forbidden" in a physical theory, because it violates Lorentz invariance and leads to logical paradoxes. (Although there are supposedly viable models such as De Broglie–Bohm that are a-causal and yet somehow OK because the a-causality is not accessible to experimental apparatus -- this only brings further confusion to the table.) 'Non-locality' on the other hand, seems to refer to, for example, correlations between events at space-like separation. In this sense 'non-locality' does not imply 'a-causality.' On the other hand Bell (1964) uses the term 'non-local' to refer to, as he says in his conclusion, "not Lorentz invariant." So I think he is using the word 'locality' interchangeably with 'causality.' This is the sense in which many, such as Luboš Motl seem to use the term, for example here, while others, such as Ron Maimon, seem to use the term differently, for example here, where he says: > The nonlocality of gravity doesn't mean that Lorentz invariance is broken This is very confusing. Can someone give an authoritative set of definitions here that we can refer to?


title: Why moving charges causes Magnetic Field (module and direction)?

text: Why an constant electric current in a wire produces a magnetic field, that circles that wire? I know that this question was posted before. However, all answers talk about Maxwell equations, axioms, formulas Relativity Theory it's necessary, but it lacks a intuitive explanation about magnetic field direction. It's a big challenge, explain it in layman terms, as if for a teenager. I absolutely believe that it's possible! I've read some Relativity explanations in Wikipedia, etc. However, even with that explanation it's not clear why the magnetic field is around the wire. I've also read that question and its answer: How does moving charges produce magnetic field? I've liked that answer, it's nice to understand the force direction between 2 wires. http://en.allexperts.com/q/Physics-1358/Magnetism-1.htm


title: Heisenberg relation

text: > _Given that $A(k)=\frac{N}{k^2+\alpha^2}$, show that $\Delta k \Delta x > >1$._ Considering the above example, according to my textbook, it is written that I must square the above function and determine when does the square fall to 1/3 of it's peak value. What does that mean, practically speaking? This should enable me to determine a value for $\Delta k$. Similarly we proceed in order to determine $\Delta x$ but by squaring $\psi(x,0)$, the wave function and seeing where does it drop off to $1/3$ for it's peak value.


title: Why is it called "annihilation"?

text: The term "annihilate" literally means "turn into nothing". However, when a particle and antiparticle collide, they clearly do not turn into _nothing_ ; they simply transform into different particles. Did the term originate at a time when physicists thought that matter + antimatter really did turn into nothing? Does anyone else find the term confusing and/or misleading? Can we introduce a better term? (I find it especially irritating to hear physicists say that an electron and a positron _annihilate into_ two photons... that's an oxymoron!)


title: Do I think or listen - physics talks

text: I am just a student, still I have already listened to a few talks on physics. In my study program everyone has to give a talk of about 45 minutes what he did in his about 1-2 month reach project during the 'holidays'. I often sit in those talks an also can keep up for the first 15 minutes. Then it happens very often that there is something that I don't understand at first glance. I think to myself, is this really right or might there be an error. At this moment of time comes my problem: Do I give this problem a minute and if I don't come to a clue, ask a question, but if it got clear I was left behind by the talk or might have missed important details. So is it maybe better to skip it and continue. I have never been on a real physics conference, but I guess there the same problem occours. It would be nice to have some experienced answers to this 'Do I think or listen' - problem.


title: Dirac electron polarity?

text: according to Spin of an electron Dirac said the electron has Two possible spins if i'm correct. Do Electrons have polarity? measurable by its Dirac spin or probabilistically by its quantum states?


title: Help finding Delta T for a known position displacement with known accel/decel, etc

text: I'm looking for an equation to find the time it will take for a position displacement to happen, given known $V_{max}$, a (known) constant acceleration, deceleration, jerk, and displacement... and an initial velocity of 0. I am trying to estimate/calculate the time it will take for a servo motor axis to travel a certain distance. Once I know the estimated time of that move, I can solve for jerk for the other axis. That way, I choose an optimally "slow" speed for whichever axis has a shorter move distance to make the maximum use of my time. FYI, this is a pick and place XY robot gantry.


title: Does the conversion of crude oil to greenhouse gases have any measurable effect on earth's gravitational pull?

text: Oil underground is much denser than greenhouse gas in the atmosphere. Does the conversion in anyway effect the gravitational force from earth.


title: Determine particle velocity from density function

text: I'm modeling a 1D system which consists of a large number of discrete particles distributed on a line. As a continuous approximation, I'm defining $c(x,t)$ to be the space density function of these particles, such that $\int_a^{a+\epsilon} c(x,t) \, dx$ is the number of particles between $x = a$ and $x = a + \epsilon$. Is it possible, from just the function $c(x,t)$, to determine the velocity distribution of the particles $v(x,t)$? If so, how would that be done? It's safe to assume that particles are not being generated or destroyed, so they obey some form of continuity equation. I've tried modeling particle flow into/out of a small pillbox on the line, but I'm having trouble forming an accurate equation for the motion.


title: Making fire using a filled water bottle

text: I have seen videos where a fire was started using a water bottle filled with water. I guess the bottle acts like a convex lens that converges light to a focal point to start a fire. But why does water have to be added?


title: Global part of a local symmetry?

text: 1. What is exactly meant by "Global part of a Local symmetry"?    2. What are its implications on a field theory at classical level?   3. What are its implications at quantum level?    4. How is it related to symmetry breaking?


title: What is the origin of the many-body expansion?

text: I'm looking for the original introduction of the many-body expansion (MBE) in the scientific literature. More specifically, I'm interested in a theoretical justification of the rapid convergence of the expansion, especially in the context of molecular physics. The MBE is often introduced in scientific papers without referring to foregoing work that introduces the concept. Instead, one often states something like: "Following the well-known many-body expansion, one writes ...". See for example http://pubs.acs.org/doi/abs/10.1021/ct600253j. (freely available at http://t1.chem.umn.edu/Truhlar/docs/758FAV.pdf) The many-body expansion is a scheme to decompose the energy of a general system of $N$ particles as follows: $$ V = \sum_{i = 1}^N V_i $$ with $$ V_1 = \sum_{i=1}^N E_i $$ $$ V_2 = \sum_{i=1}^N \sum_{j=i+1}^N E_{ij} - E_i - E_j $$ $$ V_3 = \sum_{i=1}^N \sum_{j=i+1}^N \sum_{k=j+1}^N \biggl( (E_{ijk} - E_i - E_j - E_k) - (E_{ij} - E_i - E_j)\\\ - (E_{jk} - E_j - E_k) - (E_{ki} - E_k - E_i)\biggr) $$ and so on. In these equations, $E_i$ is the energy consisting only of particle $i$, $E_{ij}$ is the energy of a system containing only particles $i$ and $j$, $E_{ijk}$ is the energy of a system with three partilces, $i$, $j$ and $k$, and so on.


title: four boson quantum system contact interaction

text: I have to solve this problem. Four bosons moving in 1d harmonic potential (their spin is 0) and interacting through contact interaction defined via delta function. Now, methods that I have to use: a) exact diagonalisation(numerical method) b) mean field approximation. For a) part a set of quantum states of the system must be formed using the states of non interacting system. We only work with quantum number less then 3 i.e., only 3 first solutions for harmonic pot. For b) part we have schro eq with hamiltonian of interaction given through some Vmeanfield defined as: $$\int U(x-y)r_0(y)\mbox{ dy}$$ where $r_0(y)$ is density of remaining 3 particles... harmonic pot is given in the usual form, $\frac{1}{2}\omega^2mx^2$. contact pot is $\delta(\mbox{Particle}_1-\mbox{Particle}_2)$ times some parameter $u$. Plot dependency of ground state energy on $\frac{u}{\hbar\omega}$ for both methods. plot overlap of wave funct from the first method with the one from the second method depending again on $\frac{u}{\hbar\omega}$. Thank you.


title: Capacitance per unit area and CMOS case

text: In a modern 0.35μm CMOS processor, the gate oxide thickness is around 80Å = 8nm. This gives us a capacitance per unit area of $430nF/cm^2$ I am not getting how one gets this capacitance per unit area. Can anyone explain this? (i.e. how formula are constructed and used.)


title: Intensity of light

text: If we have 2 beams of light with equal intensities, but with different frequencies, wouldn't the one with the higher frequency generate more power? If so, how come the intensity, which is in $W/m^2$, of the higher frequency beam is not higher?


title: Modulus of Elasticity

text: Consider a cube of unit dimensions. Let $\alpha$ and $\beta$ be the lateral and longitudinal strains. The expressions for moduli of elasticity on applying **unit tension** - 1) At one edge: Young's modulus $E=\frac{1}{\alpha}$ 2) Normally to all the sides: Bulk modulus $K=\frac{1}{3(\alpha-2\beta)}$ 3) Tangentially: Rigidity modulus $N=\frac{1}{2(\alpha+\beta)}$ Here, I was able to understand the first expression... But, How do we obtain the expressions for Bulk & Shear moduli..? Explanation please...


title: How can one reasonably theoretically model polycrystalline materials?

text: Many techniques are taught in advanced solid state courses but they are almost _all_ derived for perfectly crystalline materials. For example, band structure really only appears theoretically when you look at periodic potentials that are pretty big in at least one direction. But in experiment you often end up using materials that are polycrystalline (e.g., an evaporated film). Then, it is only periodic inasmuch the individual grains making up the sample are periodic, but they are both small (if your grains are ~1um wide, then you really only have 1000-10000 atoms in one direction, per grain) and randomly oriented, which messes up any theory I possibly know. How _can_ one analyze these? Is it possible? Which theories can still be used reasonably and which have to be thrown out? Thank you! edit: Sorry, I realized this could be a little ambiguous. I know you can probably model them computationally, but I mean more analytically, not just brute force.


title: Calculating equation of motion using path integral

text: Suppose my action integral is $S=\int d^4x(\nabla \times A)^2$ and $\delta S$ gives $\delta S =\int d^4x [2(\nabla \times A).(\nabla \times \delta A)]$ I would like to calculate the coefficient of $\delta A$ from this action integral . But I am stuck . How can I separate the $\delta A$ from the term like this ?


title: Does electric field cause changing magnetic field also?

text: According to Faraday's law, changing magnetic field causes eletric field (imprecise wording, but generally accurate). My question is, can Faraday's law be interpreted in opposite way - that is, electric field causing changing magnetic field? Equation itself doesn't speak for the direction, so I ask.


title: Why does the induced charge have to have the same magnitude as the inducing charge?

text: Why is it that the total induced charge on a conducting, grounde,d infinite plane must be of the same magnitude as the inducing charge?


title: parallel universe- are there an infinite amount of universes?

text: Parallel universe: in every universe, you are presented with a different decision. Does that mean there are an infinite amount of parallel universes? I.e., if in one universe I choose to go left, I am then presented with different choices vs if i choose right, and that creates more universes with more decisions to be made. Or does it mean that in the end of one's life we end up in the same place, meaning that its just one parallel universe that eventually collides with the other.


title: Is this a standard projectile motion equation?

text: Is Initial Velocity = Time * Acceleration a standard projectiole motion equation?


title: Do calculations support the idea that our universe should be a black hole?

text: In "The Physics of Star Trek" by Lawrence M. Krauss, he mentions that our universe, by all calculations, should actually be a black hole. I read it a while ago, but I think he mentioned that the mass in our (observable) universe is higher than the size of it, to the point where the observable universe is smaller than the Schwarzschild radius. If that is correct, then our universe should collapse into a singularity. Maybe I don't remember it correctly, or the problem is that we do not "see" the actual size of the universe, but only a small part (however, due to the homogenicity of it all, the density would be the same). My question is if Krauss is correct in what he says (assuming I remember correctly), and if there is a reference to the original paper?


title: Finding dv/dx when given x and v as functions of t

text: This isn't a homework question, I tried to word this as a physical problem and it got re tagged as homework by someone Say I am given the equation of position in one dimensional kinematics. Say its the usual free fall kinematics, with x being the up down motion, and v= dx/dt. starting from rest. How do we find dv/dx when given x(t)? Would taking the derivative of v(t)/x(t) work? I assume I'll need the chain and quotient rules. If you're wondering, I want to see how to use the derived relation a = v dv/dx. I know this holds, but I don't know how to apply it when given with regard to time. I'm using parametric equations at the moment As per the comments, I realized I mis-wrote seine things. I corrected it. As per comments: so there's nothing more to it, I was just overthinking it? What about quotient rule? I'm thinking w the chain rule it would be dx/dt = dx/dv * dv/dt then I would divide by dx/dv to invert it? Which would give me dv/dx * dx/dt = dv/dt Which gives me dv/dt = dv/dt? I figured it out. Thanks for the answer though Dv/dt= dv/dx dx/dt => dv/dt * (dx/dt)^-1 = a/v. So to get a, wee multiply by v giving us a= v*dv/dx. I get it meows


title: Breathing Air Underwater From A Car Tyre

text: I've seen in many movies and programs the event where a car plummets off the road and in to a body of water, sinking rapidly. The car slowly fills with water as it sinks and the occupant(s) don't break free until well under the water (50m say). At this point, when outside of the sinking vehicle, they then breathe air from the tyres and swim to the surface. Obviously it's not that easy to breath air from a tyre due to the valve set up (having to push the pin in to draw air under pressure out). But what I really want to know is, if a tyre is at 30psi and there is no pressure regulator used, and your under 50m of water pressure... Could you actually do this? Surely there'd be issues with the pressure at that depth, or even at atmospheric!


title: A physicists perspective on a material science/engineering problem

text: I am looking into some research that involves engineering and material science. As a physicists I wondered what other physicists would think of this problem and how they would approach it. Much of the experimental work is already in progress so this can be ignored. We would like to know the impact of humidity and temperature on the stress/strain in very large fabrics. To start let's say we have a very large piece of some fabric (e.g. wool). It may be pristine or may have degraded over time (e.g. a historical tapestry). We wish to measure the stress/strain relationship using sensors (that do not impact the stress/strain within the large fabric) as well as the temperature and humidity in or around the material and send this data to a computer (I would assume). How we would begin to model this relationship and what would the model look like? Can anyone recommend any papers upon which I can expand my research or has a similar model I can work with? The main problem I am having is where to begin, I can see where it would begin from a technical stand point but (setting the test up to collect data). But how would this then be used to create or expand upon an existing model? What would such a model look like? Finally if a model were to be developed what accuracy could one place upon it? Any help with this would be so amazing! If I figure out how to add a bounty for a good question then I surely will! Regards,


title: Free spin (Curie) Paramagnetism

text: I'm working through a derivation for Curie paramagnetism and hope someone could help clarify a couple of steps. The way that makes sense to me (although now I have seen the wikipedia derivation below I realise this way is pretty long) is to not take any high temperature approximations until near the end of the derivation where I have: $M=g_J\mu_B[(J+1/2)coth[g_J\mu_B\beta(J+1/2)]-\frac{1}{2}coth(g_J\mu_B\beta/2)]$ now to get to the curie susceptibility it seems that when taking the high T limit of the above expression the leading $\frac{1}{x}$ term of the coth expansion is ignored and the second $\frac{1}{3}x$ term is considered (this pops out the correct answer $\chi_{curie}=\frac{n(g_J\mu_B)^2}{3}\frac{J(J+1)}{k_BT}$). I can't find or think or any sensible reason for this apart from when we take the limit of zero B the infinity is just a constant which has no temperature dependence (which is what we're interested in) so we happily ignore it. The wikipedia method below almost makes sense aside from the last equality where I can't follow how they've simplified the sums (I can see that you could drop the first parts of the sums as they have no H dependence so won't matter when it comes to finding $\chi_{curie}$ but this still doesn't seem to work) $\bar{m}=\frac{\sum\limits_{M_{J}=-J}^{J}{M_{J}g_{J}\mu _{B}e^{{M_{J}g_{J}\mu _{B}H}/{k_{B}T}\;}}}{\sum\limits_{M_{J}=-J}^{J}{e^{{M_{J}g_{J}\mu _{B}H}/{k_{B}T}\;}}}\simeq g_{J}\mu _{B}\frac{\sum\limits_{M_{J}=-J}^{J}{M_{J}\left( 1+{M_{J}g_{J}\mu _{B}H}/{k_{B}T}\; \right)}}{\sum\limits_{M_{J}=-J}^{J}{\left( 1+{M_{J}g_{J}\mu _{B}H}/{k_{B}T}\; \right)}}=\frac{g_{J}^{2}\mu _{B}^{2}H}{k_{B}T}\frac{\sum\limits_{-J}^{J}{M_{J}^{2}}}{\sum\limits_{M_{J}=-J}^{J}{\left( 1 \right)}}$ (Copied from Wikipedia paramagnetism article)


title: How does an atomizer work?

text: Will someone please explain how a basic pump atomizer works? I have a feeling it has something to do with pressure and the Venturi effect, but I'd really like to know precisely how they work as completely as possible. If you know, please feel free to use this image as a reference in explaining. EDIT: Please note that I'd specifically like to know how atomizers of the type pictured in the link I provided, the kind with a spring-based finger pump, work. I'm not talking about e-cigarette atomizers or atomizers with the bulb design.


title: Does an empty refrigerator require more power to stay cold than a full one?

text: Given that everything else is equal (model of fridge, temperature settings, external temperature, altitude), over a given duration of having the door closed, does it require more electricity to cool an empty refrigerator AND maintain that temperature, than a full one?


In various formulae for black-body radiation where $c$ appears, there is an implicit index of refraction dependence, since $c=c_0/n$, where $c$ is the speed of light, $c_0$ is the speed of light in vacuum, and $n$ is the index of refraction into which the blac kbody is radiating. This comes up, for example, in Planck's law, the Stefan-Boltzmann law, and Wien's displacement law.$^1$ I find this observation surprising, because it implies that black bodies radiating into $n\neq 1$ materials emit a factor of $n^2$ more power than otherwise identical bodies emitting into vacuum. To me, it seems that this would violate the laws of thermodynamics. Consider the situation where two black bodies of equal area face one another. Suppose that the gap between the two black bodies is partly filled an index-$n$ material, with one black body in contact with the index-$n$ material, and the other surrounded by vacuum. Then, according to the argument of the preceding paragraph, one of the black bodies will radiate $n^2$ more power than the other. If the two black bodies are thermally isolated from the rest of the universe, then they will equilibrate to different temperatures. As I understand it, this violates the zeroth law of thermodynamics. There must be something wrong with the above argument. None of my books mention an $n$-dependence, so at first I thought that perhaps the $c$ in Planck's law actually indicated what I call $c_0$, the speed on light in vacuum. However, this does not seem to be the case; I've found at least one reference that explicitly mentions this $n$-dependence.: "For radiation into a _medium_ within which the speed of light is not close to $c_0$, [Planck's law] must be modified by including an index-of-refraction multiplying factor." How is the index of refraction dependence in Planck's law compatible with thermodynamics? * * * $^1$ The $n$ dependencies in the Stefan-Boltzmann law and Wien's displacement law follow from the one in Planck's law, whereas the two former can be derived from the latter.


title: does force affect light's path?

text: Say If I'm running to north at a very high speed. And as I'm running, I'm shooting a beam of light toward west, will the light go completely west, or it will have some degree toward north too?


title: Does a resistor absorb and dissipate energy or just regulate the charge flow?

text: I've this doubt regarding resistor: suppose I make a simple circuit with a power generator of 3 Volts and 1 Ampere and a resistor of $10 k\Omega$ I know from Ohm law that the current flow $i$ is: $$I=\frac{V}{R}=\frac{3 V }{10000 \Omega}=0.3mA$$ So if I place my multimeter in series after the resistor I can measure exactly that current , and if I place the probe in parallel I can measure $3V$ so in this case I think that the resistor regulate the charge flow to 0.3 mA but in fact is the whole circuit to dissipate this current after the resistor regulated it, because I can see it passing through the multimeter ( and indeed 0.7 Amp give by the generator are not dissipated). Shorting out the circuit with no resistance attached I can't measure an increase of temperature (I think because I'm not working with high power) but if a use a smaller resistor (e.g. $2 \Omega$) I can fell it getting hot so I infer that a smaller resistor dissipate more energy (in this case I've $1 Amp$ passing through it) but I think that this is no more a good charge regulator because it dissipate a lot of energy through Joule effect. So I don't know if exists materials that can be a good "charge regulator" (e.g. a good resistor) and material that can be good "energy dissipator" (e.g. good heater). I've tried to make my homemade analogous resistor cutting $3,5 cm$ of a kanthal wire with a resistance of $57 \Omega / m$ but I can't measure correctly if this dissipate better the energy. Can anyone tell me what really do a resistor?


title: Good book for Analytical Mechanics

text: What is a good book for Analytical Mechanics? To be more specific, I would prefer a book that:   * Is written "for mathematicians", i.e. with high mathematics precision (for example, with less emphasis on obscure definitions such as "virtual displacements").   * However, it must not assume graduate-level mathematics such as differential geometry. Does this kind of thing exist?


title: Calculating vertical velocity component of a particle with mass, given the hit point of parabolic motion

text: Consider the following situation: ![enter image description here](http://i.stack.imgur.com/ZhUhk.png) I have a particle with a given mass that at a given instant of time (let's say $t_{0}$) is placed at the system origin. The particle has a constant velocity component $V_{0x}$. I have to calculate the value of the vertical component ($V_{0y}$) to apply to that particle at time $t_{0}$, in order to provoke a parabolic motion that makes the particle hit the point $P$. The data I know are the following:   * $P$ coordinates   * $dx$   * $V_{0x}$   * $t$ (that can be computed from $dx$ and $V_{0x}$)   * $m$ (the mass of the particle) From the data above, is possible to calculate the value of $V_{0y}$? If yes then give some hints to solve it?


title: Creation and Annialation Operators and Kinetic Energy Matrix Elements

text: I'd like to write equations for $c_{ij}(t)$, With a hamiltonian of the form $$H=\sum_{kn}a^{\dagger}_k t_{kn}a_n + \frac{1}{2}\sum_{klmn}a^{\dagger}_k a^{\dagger}_l v_{klmn}a_m a_n$$ with $t_{kn}$ and $v_{klmn}$ as matrix elements of the kinetic energy and potential in the single particle basis. Now I'm operating on a two particle state $$|\psi (t)\rangle =\sum_{ij}a^{\dagger}_i a^{\dagger}_j |0\rangle c_{ij}(t)$$ Now I got the potential part to work, as well as the time derivative part. I'm actually having trouble with the kinetic energy part (hence the title). Here's what I have done. looking just at the first term acting $$\sum_{kn}\sum_{ij}a^{\dagger}_k t_{kn} a_n a^{\dagger}_i a^{\dagger}_j |0\rangle c_{ij}(t)$$ I use the commutation relations to fanangle the set of three operators after $t_{kn}$ into $\delta_{ni}a^{\dagger}_j \pm \delta_{nj}a^{\dagger}_i$ where the $\pm$ is for both fermions and bosons. Inserting this into the above I get $$\sum_{kn}\sum_{ij}t_{kn}a^{\dagger}_k (\delta_{ni}a^{\dagger}_j \pm \delta_{nj}a^{\dagger}_i)|0\rangle c_{ij}(t)$$ Now taking the sum over $n$ I get $$\sum_k \sum_{ij}(t_{ki}a^{\dagger}_k a^{\dagger}_j \pm t_{kj}a^{\dagger}_k a^{\dagger}_i)|0\rangle c_{ij}(t) $$ Now my trouble seems silly to me, but I can't figure out what is the right move here. If I swtich the $i$ and $j$ in the second term after the $\pm$ and $c_{ij}(t)$ is symmetric then it's possible zero, but I don't think that makes sense. My total equation as of now is $$\sum_k \sum_{ij}(t_{ki}a^{\dagger}_k a^{\dagger}_j \pm t_{kj}a^{\dagger}_k a^{\dagger}_i)|0\rangle c_{ij}(t)+\frac{1}{2}\sum_{kl}\sum_{ij}a^{\dagger}_k a^{\dagger}_l v_{klij}|0\rangle c_{ij}(t) \pm \frac{1}{2}\sum_{kl}\sum_{ij}a^{\dagger}_k a^{\dagger}_l v_{klji}|0\rangle c_{ij}(t)=i\hbar \sum_{ij}a^{\dagger}_i a^{\dagger}_j |0\rangle \dot{c}_{ij}(t)$$ I'd like to remove the arbitrary ket vectors in the whole expression to just obtain a simple expression for $c_{ij}(t)$ any help would be great, thanks.


title: Toroid with variable current and Ampere's Law

text: Say you have a current $I(t)$ (notice the **time dependence** ) flowing through a Toroid with $N$ total loops and all the usual approximations: $(b-a) \ll r,\; B=0$ outside. ![Figure](http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/tor.gif) You are asked to calculate the magnetic field $B$. Could you apply _Ampere's Law_ to obtain the familiar form of $B$ found for example here?: $$B~=~\frac{\mu N I}{2\Pi r}.$$


title: What is displacement? Position relative to a reference point or change of position

text: What is the "official" or most useful definition of displacement in the context of kinematics? There are two common ones:   1. Displacement is the length and direction of a line from a fixed reference point. (Basically position).   2. Displacement is the change in position. Textbooks using the first definition frequently define velocity as $v=\Delta s/\Delta t$ (where $s$ is displacement) but then for acceleration give equations such as $s=ut+1/2at^2$ (if they were consistent, they would have to use $\Delta s$). What throws me off is that are the better textbooks. A similar confusion comes through in Wikipedia: A displacement vector is the straight path between the initial and the final position. But velocity is defined as $v=\Delta d/\Delta t$. Background: I am writing on a learning tool for students but different textbooks require them to learn contradicting definitions and I would appreciate your help on which is the right definition to learn.


title: Conservation of angular momentum for a rigid body rotating about a fixed point

text: Picture a rigid body such as a sledge hammer. Imagine that the base of the handle is attached to a fixed point such that it can rotate but not translate. I give the hammer a good push to get it rotating laterally about the pivot point, with its angular velocity vector pointed straight up. (Note that it's NOT rotating about its center of mass.) Assume there's no friction, but gravity is present. Note also that it's not quite in the horizontal plane because of the force of gravity. The path of the body describes a shallow cone. Here's my question: It seems to me that the body would rotate forever with its angular velocity vector pointed straight up. So the rate of change of angular velocity is zero. But there is a net torque on the body about the pivot point because of the force of gravity. This net torque implies that there should be a rate of change of angular velocity. What am I missing?


title: Is it true that capacitors closer to a power source charges quicker and gets priority?

text: Let's say I hook two capacitor in a parallel circuit with a voltage source. Would the capacitor closer to the battery be charged up first? Because when the voltage excites and draws electrons from the plates, the electrons doesn't know where to go, so it goes through the first path it sees (i.e. the first capacitor) and it builds the plate of the first capacitor until it is done and then builds the next capacitor that follows? Or would it start to build the first one first and then "evenly" builds charges on both capacitors because some of the electrons are actually getting repelled from the first plate of the first capacitor?


It would still be almost impossible for me in 21th century to take this picture: ![enter image description here](http://i.stack.imgur.com/7D9UP.jpg) (image courtesy of wikipedia) How would you figure some of the methods (in order of importance) to take a picture of the supersonic bullet with the wave it produce in 1888?


title: Dropping condition

text: Imagine opening a water tap in order to have a smooth and cylindrical outflow and then slowly decrease the flow by adjusting the knob. At a certain moment, the side profile of the flow will become uneven, and even if you decrease the scale of the faucet, the water shall start to drip. It is possible to determine, based on the thermodynamic conditions of the system (pressure, temperature, and surface tension of water) the dropping condition?


title: Why don't metals disintergrate in light?

text: I've been learning about photoelectricity. An electron can gain the energy from a single photon, and if that energy is greater than the work function of the metal the electron can leave the metal. However I was under the impression that the electrons in the metal are responsible for holding the nuclei in the metal together? Surely if the metal is exposed to light, where the photons have more energy than the work function, for long enough (or very intense light), all/majority of the electrons will leave the metal and no longer be holding the nuclei together. Also will the work function increase with time, as there are less and less electrons, so the ratio of positive nuclei to negative electrons increases and the electrons are more attracted to the nuclei, so more energy is required to break that attraction? (addtionally, how come the photoelectric effect is not noticed in daily life, with metals becoming positively charged just by being in light?)


Why is there a hiss sound when water falls on a hot surface? I have searched a lot, asked my teachers but none of them seem to give me the logical answer to it.


title: Behavior of shock waves at relativistic speeds

text: Suppose I am in a spaceship traveling inertially at a velocity $v$ that is of the same order as $c$. As I pass by a metal bar that is oriented parallel to $v$, someone hits it with another metal bar, causing it to vibrate. The vibration waves travel down the bar with a velocity of $u$. Observing the bar from my spaceship, I see the waves travelling with velocity $u+v\over 1+uv$.   1. Suppose that the waves are longitudinal, so that $v$ and $u$ are parallel. The atoms in the bar are individually moving back and forth, with a maximum velocity $w$ which is quite different from $u$. $w$ and $u$ are related in a way that depends on the material properties of the bar; I think on its elasticity its density. By comparing $u$ and $w$ I can calculate these properties of the bar. If I observe the motion of the individual atoms, I will see them moving back and forth with a maximum velocity of $v+w\over 1+uv$ and by comparing this with the observed velocity of the travelling wave I will obtain a measurement of the stiffness and density of the bar. But this value will be different from the value that an observer would calculate at rest. What explains this discrepancy? Is it due to relativistic dilation of the bar's mass and volume, and hence its density? Is there some other effect?   2. Now consider transverse waves. Again $v$ and $u$ are parallel. But this time the individual atoms are moving back and forth _perpendicular_ to $u$ so the observed dilation of their velocity $w$ is different than it was for longitudinal motion. If I do the same calculations as in (1) I should get different results for the physical properties of the bar: I see the transverse and longitudinal waves moving at the same speeds in the bar, but when I look closely at the motion of atoms, and try to calculate material properties of the bar I get two different sets of results, because the atomic motion causing the longitudinal wave is relativistically dilated to a different degree than is the atomic motion causing the transverse wave. What is going on here? What does it really look like? Presumably there is no discrepancy and I see a consistent picture regardless of $v$. How do all these apparently conflicting measurements iron out in special relativity?


title: Angular momentum operator and expectation values

text: I was reading some notes and it says that $\langle L_z^2\rangle=\langle L^2\rangle$ IFF the system is radially symmetric. I can see that in order that the LHS of the statement implies that $\langle L_x^2\rangle=0=\langle L_y^2\rangle$. But I am not sure how to rigorously prove to myself that in order to make those 2 vanish we must have an isotropic system. Could someone please kindly explain this? Many thanks.


title: How to interpret the continuity conditions in the PDEs (for example, Maxwell equations) originated in physics?

text: I am currently working on _PDEs_ in physics, mostly Maxwell equations. I am a mathematics graduate student, and this question has been haunting me for years. In PDE theory, or more specifically the _Sobolev space_ theory, the solution to the _Galerkin-type_ weak formulation of a PDE normally satisfies some continuity conditions across any interface in the domain of interest. From a mathematical point of view, the continuity conditions guarantees that the weak derivative of the function is well-defined. That is, whenever we do integration by parts in each subdomain and then sum them up, the results should be the same with doing the integration by parts on the whole domain. * * * For example, the Maxwell equations like the following I was working on: $\newcommand{\vect}[1]{\boldsymbol{#1}}$ $\newcommand{\vH}{\vect{H}}$ $\newcommand{\vE}{\vect{E}}$ $\newcommand{\vB}{\vect{B}}$ $\newcommand{\vD}{\vect{D}}$ $\newcommand{\vJ}{\vect{J}}$ $\newcommand{\vn}{\vect{n}}$ $$ \left\\{ \begin{aligned} \nabla \times \vE &=- \frac{\partial \vB}{\partial t} \quad &\text{ in } \Omega\times (0,T) \\\ \nabla\times \vH &= \frac{\partial \vD}{\partial t} + \vJ \quad &\text{ in } \Omega\times (0,T) \\\ \nabla \cdot \vD &= q \quad &\text{ in } \Omega\times (0,T) \\\ \nabla \cdot \vB &= 0 \quad &\text{ in } \Omega\times (0,T) \end{aligned} \right. $$ If we have two different mediums, being labeled as $a$ and $b$, as in the following picture (shamelessly ripped off from the book Electromagnetic Theory and Computation: A Topological Approach): ![Continuity condition](http://i.stack.imgur.com/NGDAV.png) the continuity conditions of the electric and magnetic fields/fluxes are given as: $$ \begin{aligned} \vn \times (\vE^a - \vE^b) &= 0 \\\ \vn \cdot (\vB^a - \vB^b) &= 0 \\\ \vn \times(\vH^a - \vH^b) &= \vJ_S \\\ \vn \cdot (\vD^a - \vD^b) &= q_S \end{aligned} $$ where the superscripts denote the limiting value of the vector fields on the interface being approached from each side, and $\vJ_S$ and $q_S$ are the surface current and surface charge respectively. Here $\vE$ and $\vB$ are continuous in the tangential and normal direction on the surface respectively. And these conditions play a pretty important role in the numerical simulation for Maxwell equations, for example, the use of Nédélec elements in computing $\mathbf{curl}$-$\mathbf{curl}$ type equation derived from time-harmonic Maxwell equations. (The introduction ends here.) * * *   * How do we interpret the physical meaning of these tangential/normal continuity conditions in real life (analogous to the interpretation of Stokes theorem as the conservation of a certain quantity)? Are the real electric fields continuous in the tangential direction of a surface? Or are these continuity conditions governed by certain physical laws?   * From my understanding, most PDEs from physics are derived from conservation like Ampère's law and many others, and in the integral form of Maxwell equations no differentiabilities are assumed, hence no continuity conditions are enforced. Then are these continuity conditions artificial just because we would like to get some PDEs?


title: How does a star wobble due to orbiting bodies

text: What equations determine how a star wobbles in response to an orbiting planet, and can it be used to determine the mass of distant objects based on the wobble? If there are other more reliable methods of determining mass than the one I am asking about here, I would appreciate a few links explaining these methods, or an explanation of those methods and their benefits/limitations.


title: Why the electric force does no work on the charge when perpendicular to the field?

text: I was reading my physics textbook and came across this sentence: > _When a charge moves in an electric field, unless its displacement is always > perpendicular to the field, the electric force does work on the charge._ So it is saying that if the displacement is perpendicular to the field, the electric force does no work on the charge.   1. Why is it so?    2. By perpendicular to the field does it mean perpendicular to certain field line?    3. Is it implying that if the displacement is perpendicular to certain field line, some other force does work on it (but not the electric force)?    4. But how to be "perpendicular to certain field line" when field lines are normally curved?    5. Let's say it means literally the field but not field lines, then how to be "perpendicular to the field" when the field is not even a straight line but a 3 dimensional region in which electric force is effective regardless of the presence or absence of a material medium?


title: Is "Egyptian Year" the same as a modern sidereal year?

text: Copernicus uses the term "Egyptian Year" throughout his discussions of the movements of the Earth, and of his and other models of the movements of the planets; but is unclear from his text, or from the general definitions I've found, what this corresponds to in modern astronomical terms. What, precisely, is an "Egyptian Year"? Is it identical with a modern sidereal year; if not, what are the correct conversions between the two?


title: Extending the idea of superdense coding

text: I was reading through the superdense coding protocol, that lets A convey two classical bits to B by sending one qubit (assuming B sends A a qubit beforehand). So B creates a 2-qubit state and sends the first qubit to A. A performs a transformation on this qubit and sends it back. Based on that, B can distinguish whether the two bits of A were 00, 01, 10 or 11. The question is, why can this idea not be extended to convey more than 2 bits? Can A convey n bits to B this way? More specifically, can B create an n-qubit state and send the first qubit A? A can then apply a unitary transformation on this qubit and send it back to B, who can distinguish between the 2^n possibilities and figure out which n bits A had.


title: Satellite Orbital Period

text: I know I can calculate the period of a satellite orbit by Kepler's third law, but somehow it does not work out. The sattelite is 20200km from surface of the earth.   * $r=$orbits radius=earths radius+satellites distance from surface of earth=20,200,000+6,378,000 = 26,578,000 m   * $G=6.67\cdot10^{-11}$   * $M = $mass of earth $= 5.9722\cdot10^{24}$ now $T=(4\pi^2r^3/GM)^{1/2} = 43108,699\ \mathrm{s} \Rightarrow T=11.975\ \mathrm{hours}$ BUT that isn't correct, as all the calculators say it is 16,53 I have no idea what I am doing wrong. I even followed this example and I got everything right using the numbers in the example, but as soon as I put in my 26,578,000 m I got a different solution. Even though I did not change anything else. What am I missing?


title: Calculating torque in a structure

text: I posted this on math stack exchange but realize it is more a physics question. I have a structure which is set up as shown in the image. A weight hangs from point A with mass $m$. Joint B is free to rotate. Joint C connects the two parts ABC and CD. It is intended to be a fixed joint so that the two parts do not move relative to each other. The end D is free to slide along the ground plane. The problem is to calculate the torque that is trying to rotate the two parts at joint C. I need to know if the joint will be strong enough or if it will fail when too much mass $m$ is applied. In actual fact the joint C is actually a motor and I need to know if its stall torque is enough to ensure it can hold the structure stable given a designated mass $m$. Missing from the diagram is the angle $\theta$ which is the angle between the vertical and line AB. I know that the mass produces a torque around B of $dmg \sin \theta$. I can't quite work out the torque which is trying to open up the angle BCD. ![Jointed structure](http://i.stack.imgur.com/n72fn.jpg)


title: Calculation of 12000 Lunar Orbits/Earth Day

text: I am really interested in the calculation of the following speed value in meter-per-second unit: Speed of something that is able to travel in one earth day the distance that it would take for the moon to orbit the earth 12000 times. Some people have calculated this using Einstein' theory but I am not mastering this so I resort to you to see if some scientist is able to calculate this.