Behavior of multiple flat coils in a cylinder

I am trying to wrap my head around how this would work. The setup is quite simple - there are multiple flat coils sealed in insulated disks, and an active coil with alternating current underneath. All is placed in a cylinder. The question is, how will the disks behave - all should induce the same magnetic field and thus repel each other. Will this force be stable enough, when the field collapses on each pulse? Thanks!


Particle Collision with Static System

I have a system of particles with equal distance with each other and another at random positions which is moving with time. What I want to know is :   1. The method by which I can reduce the number of particles from the first system, as I know the maximum motion of any particle is X ( **Meaning: Maximum displacement from starting to end of simulation is X)**.   2. How to efficiently calculate the collision between them, I have heard about quadtree and octree but (as per I understood till now) they are for collision of particle from each other. In my problem,second system of particles doesn't collide with each other. Note: Sorry, if it is a very basic question, I am (very) new to this field. **Update:** ![enter image description here](http://i.stack.imgur.com/ZTixa.png) ## **The combined System** ![enter image description here](http://i.stack.imgur.com/uEgwX.png) ## **Movable parts (Same color means same radius and mass)** ![enter image description here](http://i.stack.imgur.com/i3whf.png) ## **Unmovable Grid (Colors means nothing and yes, it's a cube of spheres)**


Relativistic addition of velocities of spaceships

If Spaceship 1 is traveling at speed $.5c$ relative to Earth, and Spaceship 2 is traveling at speed $.3c$ relative to Earth in the same direction, what does Spaceship 2 see Spaceship 1's speed as? I don't think it is quite as simple as $.5c-.3c = .2c$.


Was the Universe's entropy equal to zero at the Big Bang? Is zero-entropy state unique?

It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state. Does this claim specifically mean that the entropy of the initial universe was zero? Is zero-entropy state unique for given physical laws? Is it possible that entropy was growing always so that only difference in entropy has physical meaning rather than absolute value? Was there ever negative entropy state?


Find total energy and momentum of an moving electron in a rest frame

I have an electron moving with speed $u'$ in a frame $S'$ moving with speed $v'$ relative to a rest frame $S$. How do I find the total energy and momentum of the electron in the rest frame $S$? I thought the equations were: $E_{total} = \gamma \times mc^2$   $p = \gamma \times mv$ But, that doesn't look right... Could someone point out to me what is wrong here?


Are the only observables in string theory the S-matrix?

Is the S-matrix the only observable in string theory? What about time varying spacetime backgrounds, or thermal states then?


What is pseudo tensor?

What is the pseudo tensor in relativity? How do we transform tensor and pseudo tensor under parity?


Why does nuclear fuel not form a critical mass in the course of a meltdown?

A BWR reactor core may contain up to 146 tons of uranium. Why does it not form a critical mass when molten? Are there any estimates of the critical mass of the resulting zirconium alloy, steel, concrete and uranium oxide mixture?


Why quantum states are classified using only conserved quantities?

While studying quantum mechanics from standard textbooks I always felt some conceptual gap that was never mentioned or explained. In what follow I tried to formulate my question, please be patient with me. For a quantum particle in an infinite potential well the stationary states are labelled by the quantum number $n$ which labels the eigenenergies. An eigenenergy, that corresponds to a stationary state, does not change with time, hence is a conserved quantity. For a spinless electron in Coulomb potential, to model the hydrogen atom, again we have the same story, the stationary states are labeled by the quantum numbers $n$, $l$, $m$ which corresponds to conserved quantities. My question is rather general since I am trying to understand conceptually why only conserved quantities are used to label the quantum states. I mean how would someone think in advance that he has to look for conserved quantities, and then use such conserved quantities to label the states ?


Scanning electron microscope imaging

In a scanning electron microscopy, secondary electrons are defined as the electrons which obey inelastic scattering whereas backscattering electron follow elastic scattering. Now my question > Can backscatter electrons produce same level of solution as secondary > electrons?


Negligible Mass String

I've recently been working through a lot of physics problems and a lot of them say to assume that the mass of the string used in a problem involving a pulley, for example, is negligible. Why is this important? What would happen if the mass of the string wasn't negligible?


Is it possible to work on physics independently outside academia?

The traditional physics career is an academic job at some university, with the eventual goal of becoming a tenured professor. Is it possible for a mostly self-educated outsider working outside academia to come up with significant results in physics? Let's take significant to mean accepted in a high ranking peer review journal with a high citation count. Let's just say due to external life circumstances, the academic path is unfeasible. Are there any examples of notable physics results coming from outsiders? e.g. a third class patent clerk coming up with light quanta, Brownian motion and relativity.


Mass points of a Mass-spring model

Let's say I have a mass spring model like the one in the picture below: ![enter image description here](http://i.stack.imgur.com/JXnUn.png) So, there are 3 parts of the spring joined together in an _equilateral_ triangular manner. Each of the joints has a mass of $m$. The resting length of each of the springs is $l$. The top joint point of the spring is fixed to the ceiling. Now, if I were to pull both the lower points of the spring model such that each of the springs extend proportionally by $\Delta l$ change of length, and release. Now, I want to find an equation for Point A (indicated in the picture above) under gravity and sprint forces when springing back to position. The assumption is all the angles remain at $60$ degrees in every iteration when it springs back. What I did is: Let $k$ be the elasticity of the spring. Then, for the X-axis component of the equation, $k \cdot \Delta l \cdot cos(60) + k \cdot \Delta l = m\cdot a_x$ The acceleration of the spring going back to original x position would then be dividing both sides by the mass $m$. For the Y-axis component of the equation with consideration of gravity as $g$, $k \cdot \Delta l \cdot sin(60) + k \cdot \Delta l - mg = m\cdot a_y$ Similar to the X-axis, I thought I would consider the total of the extended length plus the projection from the x-axis onto the y-axis, and then minus the gravity resistance. However, it turns out that I am wrong for the Y-axis component. The given answer is: X: $k \cdot \Delta l \cdot cos(60) + k \cdot \Delta l = m\cdot a_x$ Y: $mg - k \cdot \Delta l \cdot sin(60) = m\cdot a_y$ I don't understand why is it so for the Y-axis, especially when the the gravity turns out to minus the projection and the extended $\Delta l$ is not added as part of the force.


BEC for holography?

I am spending some time reading about Bose-Einstein condensation. I want to know if it is possible to use atom lasers to realize the kind of holography traditionally associated with nano-fabrication. Many papers say that the motivation for BEC is the aforementioned holography, but I can't find if they were able to actually realize it. I am very much a novice at searching through academic literature. The closest I have found is the work of some Japanese scientists in the 90s who were able to make 2D hologram, without a laser style beam. * * * Does anybody know if it was done, or possible can comment on some of the challenges.


Correlation in electron gas

In the textbooks that I read (namely Ashcroft/Mermin , Marder, etc.) it seems that a distinction is made between the correlations in electron gas and a Couloumb interaction between the electrons. What is exactly meant by the concept of correlations? How is that connected to the interactions in electron gas, and how does the screening enters the picture?


Color of sky scattering by sky dust

> Why does we see sky like blue in maximum time? We know violet has less wavelength, so we should see sky like violet. My assumption is that, violet is not primary color and not sufficient in the spectrum so we see blue because after violet, blue has the shortest wavelength? **Edit: Because our eyes have sensibility for three primary colors so we may see primary color most but, If a people is blue color blind then what sky color will he see?**


Why is the sky blue?

> **Possible Duplicate:**   >  Why does the sky change color? Basically what the title says. What mechanisms are significant and how do they contribute to make the sky blue. Also when the sky is not blue, like when the sun sets, how does it happen?


Why does the sky change color?

Why the sky is blue during the day, red during sunrise/set and black during the night?


Would something like the uncertainty principle arise even if the universe was built on something like Newtonian mechanics?

I am thinking of a (greatly simplified) computer simulation of a universe that followed something like Newtonian rules. Inside the simulation are A.I.s that are made from those same rules, and can only use those rules interact the world around them. Would there be some fundamental limits on what those A.I.s could work out about their universe, like their own version of an uncertainty principle? Sorry for phrasing this question in such a convoluted way. If anyone recognises what I am asking, and can point me in the right direction that would be appreciated.


Chiral anomaly in odd spacetime dimensions

In odd number of space-time dimensions, the Fermions are not reducible ( _i.e._ do not have left-chiral and right-chiral counterparts). Does this mean that there is no such thing as 'chiral' anomalies in odd number of space-time dimensions, when these fermions are coupled to gauge fields?


Is the wind's force on a stationary object proportional to $v^2$?

I am on a boat docked at Cape Charles, VA, about 30 or 40 miles from the center of Hurricane Irene. This understandably got me thinking about the force of wind on the boat. Since air friction is proportional to the speed squared (except for some friction types I'm sure someone will be kind enough to remind me of), is the wind's force on the boat also proportional to the wind's speed squared? In other words, will a 70 knot wind produce almost twice the force on the stationary boat as a 50 knot wind, all other factors being equal?


Does rate of acceleration affect the amount of energy used to accelerate?

Assume you start with a car at rest. Then you accelerate the car to 100 kilometers per hour. In terms of the energy needed, does it matter how fast you accelerated the car? In other words, do you need to provide the same amount of energy to accelerate a car from 0 to 100 kilometers per hour whether you do it in 4 seconds or 20 seconds?


proof of gauge invariance for quantum 1D ring

This is a question on gauge invariance in quantum mechanics. I do some simple math on a 1D wave-function with periodic boundary conditions, and get that gauge invariance is violated. What am I doing wrong? Consider one coordinate dimension configured as a ring. The gauge dependent momentum operator can be written: $p_{op}=-i \frac{\partial}{\partial x} - k$ Units have been chosen so that $\hbar = 1$, $k$ is an arbitrary real constant different for each gauge and $x$ represents the coordinate. The gauge dependent eigenfunction can be written $\psi(x)= Ae^{i(n+k)x}$ where A is a constant determined by normalization. As is well known in quantum mechanics, an operator applied to one of its eigenfunctions should yield a real constant eigenvalue multiplying the same eigenfunction: Thus $[-i \frac{\partial}{\partial x} - k] Ae^{i(n+k)x}= nAe^{i(n+k)x}$ so that the real number n is the eigenvalue, which must be determined by the boundary conditions. The boundary condition for this periodic system must be that the wave function should join onto itself smoothly everywhere. Thus, if the coordinate is chosen such that x extends from –$\pi$ around the ring to $\pi$ then the eigenfunction in equation 3 must have (n + k) = m, where m is an integer. Under these conditions, the eigenvalue n in equation 3 will be n = m – k. This eigenvalue depends explicitly on k, and so is not gauge invariant. I'm assuming this simple situation should be gauge invariant, but I don't see where I goofed. I'd appreciate any help.


Why is exhaling more forceful than inhaling?

By blowing at pencil, a piece of paper, or another object up to fifty centimeters away, I can cause it to move away from me significantly. But I can't move an object toward myself by inhaling sharply from that distance, even if it is extremely light. Why is that?


What is the historical origin of the term action

In Physics ordinary terms often acquire a strange meaning, action is one of them. Most people I talk to about the term action just respond with "its dimension is energy*time". But what is its historial origin? http://en.wikipedia.org/wiki/Action_(physics)#History doesn't really give much insight, as it lacks citations and depth. So, how did "action" become to mean what it means now? Cheers


Schroedinger field operators and their commutation relations

I've got several questions regarding the so called second quantization of the Schroedinger equation. My professor introduced the field operators for the Schroedinger field by simply stating them as follows: $$ \hat\psi (\vec{r},\xi)=\sum\limits _i \psi_i(\vec{r},\xi) \hat a_i\\\ \hat\psi^\dagger (\vec{r},\xi)=\sum\limits _i \psi_i^\star (\vec{r},\xi)\hat a^\dagger_i $$ Where $\psi_i(\vec{r},\xi)$ are the time independent one particle wave functions and $\hat a_i,\, \hat a^\dagger_i$ the corresponding creation and annihilation operators. Is there a way to explain, why one does this? If I understood correctly what I've been taught so far, in QFT one must find some way to quantize the fields obeying the field equation in question. I do, however, not quite understand why in this particular case it is done like this. Shouldn't the $\psi_i(\vec{r},\xi)$ be the time dependent one particle wave functions? Because I thought the field operators for a system in a box look like this: $$ \hat\psi (\vec{r},\xi)\sim\int\text{d}^3k\ \exp(i\omega_k t-i\vec k\vec x) \hat a_k $$ My professor then proceeded to prove the (anti)commutation relations between the field operators, postulating the corresponding relations between the fermionic or bosonic creation and annihilation operators: $$ \left[\hat\psi (\vec{r},\xi);\hat\psi^\dagger (\vec{r}',\xi')\right]_\pm= \left[\sum\limits_i\psi_i (\vec{r},\xi)\hat a_i;\sum\limits_j\psi^\star_j (\vec{r}',\xi')\hat a^\dagger_j\right]_\pm =\sum\limits_i\psi_i (\vec{r},\xi)\psi^\star_i (\vec{r}',\xi')\\\ =\delta(\vec{r}-\vec{r}')\delta _{\xi,\xi'} $$ Here I do not understand the last step. Is that conclusion possible? And shouldn't or couldn't one postulate the commutation relations between the field operators and arrive at the relations for the creation and annihilation operators?


How to calculate the equation of projectile motion for curved ramps?

Consider the following cases (these are sections): ![straight line ramp](http://i.stack.imgur.com/cnea1.png) ![curved ramp](http://i.stack.imgur.com/HfNpp.png) I can find the equation of motion for Case a however I don't know how to deal with Case d. Normally I would need the angle α otherwise I can't manage to find the function for x and y with respect to time. There is also friction involved, and v0 is known. How do I find equation of motion for Case d?


What makes charges flowing in a circuit with a higher potential difference perform more work?

I understand that a 1.5 V cell will not deliver as much energy per coulomb as a 150 V power supply will. What I do not understand is that why it is so. I am digressing now. If we place two point charges at a distance r, then to increase the force between them, we need to increase their charges. This makes sense. However, if we need to increase the Energy carried by 1 Coulomb of charge in a circuit, we need to increase the potential difference. Here, the number of electrons remain the same but still, somehow, they are able to do more work. The definition of electric potential is "electric potential at a point is the amount of electric potential energy that a unitary point charge would have when located at that point" But why does electric potential energy act upon it at all if there is no charge to attract or repel it? These seem to be different questions, but they are all linked to a fact that I cannot understand "The same amount of charge performs more work when a higher potential difference is applied"


Is 'now' smeared over time?

Conventional physics as is usually presented in textbooks deals with the evolution of states in phase space parameterized by sharp instances in time, a real parameter. However, quantum fluctuations seem to suggest we have to smear a little over time to average over vacuum fluctuations and the like. What implications does this have over the meaning of 'now' and the nature of time?


Strange electrical circuit

This is a question I would like to have an explanation with: It's in this PDF, question 9. ![circuit](http://i.stack.imgur.com/euGXK.png) > In that circuit, if switch 1 is closed, bulb A burns normally. If 2 is > closed as well, do other lamps burn normally as well? The answer is D: yes, both B and C, but why? Could somebody explain the steps in order to think? This is not homework (even though in principal it is) but I did this voluntarily on my own interest in how more advanced electrical circuits work.


Will there be any force of attraction or repulsion between an electrified body and a non-electrified body?

Up to my knowledge an electrified (charged) body can attract a non-electrified (neutral) body. I thought this because, when we bring a charged (suppose negatively charged) body near a neutral one. Electrified body can attract a non-electrified body by the opposite charge induced on neutral body due to electrostatic induction, then the answer to the above question would be likely to say that electrified body exerts attractive force on non-electrified body.   But going through the Wikipedia's encyclopedia of electric charge, I found the following line: > _No force, either of attraction or of repulsion, can be observed between an > electrified body and a body not electrified.[3]_ My view on the concept is contradictory to the statement. **EDIT:** I have seen a article supporting my view.You can see at the bottom of this link page about interaction between charged(electrified) and neutral(non-electrified)body.


Gossip in Physics

Given, $M_4 = \Sigma \times C$, How do you get an effective theory by studying maps $\Sigma \rightarrow M_4$ . Technically, the physics in one manifold is supposed to gossip about the overall affairs of people in the entire manifold at least up to a certain limit. To be direct I am trying to know how the algebra bundles come about as a twist in $\sigma$ models. I am sure my question is not well posed, as usual feel free to edit it.


Madelung constant list (for surfaces as well)

Searching for this on google proved to be quite tedious, but I reckon that someone working with crystals a lot might know this off the top of his head: Is there a good source that lists the Madelung constants for a variety of geometries? I'd be particularly interested in that for a NaCl-type 110 surface.


Affine connection notation

Can ${g}^{\mu\sigma}{\Gamma}^{\rho}_{\sigma\nu}$ be written as ${\Gamma}^{\mu\rho}_{\nu}$? If so how come this symbol never appears in any GR book?


Non-interchangeability of time-like intervals

I am reading Landau's Volume 2 of the course of theoretical physics. I have a doubt after reading the first few pages of it which I explain below. Landau first defines intervals and on pages 5 and 6 shows that two events having time like interval between them can never occur simultaneously in any reference system. Then he goes on to construct a 2D space-time graph (for visualization) with an event O occurring at (0,0,0,0). Then he considers any event which occurs in future in that frame and is time-like w.r.t. origin and says on page no. 7, > But two events which are separated by a time-like interval cannot occur > simultaneously in any reference system. Consequently, it is impossible to > find a reference frame in which any of the events in region aOc occurred > "before" the event O, i.e. at time t<0. The argument above just proves that because interval square should be positive, i.e. the events can't be simultaneous. But, if I replace the difference in time in the original frame with its negative in my proposed frame and let the space distance between them to be same in both frames, then I get an in my proposed frame an interval which is time like but in it the order of events is changed. Am I making some gross error or Landau has missed some argument?


Do we need a quantum deformation of the diffeomorphism group in string theory?

Let me justify my question before I go on. In string theory, gravitons are strings extended over space. Longitudinal gravitons are pure gauge modes of the diffeomorphism group. However, in string theory, longitudinal gravitons are also extended objects. A condensate of longitudinal gravitons is equivalent to a diffeomorphism, but this diffeomorphism has to be smeared out over the string scale. Is the diffeomorphism group in string theory a quantum deformation smeared out over space? In the weak field small string coupling limit, the string theory algebra and the classical diffeomorphism algebra ought to coincide, but in this limit, all such algebras over a Poincare invariant background are isomorphic. Away from this limit, what is the form of this quantum deformation?


Wheatstone Bridge

Why is using a Wheatstone bridge such an accurate way of calculating an unknown resistance? What are the benefits of using it over Ohm's law? It seems that it has something to do with the wires heating up during ohm's law calculations, and the fact that an ammeter/voltmeter still draw some current and provide some resistance which makes results unreliable.


Why is copper diamagnetic?

Cu has an unpaired electron in 4s, but it is diamagnetic. I thought that it has to be paramagnetic. What am I missing?


How does one estimate the electrical power of a power plant?

I have two related questions that I would like help on:   1. When a power plant creates power like the Hoover Dam, it can provide 2.07 GW of electrical power. My question is what does this mean? I assume from Faraday’s law that the induced voltage across the generator coil produces an current, and this combination (P = VI) is the output power. So in the case of the Hoover Dam, P = VI = 2.07 GW. I feel that this is naïve thinking but when I do a search to get more information, I am not able to find any. Can someone roughly sketch out how the electrical power of a power plant is computed?   2. If possible, what kind of voltages and currents are power plants producing before the Step Up transformers?


Frequency of nomad planets passing within 30 AU of the sun

A recent estimate by the Kavli Institute for Particle Astrophysics and Cosmology (a joint institute of Stanford and SLAC) is that there are circa 100000 times as many 'nomad planets' as stars I found "The Close Approach of Stars in the Solar Neighborhood, Matthews, R. A. J., Quarterly Journal of the Royal Astronomical Society, Vol. 35, NO. 1, P. 1, 1994" which estimated that the frequency of other stars passing within a given distance to be $$ F_{r}(r) = \sqrt{2} \pi r^{2}\rho_{s}V_{s} $$ where $$ V_{s} \approx 19.5 \text{ km}/\text{second} $$ and $$ \rho_{s} \approx 0.11 \text{ stars}/\text{parsec}^3 $$ resulting in $$ F_{r}(r) \approx 10^{-5} r[\text{pc}]^{2} \text{year}^{-1} $$ Assuming that those estimates are accurate and substituting $$ \rho_{s} \approx 11000 \text{ planets}/\text{parsec}^{3} $$ and $$ r[\text{pc}] \approx 0.000145 \text{ parsecs} $$ we get a frequency of $$ F_{r} \approx (10^{-5})(0.000145^{2})(10^{5})/\text{year} $$ or $$ F_{r} \approx 2 \times 10^{-8}/\text{year} $$ This gives us a net 'close encounter' of the solar system with a nomad planet roughly every 50 million years. Does this seem a reasonable estimate?


Spontaneous emission and induced radiation

In Einstein A., Zur Quantentheorie der Strahlung, Phys.ZS., 18, 121-137 (1917) spontaneous emission is considered to occur together with induced radiation so that one can write the following condition for equilibrium (which also includes induced absorption): $$ p_n e^{-\frac{\varepsilon_n} {kT}} B_n^m \rho = p_m e^{-\frac{\varepsilon_m} {kT}} \left( B_m^n \rho + A_m^n \right) $$ where $p_n$ and $p_m$ are statistical weights of the states $n$ and $m$, $\rho$ is radiation density of frequency $\nu$, $A_m^n$ is a constant characteristic of the spontaneous $m \rightarrow n$ transition (spontaneous emission), $B_m^n$ and $B_n^m$ are constants expressing the change of state under induced emission and absorption. To arrive at Planck's radiation density law it is considered that at high temperatures the above equation becomes $$p_n B_n^m = p_m B_m^n .$$ What is the justification, however, to substitute $B_n^m$ expressed through the latter equality (valid for extreme temperatures) into the initial equation above (valid for lower temperatures)?


Why absoluteness of time implies galilean transformations?

In Landau course, vol.1 Mechanics, one finds the statement: > ...the absoluteness of time necessarily implies that the ordinary law of > composition of velocities is applicable to all phenomena. I don't see this implication clearly.


How to get energy of collision if you know force of gravity of an object($m \rightarrow F=mg$)? You get energy of collision by kinetic energy $E_k= \frac{1}{2}mv^2$, but if you use just force of gravity($F=mg$), how you get then the energy of collision? I know that work(energy?) $W$ made by object is $W=F \Delta s$, where $F$ is force exerted to object and $\Delta s$ traveled distance, but this distance makes it hard to calculate any collision energy of a meteorite for example.


Under what conditions a person can lift a car alone?

I'm thinking about starting my work of physics with this question but do not know how to answer.


Why does the presence of a battery change whether a circuit is in parallel or series?

If I take a closed circuit with two capacitors and a voltage difference, the circuit is apparently in parallel, but if I introduce a battery, the circuit is in series. Why does the presence of the battery make a difference? Here's a diagram of what I mean: ![enter image description here](http://i.stack.imgur.com/CRwHQ.png) According to my book, the left circuit is in parallel, but the right circuit is in series. I don't see why—after all, for any voltage to run through the circuit on the left, it has to pass through C1 before C2 (or vice versa).


Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k \int\int\int_V \rho\:dV$$ As far as I can tell, the "outward pointing area normal" $F_\perp$ is the same as the current density or flux $J$ magnitude. I.e., $$F_\perp=J\cdot n=\frac{d}{dA}\left(\frac{dq}{dt}\right) \cdot n$$ $$\int\int_{A} J \cdot n \:dA\sim 4\pi k \int\int\int_V \rho\:dV$$ Now, if we assume the vector field is isotropic (flowing across a spherical surface), then $J \cdot n$ is constant across the surface, and so the LHS integral evaluates to the surface area of the sphere times the constant $J\cdot n$: $$\int\int_{A} J \cdot n \:dA=J \cdot n \int\int_{A} \:dA=J\cdot n 4\pi r^2$$ where $r$ is the radius of the sphere. And then we get: $$ J\cdot n 4 \pi r^2\sim 4\pi k \int\int\int_V \rho\:dV$$ $$ J \cdot n 4 \pi r^2\sim 4\pi k E$$ $$J \cdot n \sim \frac{kE}{r^2}$$ This already seems suspect since I believe by Coloumb's Law the RHS is proportional to the acceleration of a charged particle in the field. So this equation is tantamount to equating current density to acceleration. I do not have enough background in electromagnetism to know if such a statement makes sense or not. But then also consider that by the conservation of charge we know that (continuity equation): $$ \bigtriangledown J = -\dot{\rho} $$ Substituing in the result obtained from the Divergence Theorem ($J\cdot n\sim \frac{kE}{r^2}$) gives: $$ \bigtriangledown \frac{k E}{r^2} \cdot n = -\dot{\rho} $$ Working out $\bigtriangledown \frac{k E}{r^2} \cdot n$ gives a mess that doesn't seem related to $\dot{\rho}$. Please help show how it is true or where I have gone wrong in my derivation.


Reference for stochastic processes which helps moving from a basic level to a measure theory one

I'm looking for a reference (books, notes, lectures) which helps a physicist to understand the language of measure theory in the context of stochastic processes (in particular markov chains). I've studied markov chains and measure theory but now I'm looking for something which helps me filling the gap and making this two topics converge. I've already read: _Measure, Integral and Probability_ \- Marek Capinski, Peter E. Kopp Maybe something with direct comparison (which writes the same probability both at a basic level and in measure theory) would be great! Thanks in advance!


Torque in a heavy and light Body

Suppose we have two wheels attached to axis (each wheel has its own axis). One wheel is heavy compared to the other. The moment arm of force is same for the both wheels. A force F is applied on both the wheels. The applied force is also same for both wheels. The light wheel will rotate fast compared to the heavy wheel. Will the torque for both wheels be same? Torque is also defined as "The turning effect of a body." But the turning effect of both the bodies is different here so, will their torque be different?


What is Einstein regarding as the problem of physical relativity in his lecture of 1923?

The following is the extract from _Albert Einstein's lecture_ to the Nordic Assembly of Naturalists (July 11, 1923). > _If we consider that part of the theory of relativity which may nowadays in > a sense be regarded as bona fide scientific knowledge, we note two aspects > which have a major bearing on this theory. The whole development of the > theory turns on the question of whether there are physically preferred > states of motion in Nature (physical relativity problem). Also, concepts and > distinctions are only admissible to the extent that observable facts can be > assigned to them without ambiguity (stipulation that concepts and > distinctions should have meaning). This postulate, pertaining > toepistemology, proves to be of fundamental importance._ I am not able understand Einstein's question in the extract, i.e _are there physically preferred states of motion in Nature?_ As what I can think as layman, I didn't understand the meaning of _physically preferred states of motion_. Does Einstein mean physically preferred states of motion as wave motion, particle motion? Einstein uses the term _physical relativity problem_ , what is the problem of _physical relativity_? Why does Einstein regards epistemology principle mentioned in the extract as of fundamental importance? I am the beginner in this concept, if some where I have gone wrong in explaining pardon me.


Schottky Barrier - Why energy band levels at interface are assumed to remain the same that bulk

I have been chewing up some time ago the Schottky-Mott theory of Schottky Barrier height (which ignores the surface states). All the deduction seems to ground on fundamental thermodynamical principles (as the equality of Fermi levels- i.e. equality of chemical potential in equilibrium) but there is something which I can't clearly see and is one of the key points to calculate the height barrier: Why the energy bands on the semiconductor side just at the interface are assumed to be the same that the ones of the isolated semiconductor? It is clear that the band have to bend (because of the electric field) but I see no reason to why the bands values should "start" to bend from the original values (the values of the isolated semiconductor). Thanks.


Why path integral approach may suffer from operator ordering problem?

In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path. What did he want to say? I don't think there is any problem related to the ordering of operators. References:   1. Assa Auerbach, _Interacting Electrons and Quantum Magnetism,_ p.102, just below eq. (10.6).


US time zones and Daylight saving time, energy efficient?

As a foreigner, United States has a very complex time system for me. `Central Time Zone`, `North American Eastern Time Zone`, `Mountain Time Zone`, `Alaska Time Zone`, `Pacific Time Zone`, `Samoa Time Zone`, `Atlantic Time Zone`, `Hawaii–Aleutian Time Zone`. And also plus `DST` (`Daylight saving time`). I heard people saying this can save a lot of energy. I want to know if there is any **scientific report** to support this. Or it's just people they like this system. Thanks


What speed should have an alone planet to have a habitable zone due to relic radiation?

What speed should have an alone planet to have a habitable zone due to relic radiation, without any star involvement? How much time the planet will be able to remain in the habitable zone before the speed drops, given the planet has no engines? Are such speeds achievable using gravity assist of the galactic center or similar objects? What would be effect of non-CMB sources like particles and stellar radiation at such speed?


Nukes with cup-sized mushroom clouds

A few sequential questions:   * Is it possible for a nuclear explosion to be small enough to produce a 250-ml (one cup) mushroom cloud?   * If so, how much uranium would that take?   * How close to the explosion could one be (in normal clothing) not to suffer from burns or excessive radiation exposure?


Understanding the basics of electromagnetic induction

Suppose two rings are kept facing each other and that one ring have some current which increases constantly. Will the other ring be attracted or repelled? Does this also depend on _how they are kept_?


Is the Higgs mechanism needed for Quantum Field Theory?

The NY Times article on Firewalls today has the following paragraph: > _Quantum field theory is how the world works [quoting a physicist]. It had a > major triumph just a year ago, when the Higgs boson, a subatomic particle > responsible for the mass of other subatomic particles, was discovered after > a 40-year search, at the Large Hadron Collider at CERN._ Is it correct that   1. the Higgs (boson, mechanism, field, etc) is needed for QFT _per se_ , or    2. is it "just" needed for the particular _application_ of QFT known as the standard model, electroweak theory etc?  Couldn't QFT still be the correct framework for "how the world works" if the Higgs model turned out to be wrong?


Can you take components of tension in a string?

Imagine there is a string, not a massless one but a heavy one, which is attached to the ceiling where the angle between the ceiling and the tangent at the end of the string is $\theta$. (First visualize it, or draw it somewhere). Let at any point the tension in the string be T. Now obviously there are components of forces acting, as T$\sin\theta$ is balancing its weight. But if I nudge the string from that point with a very lightly, I actually do not experience a resistive force (I've tried it several times). But I know T$\cos\theta$ is acting towards me. So my question is, why do not I experience a resistive force? Also, when we derive the expression for centripetal force, we do not take components of Tension but of its weight, because it "sounds" meaningless. Is it logical to take components of T?


How does the expansion of the universe not violate causality?

It is often said that faster than light travel would violate causality. However, because the universe is expanding, there are actually distant stars that move away from us at a speed greater than the speed of light. Why is this allowed, even though it could violate causality?


Temperature Dependence of Fission

I've always heard fusion depends on incredible temperatures and pressures, but I'm curious what the temperature dependence of fission is. For instance, if I had uranium and heated it to a sufficiently hot temperature wouldn't it decay at a faster rate at some point? I'm not talking about 300 K, but instead say we had 5800 K or 11600 K or 17400 K. At some point I would expect the decay rate to increase, so does anybody have more information on this?


This question (What is the capacitance between the Earth and Moon?) on EESE makes me wonder: How can a vacuum have a breakdown voltage? If electrons can find the shortest path through a vacuum, how is that possible? With nothing to carry the charge, I can't understand how the charge can traverse a vacuum. The value for dielectric strength of a vacuum comes from Wikipedia


Voyager local time dilation (caused by gravity)

Voyager I, as an example, taking account gravity   and setting aside effects of speed as cause of time dilation. If it is very far away from earth and sun, so then there must be a difference in the spacetime curvature there in the ship compared with here in earth, It means a detectable difference between our local clocks and its onboard clocks. Imagine a signal transmision was designed to be at 1 byte for second at local Voyager clock Should we receive it at higher and higher rates ? ( because of solar system gravity decrease as it(Voyager) moves away and it will keep decreasing while it doesn't reach a middle point between another massive object) Or the middle Voyager-Earth light path would compensate the effect, making the high rates generation from low curvature zones being delayed enough for us to receive it at same rate that it was generated?


How to calculate distance travelled from velocity vector and angle?

I am trying to get the distance a projectile travels, so I can display it in my program. I'm sort of new to physics, but I've tried looking this up. I'm not getting the right results however, and me being new to physics, I'm not sure if I'm just using the wrong formula or what. This is the formula I have tried using: ![](http://upload.wikimedia.org/math/c/1/d/c1da5860501561519415962ddda5e85e.png) As far as I've read, a projectile launched at 15 degrees would travel the same distance as one launched at 75 degrees, however when I run the calculation I get two different distances for those two instances. Is this not the correct formula, or maybe I'm using it wrong? These are the values I get for 15 degrees and 75: 15: velocity vector = (5,-19) magnitude = 20 vCos = -15.2 vSin = 13 gravity = 9.8 output = 41 75: velocity vector = (19,-5) magnitude = 20 vCos = 18.4 vSin = -7.8 gravity = 9.8 output = 2 The projectile starts on the ground and gets launched at the specified angle over a flat surface. Not sure where I'm going wrong. All help is greatly appreciated.


If you had two "perfectly" flat surfaces of the same material?

Let's say you had 2 nano-engineered surfaces of diamond which were as 'flat' as possible (of course considering the radii of each carbon atom in the lattice)... would there be any friction between these 2 flat diamond surfaces when rubbed together? My thinking is that there would be very little to no friction due to the electron repulsion and there being no imperfections in the surfaces.


How to identify the objects in an astrophoto, and what portion of the sky it covers?

Given an astrophoto with a resolution between 0.5 and 5 arcseconds per pixel, which ways exist to identify the direction of view, field of view, and objects in the picture? I believe most amateur astrophotographers are in this resolution range, and I believe most of us would like to confirm the captured images. I have read about the http://astrometry.net project and I'm wondering if there are any similar services available.


Most accurate ways to find the average distance between stars in Milky way galaxy

I've already posted here on quora. But, I'm not totally sure if it's the most reasonable method. Would anyone care to elaborate on how to find the average distance between stars in a given galaxy (For instance, let's take Milky way), somewhat efficiently and accurately - or at least clarify that my method is sufficiently efficient and accurate?


Advantages of $e^-e^-$ or $e^+e^+$ collisions over $e^+e^-$ collisions?

Is there any (interesting) HEP process whose study would take advantage from $e^-e^-$ or $e^+e^+$ collisions with respect to $e^+e^-$ collisions?


Divergence theorem over entire space on non euclidean spaces

I'm a physics major so bear with me here on the math. This is related to a problem from the textbook General Relativity - Wald. In classical electromagnetism if we have a vector field say $V$ defined on all of $\mathbb{R}^{3}$ such that $V\rightarrow 0$ , dropping off as $O(1/r^{3})$, in the limit as $r\rightarrow \infty $ then when calculating $\int_{\mathbb{R}^{3}}\partial _{i}V^{i}d^{3}x$ one usually takes a closed ball $\bar{B_{r}}(x)\subset \mathbb{R}^{3}$ and, using the fact that $\bigcup _{r}\bar{B_{r}}(x) = \mathbb{R}^{3}$ gives us, with an appropriate limit theorem, that $\int_{\mathbb{R}^{3}}\partial _{i}V^{i}d^{3}x = lim_{r\rightarrow \infty }\int_{\bar{B_{r}}(x)}\partial _{i}V^{i}d^{3}x$ to which we can then apply the divergence theorem to state that $lim_{r\rightarrow \infty }\int_{\bar{B_{r}}(x)}\partial _{i}V^{i}d^{3}x = lim_{r\rightarrow \infty }\int_{\partial \bar{B_{r}}(x)}V^{i}n_{i}d^{2}x = 0$ where the zero comes from the fact that the integral will drop off as $O(1/r^{2})$ as $r\rightarrow \infty $ so the sequence of surface integrals will eventually converge to zero. This is all fine and dandy but my problem deals with a background flat space - time with metric perturbation $(M,\eta _{ab} + \gamma _{ab})$ where $\eta _{ab}$ is the minkowski metric and $|\gamma _{ab}| << 1$ as usual. We have a space - like hypersurface $\Sigma $ of this manifold, the Landau Lifshitz pseudo tensor $t_{ab}$, which is divergence free, and the total energy $E = \int_{\Sigma } t_{00}d^{3}x$. We must show that $E$ is time translation invariant. Using the facts that $\partial ^{a}t_{ab} = 0, \partial _{0}E = -\partial ^{0}E$ we proceed: $\partial _{0}E = -\partial ^{0}E = -\partial ^{0}\int_{\Sigma }t_{00}d^{3}x = -\int_{\Sigma }\partial ^{0}t_{00}d^{3}x = \int_{\Sigma }\partial ^{i}t_{i0}d^{3}x$. We are also given that $t_{\mu \nu }\rightarrow 0$ identically, dropping off as $O(1/r^{3})$, in the limit $r\rightarrow \infty $. This is, of course, very similar in situation to the electromagnetic case and one would ideally like to use the divergence theorem to get the desired result that $\partial _{0}E = 0$ however here we do not have a prescribed metric $d$ on $\Sigma$ to make sense of closed balls as far as I can tell and even if there is some natural choice of metric $d$ for $\Sigma$ how will we know if the closed balls with respect to $d$ will be orientable? Thanks for any and all help and sorry if this was a bit long winded; it is my first post here so I'm not sure how it is meant to work :[; I just wanted to be thorough in explaining my issue. Thanks again.


How does the windchill factor exist above 98.6 degrees?

As I understand it, the explanation of the windchill factor goes like this: > Your body is warmer than the air around it, therefore it loses a certain > amount of heat to the air. This warms up the air immediately around you > first. The heat will then gradually be transferred to the air further away > through convection, but there's so much more of the air than there is of you > that the air essentially acts as a perfect heat sink, and your body heat > isn't likely to raise the overall temperature of the air in even a > moderately-sized room by any measurable degree. > > However, you're still warming the air immediately around your body first. > When the air is moving, it blows away the air immediately around your body, > which is slightly warmer than the rest of the air, and replaces it with the > slightly cooler air that hasn't been warmed up yet. Since the speed of > convective heat transfer is based on the difference between the temperatures > of the bodies involved, this means that you lose heat faster, and feel > chilled more than you would at the same temperature if there was no wind. However, I have memories of days when the temperature was well over 100 degrees, and breezes were still a relief. By the explanation above, wind should have made the heat _even more oppressive_ because the convective heat transfer is flowing in the opposite direction, into my body rather than out of it. What's the principle here that makes this possible?


An Electric Potential Glued to a Cube-Shaped Insulator to Replicate a Point Charge: Charge Distribution

I have been going back over this problem with a friend for the better part of a day: A potential is glued to a cube-shaped insulator so that outside of the insulator the field is the same as a point particle. How can we calculate the surface charge distribution and the volume charge distribution?


relation between photon number and energy

Suppose there are two light beams. One is red while the other is violet. The energy of both is the same. Which one of these beams has a larger number of photons, or is the number of photons relevant?


Consequences of tensor form due to various symmetries

I'm reading a paper on 2D hydrodynamics, specifically on the drag of a rod in a 2D fluid. It is a low-Reynolds number regime, therefore linear hydrodynamics and the velocity of the rod can be expressed via: $$v_i^{rod} = \mu_{ij}F_j$$ then it says: By in-plane rotational symmetry combined with the $\hat{n} → -\hat{n}$ symmetry of the rod, the mobility tensor must take the form: $$\mu_{ij} =\mu_\parallel\hat{n}_i\hat{n}_j + \mu_\perp(\delta_{ij}-\hat{n_i}\hat{n_j})$$ Here, $\mu_\parallel$ and $\mu_\perp$ are the mobilities for motion parallel and perpendicular to the rod's long axis, respectively. I'm having a hard time connecting the dots with this logic, can anyone show me how this follows?


Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum physics, the set of all states is not a simplex. Does this have anything to do with the superposition principle? If we didn't have the superposition principle in quantum mechanics, would the set of states be a simplex, like in the classical case? Thanks for your help!


What determines the probability of a pair of photons interacting, and producing a positron and an electron?

The second answer to this question describes how this process might occur, and I'm curious for more details about it:   1. What is the probability distribution of the interaction producing electron-positron pairs (and what's the general process for calculating it)?   2. Is it possible to produce beams of positrons and/or electrons, through this process?  I would love some references that describe this kind of interaction in depth.


Seesaws and Dark Energy

Lawrence Krauss and James Dent recently proposed a mechanism for producing the observed scale of dark energy. This proposal was inspired by the see-saw mechanism that produces light yet non-zero neutrino masses. I can't help but notice there are many reasons to doubt the see-saw mechanism package since it suffers from the the flavor, CP, and gravitino problems and several alternatives have been proposed. Would it be feasible to come up with a mechanism based on the alternatives to the seesaw and hence extend Krauss' and Dent's proposal?


Has QFT successfully mediated between QM and Special Relativity?

I understand that QFT is the theoretical framework for combining QM and Special Relativity, but as I understand it, though even without proof or experimental confirmations; has QFT managed to "behind all the rigor" design a mathematical construct that fully explains and logically computes there conflicts? Or does it continue to struggle for a formulary solution?


Temperature of the CMB when the Earth formed and the faint young Sun paradox

The cosmic microwave background (CMB) has a modern temperature of about 2.7 K. At the time of the origin of the CMB, about 13.6 billion years ago, it had a temperature of about 3000 K. There is a well-known problem that the Sun should have been too faint at the time the Earth formed, about 4.6 billion years ago, to allow the Earth to avoid becoming a permanent Snowball Earth. This problem is called the faint young Sun paradox. I was thinking about that, and it occurred to me that those two things may not be completely unrelated. What was the temperature of the CMB at the time the Earth formed, and what effect would that temperature have on the equilibrium temperature of the Earth? It seems to me that there should be two effects in play.   1. The equations describing the equilibrium temperature of the Sun then needs to be adjusted for the fact that rather than being a blackbody radiating to a near zero background, it would be radiating to a background with a significant temperature of its own. I would think that would raise the required temperature for the Sun to achieve radiative equilibrium there-by making the Sun brighter.   2. The equilibrium temperature of the Earth should also be boosted by the increased temperature of the CMB for similar reasons of having a less efficient heat 'sink'. Could those two effects together have shifted the equilibrium temperature of the Earth enough to solve the faint young Sun paradox? Edit: Having done some more googling on it, the CMB would only have been about a degree or so warmer than it is now because 4.6 billion years only corresponds to a Z of about 0.4. This isn't anywhere near enough to solve the faint young Sun paradox. I'm going to leave this question in place just so if someone else has the same idea this will explain why it can't solve the paradox.


Why there is a 1/2 in kinetic energy formula?

> **Possible Duplicate:**   >  Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$? Hèllo, I have a question about kinetic energy formula. As you know, in kinetic energy formula, we have: $\large\frac{1}{2}mv^2$ Okay. And we know, Joule (energy unit), is: $\large J= kg~(\frac{m}{s})^2$ (Guys, please light me up if I'm wrong.) Here's my question: Why do we have a $\frac{1}{2}$ in our formula? Why do we divide our $mv^2$? Please answer in simple word.


Other ways of checking whether particular system result in non-locality

In quantum mechanics, when hamiltonian $H$ is constrained ($H = \sqrt{m^2 - \hbar^2 \nabla^2} $) so that it would produce simple "relativistic" model of quantum mechanics, we can show that it results in non-locality (Reference: $\nabla$ and non-locality in simple relativistic model of quantum mechanics ) The question is would Taylor-expanding every constraint equation on some quantity/operator, such as Hamiltonian, show that it will result in non- locality? Or in some case, should we check other expansions/methods?


Is my understanding of the mechanics of skidding correct?

I'm trying to understand the mechanics which determine if a car making a turn will skid. Are the following correct or incorrect:   1. A vehicle making a turn will skid unless the centripetal force is adequate to produce the centripetal acceleration. In a simple turn, where $r$ is constant, the force needed is $mr\omega^2$.   2. If the road is flat, this force can only come from friction created by turning the wheel. The maximum force is $\text{weight}\times\mu_\text{static}$. All of this force will be directed centripetally, and will therefore be available to prevent the skid.   3. If the road is banked by $\phi$, the friction force will be lessened by $\cos\phi$, but there will also be a centripetal component of the normal force, equal to $\sin\phi\cos\phi$. Are these all correct? I believe they are but my results using them don't seem to work. **UPDATE:** I believe my mistake was in the direction friction will be in. Determining the direction of friction in this case is tricky, because it has to both counteract the sliding due to normal force of the banked road, and also accelerate in the centripetal direction. It requires 3 dimensions. How do I determine the direction of friction, with respect to $r$ and $\theta$ vectors?


Why must an integrating sphere be a sphere? Why can't it be an integrating cube? What is the difference? Could I use a cube to measure total illuminance like an integrating sphere does? ![enter image description here](http://i.stack.imgur.com/kf0Rz.gif)


Is there an analogue to the role of vapor in liquids and gases, but for solids and liquids?

It seems common for an ordered phase to have some amount of disorder present. For example, the average moment of a ferromagnet is less than maximum except at T=0 due to the presence of fluctuations. Also, a liquid is typically only in equilibrium if a portion of it is vapor at the right vapor pressure. Is there an analogue for the solid-liquid transition? In other words, for, say, an elemental solid below the melting point, should we expect a portion of its surface to be liquid at any given time, with this portion increasing steadily until the melting point when the whole thing becomes liquid?


Subnuclear physics vs wave function

This question is more a philosophical question than a physics one. When we appreciate particle physics we study that in order to explain some experimental results we have to introduce a new particle (for instance thinking about neutrinos). This is obviously true but I just want to ask you: is there a wave interpretation of this results? I mean, consider for example the so-called sea quarks, which coming up as a mixture of different quarks, if I describe this processes in a wave model can I see this as an interference of wave function? I am not sure that this question is clear. generalizing, why do not we study subnuclear physics both in particle and wave model, as quantum mechanics suggest?


Where's the missing helium in the Universe?

I'm confused: Big Bang nucleosynthesis is adamant about the 1 neutron to 7 proton ratio which yields 75% hydrogen to 25% helium (with a nominal amount of partially-reacted deuterium and heavier lithium). But everything I read about the interstellar medium gives a helium figure closer to 10%, so what happened to the missing 60% of the helium in the Universe? Of the gas in the ISM, 89% of atoms are hydrogen and 9% are helium, with 2% of atoms being elements heavier than hydrogen or helium, which are called "metals" in astronomical parlance.


Expression for the (relativistic) mass of the photon

I started learning a bit ahead from an old physics book, and they were discussing the photoelectric effect and after that Planck's hypotheses and energy quantas. The book said that the mass of a microscopic oscillator (what is that?) is not continuous, but discrete and the difference between states is an energy quanta: $ \varepsilon = h\nu = E_k - E_i $ And since $ E = mc^2 $ then the (relativistic) mass of the photon is $ m = \frac{h\nu}{c^2} $ How did they deduce that?


Particle sources and particle detectors in quantum field theory

I am looking for a resource that clearly exposes the concepts of a particle source and a particle detector in the context of Quantum Field theory. I want to understand Irreversibility in this context.


Need an intermediate resistivity part/material

I need a part or material for a planned experiment (the experiment is similar to those described in my articles http://arxiv.org/abs/1208.0066 and http://arxiv.org/abs/1109.1626 ). The problem is that the required resistivity (about 0.3 Ohm-cm or of the same order of magnitude) is much higher than that of metals and much lower than that of dielectrics. Eventually, I need a long cylindrical part, about 1.5 mm diameter and about 1 m length. So far I have considered semiconductors, conducting polymers, and absorbing materials of http://www.eccosorb.com/Collateral/Documents/English- US/Electrical%20Parameters/ls%20parameters.pdf . The latter materials seem good, but they are essentially foams, and the required part cannot be machined from them. As for semiconductors and conductive polymers, I don't have a clear idea how to get (to order) a material with the required resistivity and how to make (to order) the required part. I need the above resistivity at a frequency of about 25 GHz, so, in principle, I could use a nonconductive, but absorbing (at the required frequency) material, but I would prefer a material that is conducting for direct current as well, to be able to measure the absorbed power. I would prefer a material with decent mechanical properties, so that I could, e.g., strain (tighten) the cylindrical part. Any advice? EDIT (02/02/2014): I have finally obtained the required parts. They are made of doped polysilicon. I am grateful for the answers.


Counterpropagating beams in a ring cavity lasers

Ring cavity lasers usually has a intracavity element like a optical diode to forbid standing wave pattern and, consequently, spacial hole burning and related instabilities. So, my question is: why to beams exist (before install the optical diode-like element) inside the cavity, since (as far as I know) stimulated emission radiation "follows" the direction of the pump beam? The beam propagating in the opposite direction is the amplification of the spontaneously emitted radiation amplified by the resonator? ![Laser](http://i.stack.imgur.com/7LVu5.gif)


Vectors-Can anyone explain me the concept of sense in vectors?

Is it same as the direction?Then , why another term "sense"is used ,instead of direction? Can anyone illustrate it?


what is the best way to collimate light emitted by a led?

I'm new to this forum. This is half a question, half a challenge. And it's more engineering then physics but I thought I might get good insights from a physics forum. I would like to cure a UV activated resin using a collimated 390 to 420nm light source. The area I need to cure is 3" (7.5cm) by 3". ( althoug the light beam can be bigger then this area and of any shape) so long as it's colimated and as efficient and low cost as possible. I want to get at least 3 watts of light power over that area and it has to have light everywhere and ideally as evenly distributed as possible. Ouff! I'll have to build some sort of DIY apparatus to collimate light coming from 390 to 420nm LED's. There are different types of LEDs on the market. Single point high power ones (1-3W) with viewing angles 40 to 160 degrees ( the angle at which the light cone expands out) or some even higher power arrays of diodes : 5w + Or low power 5mm diameter ones with witch I could build a large array of evenly spaced LEDs. ( but not necessarily) these have viewing angles of 25 to 160 degrees. In all cases, the actual light emmiting part is generally square and very small, then it is encapsulated in another package. I don't know much about optics and I have been pondering about this problem for a while now. How would you go about doing this? From lenses to mirrors, to what type of led tp use, there's pretty much an infinite different ways to approach this and I needed to get the idea out there, so others could share their insight. Feel free to throw any ideas but try to remain as technically and scientifically correct as possible. Also, although the problem makes sense to me maybe I failed to share it with you appropriately, feel free to ask questions or clarifications! EDIT I intend to pass the light through an LCD screen before hitting the resin. Which brings me to another question. At these wavelength, will diffraction come I to play if the LCD "holes " the light is passing through are 100 microns large? Edit wavelength can be between 390 and 420 blow that will damage the LCD. Above will not cure the resin.


Does it take infinite energy to create a perfect vacuum?

Question is inspired by a recent burst of perpetuum mobile-type questions. It would be nice if one could simply discard them all by an argument that shows it's impossible to create a perfect vacuum. Intuitively, I have some hope that there will be a thermodynamics/statistical mechanics argument that we can never even eliminate air friction _completely_ , thereby eliminating all these elaborate constructions requiring specific arguments from the get-go. My question is therefore twofold:   1. Does it take infinite energy to create a perfect vacuum (in a macroscopic box)?   2. If yes, can you include a derivation? If no, can you give an explicit construction with a finite amount of work being done?


Geometric picture behind quantum expanders

A $(d,\lambda)$-quantum expander is a distribution $\nu$ over the unitary group $\mathcal{U}(d)$ with the property that: a) $|\mathrm{supp} \ \nu| =d$, b) $\Vert \mathbb{E}_{U \sim \nu} U \otimes U^{\dagger} - \mathbb{E}_{U \sim \mu_H} U \otimes U^{\dagger}\Vert_{\infty} \leq \lambda$, where $\mu_H$ is the Haar measure. If instead of distributions over unitaries we consider distributions over permutation matrices, it's not difficult to see that we recover the usual definition of a $d$-regular expander graph. For more background, see e.g.: Efficient Quantum Tensor Product Expanders and k-designs by Harrow and Low. My question is - do quantum expanders admit any kind of geometric interpretation similar to classical expanders (where spectral gap $\sim$ isoperimetry/expansion of the underlying graph)? I don't define "geometric realization" formally, but conceptually, one could hope that purely spectral criterion can be translated to some geometric picture (which, in the classical case, is the source of mathematical richness enjoyed by expanders; mathematical structure of quantum expanders seem to be much more limited).


Can a charged black hole interact via electromagnetism?

> **Possible Duplicate:**   >  Detection of the Electric Charge of a Black Hole Light cannot escape from a black hole. However light is also interpreted as the carrier of the electromagnetic force. So how can a charged black hole interact via electromagnetism with its environment? Can one see from the outside of a charged black hole, that this black hole is actually charged? Or is this information hidden, because light (and therefore information about the electric charge) cannot escape from the black hole?


Newton's rings experiment

I have performed experiments in my college laboratory on Newton's rings to find radius of curvature of a convex lens used.i always get a dark center.Is it possible to get a bright center?If yes,then how?


How do the effects of semiconductor doping affect the Hall effect?

For instance, consider number 4 and 5 in the following sample: ![enter image description here](http://i.stack.imgur.com/PP8Eo.png) Using the right hand rule, B points downwards, conventional current points to the right (because of the 5V battery), and therefore, the force on electrons points into the page. Electrons are going into the page from the red wire to the black wire and conventional current is going from the black wire to the red wire. But when conventional current goes from ground (black wire) to the higher voltage (red wire), then the voltage must be negative. Therefore, the voltmeter would read a negative reading. However, I am unsure what kind of effects doping the semiconductor would have on the voltmeter.


Difference between a quantum process and a thermal process?

I was reading an article online pertaining to quantum mechanics and I stumbled across these few sentences. > A look at the corresponding energy regimes shows (Beck and Eccles 1992) that > quantum processes are distinguishable from thermal processes for energies > higher than $10^{-2}$ eV (at room temperature). Assuming a typical length > scale for biological microsites of the order of several nanometers, an > effective mass below 10 electron masses is sufficient to ensure that quantum > processes prevail over thermal processes. I would like to know what they mean when they say "is sufficient to ensure that quantum processes prevail over thermal processes". Or possibly just what the difference is between a quantum process and a thermal process. Original Text (Section 4.4 Beck and Eccles: Quantum Mechanics at the Synaptic Cleft) http://plato.stanford.edu/entries/qt-consciousness/#4


How is the current flow perpendicular to the wire?

This answer gives a great explanation of how surface charge builds up to force the current to move perpendicular to the wire: http://physics.stackexchange.com/a/102936/41086 However, it fails to address the _magnetic field_. Moving charges generate a magnetic field, so in addition to the electric field creating a force on the charges, so does the magnetic field. The answer doesn't explain what effect (if any) the magnetic field generated by the moving charges in the transient state has on the charge build up or the effect of the magnetic field in the steady state. So could someone give me an explanation of how the current flows perpendicular to the wire, **by taking the generated magnetic field into account**? Essentially, I'm looking for an extension to the answer I linked to above by including information on the steady state and taking the magnetic field into account.


Are there any serious alternatives to QCD nowadays?

I've read several posts here where people talk about the history of the developement of the theory of strong interactions. And they mention Regge theory, pomerons, S-matrix and so on. I'm confused because I see the S-matrix in my QFT books, while wikipedia says: " it **was** a proposal for replacing QFT..."? What? Also in the article on Pomeron wikipedia says that it **is still used and that pomeron carries no charge etc...**? **Are pomerons real?** My question is whether there are any serious competitors to QCD today? Perhaps I should split this into several question, but I don't know. I would like to get an overview of the history of the development of the theory of strong interactions **from someone neutral** , but that's too much to ask for I guess. See for instance @Ron Maimon's reply to this question.


why is dark matter the best theory available to explain missing mass problems?

Why is dark matter the best theory to explain the missing mass problem? Why is dark matter mathematically necessary to explain the missing mass problem? On a side not I believe dark matter is definately intuitive the next logical step in physics is to accept the fact the direct observations can not always be the determining factor in the acceptance of a theory. Positivism is not going to be the only driving force in physics forevermore. One theory that seems almost as good is the supersymetric particle. What determination which are actually detectible and how would we distinguish the differences between the two? References:   http://blogs.scientificamerican.com/observations/2011/04/14/underground- xenon100-experiment-closes-in-on-dark-matters-hiding-place/   http://www.science20.com/hammock_physicist/dark_matter_plot_thickens. http://www.holoscience.com/wp/synopsis/synopsis-5-electric-galaxies/5/


Newton's third Law?

**Third law:** > When one body exerts a force on a second body, the second body > simultaneously exerts a force equal in magnitude and opposite in direction > to that of the first body. Newton's third law is unintuitive to me. If the earth exerts a gravitational force on me, how do I exert a force on Earth? Why is this true? It doesn't make any sense. How did Newton come to this conclusion?


Is a photon "fixed in spacetime"?

From what I've read, according to relativity, a photon does not "experience" the passage of time. (Can we say there is no past/present/future for a photon?) Would it be better to say a photon is "fixed in spacetime"? If so, how do we explain the apparent movement of a photon? Is everything else moving relative to it in spacetime?


How does a photon experience space and time?

To an an external observer it appears that time has stopped for photon. But this relation is reflexive, so for an observer travelling with the photon it appears the universe has stopped everywhere. Is this right? Space also gets distorted parallel to the direction of motion, but not perpendicular to it. Does this mean that for an observer travelling with a photon sees spacetime as a flat plane? NOTE: I'm using language _vividly_ not _literally_ when I say a photon experiences space and time. Not that I'm against idealist or panpyschist interpretations of matter or energy come to that.


How do photons experience time?

I know that as velocity approaches the speed of light the time dilation shoots to infinity as shown below. ![enter image description here](http://i.stack.imgur.com/eQWHb.png) 1)So I want to know how time is perceived from the point of view of the photon? 2)Since time stops at the speed of light how do photons move? 3)Is this why photons do not decay or are made up of any smaller particles?


How is the universe is experienced at light speed?

When moving faster, we experience time dilation and space contraction. We often state that a photon does not travel through time, i.e. if it where capable of observation, it would not experience time. But how about space? Would the photon experience a two-dimensional space?


How can we observe lights properties if it travels at the speed of light, or can we?

Special relativity says that anything moving (almost) at the speed of light will look like its internal clock has (almost) stopped from the perspective of a stationary observer. How do we see light as alternating electric and magnetic fields? Also does light never age?


If time stops at the speed of light is a photon 'everywhere' at once?

I am not a physicist so excuse my question if it's paticularly stupid. As a particle gets closer to the speed of light time slows down as for that particle as compared to a reference from the surrounding environment. Therefore for a photon travelling at the speed of light time has stopped for the particle or in a sense does not even exist for the particle....correct?? So is it true that a particle travelling at the speed of light would be everywhere that it does exist at the same time from an outside reference? For example if it travels in a line from point A to B at the speed of light wouldn't the particle be at every point along that line between A and B at the same time? I always read that photons exists as a probability wave but is it equally true to say that a photon exists everywhere that it will possibly exist at the same time? Presumably when a photon interacts with another particle (or is observed) it slows down and no longer travels at the speed of light i.e. no longer existing 'everywhere' at once. Would this explain the retrocausality of the delayed double split experiment? I think this would also explain duality. When unobserved the particle is at the speed of light and therefore exists everywhere that it could exist between A and B. When observed it no longer travels at the sppeed of light and therefore only exists at a point. Where's the mistakes? Thanks for your thoughts.


Life of a photon

I am a student of class 12th and as far as i know when anything reaches about 99.99% of the speed of light it starts traveling in time or time for it slows down so that it don't breaks the speed barrier. So according to this light photons are immortal. Please clear my doubt.


Is the quantity $mv^{2}$ also conserved?

The following is my reasoning: Suppose $\vec{F}$ is a conservative force field. Then the total mechanical energy, $E$, of the isolated mechanical system is a conserved quantity which implies that $E=T+U=k_{0}$, where $k_{0}$ is a constant, $T$ is the kinetic energy and $U$ is the potential energy. Now, $\nabla{E} =\nabla{(T+U)}=\nabla{T}+\nabla{U}=\vec{0}$. Hence, $\vec{F}=-\nabla{U}=\nabla{T}$. Now, $U=\int_{C} \nabla{T}\cdot d\vec{r}= T+k_{1}$, where $k_{1}$ is a constant of integration. Now, $E=T+U=T+T+k_{1}=k_{0}$ which implies that $E=2T=k_{0}-k_{1}$ is constant and since $T=\frac{1}{2}mv^{2}$ and hence $E=mv^{2}=k_{2}$, where $k_{2}=k_{0}-k_{1}$ is a constant and therefore $mv^{2}$ is a conserved quantity.


Surface gravity for a rotating charged black hole

I have that the surface gravity (at the outer event horizon) for a Kerr-Newman black hole is $$ K_+ = \frac{r_+-r_-}{2(r_+^2+(J/M)^2)} = \frac{\sqrt{M^2-Q^2-J^2/M^2}}{2M^2-Q^2+2M\sqrt{M^2-Q^2-J^2/M^2}} $$ where $r_\pm$ are the outer and inner event horizons, $M$ is the mass, $Q$ is the charge, and $J$ is the angular momentum. I have a simple question, almost too dumb to ask: what (natural) units are used here, such that $M$, $Q$, $r_\pm$, and $J/M$ are dimensionally equivalent?


Tesla to Newtons

Is it possible to convert Tesla to Newtons of force?   Or magnetization force H:(A/m) to newtons?


Justification for smeared fields in the Wightman axioms?

I just started reading _PCT, Spin and Statistics, and All That._ Can someone explain why we use operator valued distributions to describe fields? I read somewhere that it would take infinite energy to measure an observable at a single point. Why don't we instead use functions from some collection of subsets (i.e. the open sets) of space to the operators to emulate the fact that measurements usually occur over some area? In other words, what is the physical meaning of the test functions used to define the operator valued distributions? Are some of these functions non-physical, possibly too narrow in width that they'd violate some uncertainty principle?


How fast do I need to go in order to avoid being seen by the Police?

I was driving down the road at roughly the speed of traffic. I saw a police officer parked on the side of the road, and also noticed that a Semi was traveling in the lane right next to him. This got me thinking, is it possible to avoid being seen from the officer by using the Semi Truck and how fast would I have to go? Let's say the officer is parked on the side of the road and the semi is traveling on the lane next to the officer: ![My little Paint Drawing](http://i.stack.imgur.com/7EWmd.png) Let's also assume that the truck is traveling at roughly constant 65 mph. Also assume that I see the officer and line up my car to block the officer's view via the semi at roughly a mile away. (Ya I know a little far). What I want to know:   * How fast do I have to go to avoid being seen by the officer?   * Is this speed constant or variable? _Note: I am in NO way advocating speeding on the highways and breaking the law. This was just was just sparked as it somewhat happened while I was driving down the road._


What is band filling effect?

Could anyone tell me what is band filling effect? I have search Physics.stackexchange and Google, but didn't find any useful information. I'll appreciate it if anyone can tell me the physical image of band filling effect.


Is it reasonable to visualise an additional dimension of time as a part of 4th dimensional spacetime

_[EDIT] In the spirit of asking a "good question", this question is considerably more refined that the one I decided to blurt out earlier thanks to a little additional research and nudges from comments._ I'm not a physicist, but love to let ideas roll around in my head - so please excuse any crossed boundaries. I'm not equipped with the mathematics required to examine or perhaps even pose this question in a way many of you are probably used to. So, my question: Spacetime as we know it consists of 3 spatial dimensions + 1 temporal dimension. Is it reasonable to visualise spacetime in our next-highest dimension as consisting of 4 spatial + 2 temporal dimensions? _From another point of view:_ If we view our 3D space as a submanifold of a 4D manifold, is it reasonable to suppose that time as we experience it may be a similar submanifold of time in a higher dimension? _Or:_ **Adding and subtracting spatial dimensions is the easy bit (an axis perpendicular to all other axes in that dimension) ... do we also get to add and subtract temporal dimensions from spacetime as we journey from one dimension to the next?** (For posterity, my original question was phrased as " _Does the 4th dimension include imaginary time as part of its fabric of spacetime?_ " - referring to the concept of imaginary time as popularised by Hawking. In case it helps, this annoying little thought experiment arose from musings of the possible mechanics behind quantum entanglement) ========================================================================= _References I've found helpful so far:_ "Survey of two time physics": http://inspirehep.net/record/532282?ln=en "Dual field theories in (d-1)+1 emergent spacetimes from A unifying field theory in d+2 spacetime": http://inspirehep.net/record/750980


How to know if something is a primitive concept, a law, a definition or a theorem

Some basic Physics books are often misguiding in the sense that they don't make clear whether something is a primitive concept, a law, a definition or a theorem. This is often a little confusing. I've asked here some moments ago if there's a definition of force, and I've been redirected to a question about whether Newton's Laws are laws or definitions of mass and force. This is just an example, but there are many others, like for instance, the conservation of energy, which some books present as a theorem, and some places says that this is a law of Physics. Time on the other hand, is something that according to Feynman's lectures on Physics, cannot be defined, so we just say how to measure it and leave it as a primitive concept. In this context: how in general can we identify whether something is a primitive concept, a fundamental law of Physics, a definition or a theorem?


The Galileo thermometer: why do the bubbles float in the middle of the tube?

If the water were uniform temperature, it would have uniform density, so a bubble should either be all the way at the top (if it's lighter than water) or all the way at the bottom (if heavier). But in reality you don't see this neat separation. Sometimes you see bubbles hovering in the middle. Is this because the water temperature is not uniform? Does this mean that with time, if the room temperature stays constant, all bubbles will neatly separate along the top and bottom?


What is the difference between surface plasmon and surface plasmon polariton?

I'm trying to understand this reading article linked below and I still don't know how to explain this simply, without need to derive everything mathematically. Can someone just write here how do SP's and SPP's differ? http://dipc.ehu.es/etxenike/admin/documentos/archivos/publicaciones/307RPP2007.pdf Moreover while reading this article : http://daedalus.caltech.edu/publication/pdf/0801_opinion.pdf I think that they are writing about SPP's despite of using SP term. So maybe there's no difference at all?


what if the time is zero in one reference frame

Consider measuring the length of an object in another frame of reference.   Of course this should happen at the same instance in the frame of reference the measurement takes place in.   but using Lorentz transformation the time in the other frame of reference would be different and there would be a period   \begin{equation}\Delta t^\prime = \gamma v/c^2(x1 - x2)\end{equation} so we have $\Delta t = 0$ but $\Delta t^\prime$ has a value   doesn't this contradict with the time dilation basic law $$\Delta t^\prime = \gamma \Delta t$$


How to calculate the force in an "impulse based reaction model"?

I have a sphere moving forward with `v (pre collision) = v1i` A second sphere colliding with the first one has its own pre collision `velocity = v2i` The collision should be not totally inelastic (like, you know, the case of two human bodies colliding each other), but for my purpose I think I can consider the coefficient of restitution = 0 Using the formula $$ I = mv_f - mv_0$$ and replacing `I` with `F * (delta)t` I woul like to know how can I compute that `F`, since I don't know what will be `v(post collision)` because it is my final unknown to compute. And I think that force should be computed with the relative velocity of the two spheres, but I have no idea at the moment on how to proceed. Any suggestion will be strongly appreciated. UPDATE Thank you for your suggestion ja72. So in that case can I write something like this? $$ F *\Delta t = \frac{ (\epsilon+1) \left(v_2-v_1\right)}{\frac{1}{m_1}+\frac{1}{m_2}} $$ But in this case, how am I supposed to evaluate final velocity of the two spheres?


What is wrong in following arguments about connection of local gauge invariance and causality?

There is a question and corresponding downvoting of my answer, so I decided to ask this question. There is my answer on it: "...The most theories of free fields are invariant under global gauge transformations. It can be interpreted as instantaneous "rotation" of all space-time relatively gauge space, which contradicts the causality (of gauge transformations) in relativity case, because the speed of interactions is limited by $c$ according to it. So we introduce local gauge transformations, where "rotation" depends on space-time point. The gauge states is indistinguishable in a case of free field. But when our global gauge invariance field interacts with other fields, degeneracy is lifted, and this leads to instant changes in interaction. Thus we satisfy causality principle for gauge transformations. Also I can add some example. Let's have global gauge isotopic invariance of QFT. So we identify proton and neutron as the state with some value of isotopic spin, and then if we choose that what to call a proton at one space- time point, we also must choose what to analogically call a proton at other points, so it little contradict the principle of local field theory. If the nucleon interacts with EM field, we may instantly change it state by using global gauge transformations, which also instantly changes the interaction between nucleon and EM field in all points of the space-time. It leads to non- local theory and contradict the causality. Corresponding arguments were used by Yang and Mills in 1954...." Where did I make the mistake (I really do not see the error)?


What is voltage: strict but intuitive definition from accumulator's perspective

I know, that voltage is analogous to pressure for charge, but analogies lie. I don't see charge pressing anything and I don't understand definition of $U=A/q$ (voltage = work/charge), cause I can't see what is that work. ![enter image description here](http://i.stack.imgur.com/EAxef.png) Voltage in a circuit is determined by an accumulator. I suppose, that accumulator is characterized with voltage output and current output. I don't get how they are related, but can imaging some tweaks to the accumulator: 1) If I double the area of both metal plates, contacting with respective solutions, would it double the voltage output? Intuitively it will cause twice the amount of Ions bump into plates and give their charges to them, so it would double the current and won't change any "charge pressure", I can think of. 2) If I double the concentration of each solution, would it double the current or charge. My intuition that it is the same as if I doubled the area of plates - it would just double the amount of ions transferring their charge per moment of time. Nernst equation suggests a change of voltage in this case, but I can't see what it is. What I want to understand, is what is voltage in terms of ball-like ions, forces and such intuitive entities. Thanks.


Have I discovered how to calculate the proton's mass using only integers?

Could it be possible that the mass of the proton can be calculated by a series of integer sequences? Or is this just a curiosity? $$\sum_{m=1}^{\infty } \frac{1}{10^{26}(m^2+1)_{2m}}=$$               NSum[1/Pochhammer[m^2+1,2m], {m,1,\[Infinity]}, WorkingPrecision -> 50] /10^26       First seven digits match the proton's mass in kilograms. $1.6726218229590580987863882056891582636342622102204\times10^{-27}$   $1.672621\times10^{-27}$ - from OEIS _revised 11/15/12_   $1.672621777\times10^{-27}$ - from Wikipedia What's to say that sometime in the future, the proton's mass won't be made more accurate by adding $4.5\times10^{-35}$ to the current number? **Edit to explain motivation** Whenever I get a result I don't recognize, I look it up on OEIS. I found this number. I posted on Mathematica.SE with the intention of asking for advice on how to prove that it converges. That would make this number a constant. If this is a "fluke" or the result of "small numbers," it's still worth exploring. **Edit: It does converge.** **Final Thoughts** $f_{p}=0.16726218229590580987863882056891582636342622102204$ is the 0-dimensional value of a fractal know as the Hilbert Curve. To get the minimal 3-dimensional value: $f \times 10^{((dimension+1)!)}$ where $0\le dimension \le 3$. This results in the value for a $1\times 1\times 1$ cube (coincidentally, the definition of the gram.) To get kilograms: $f \times 10^{((dimension+1)!+3)}$. I posit that the fractalness is the stabilizing influence on the proton. **Coda** I agree with everyone that I have been wrong-headed about the importance of this constant. I have posted the constant on OEIS A219733. Thanks for your patience.


On a principal bundle, why is the horizontal vector space not unique?

On a principal bundle, at each point you have a tangent vector space. At a given point, the vectors tangent to the fiber form the vertical vector space. Then the vector space at that point is a direct sum of the vertical vector space and what's called the horizontal vector space. This is all standard stuff in gauge theory. What I don't intuitively understand is why is the horizontal vector space not unique?


Is there stringy Morse theory?

This question is pretty vague and open. I'm just curious if anyone has considered this. Morse theory has a nice physical formulation: a Morse function can be thought of as a potential, so the gradient flow is the force experienced by a particle. The equilibria are the critical points of the potential. If we take a supersymmetric extension of this as a quantum theory, its ground state structure computes the homology of the space the particle moves in. What can strings moving in a manifold subject to a potential tell us about the topology of the manifold?


Twin Paradox: Whose time is slow?

What I understand about the twin paradox is that if a person stays at rest with something lets say the earth and a traveller moves with a great velocity with respect to the firsy person, then the time of traveller becomes very much smaller than the time of person who stays back, which led to the conclusion that one would age very much and one would not. But if you see from the frame of the traveller, the person on rest on earth seems to be moving very fast, and according to this the person on earth should be younger than the traveller. So, who is actually going to be younger? One of my friends had asked me this question, and I replied that from the frame of the traveller if you measure the velocity of earth bound person you will have to take the same velocity in negative and you will get the same result. Even though he accepted my answer; I am myself not satisfied with it.


Where does additional heat energy come from in isothermal step of Carnot cycle

According to widipedia: > During step 1 (isothermal heat addition or absorption) the gas is allowed to > expand and it does work on the surroundings. The temperature of the gas does > not change during the process, and thus the expansion is isothermal. The gas > expansion is propelled by absorption of heat energy Q1. The gas temperature is the same as the temperature of the reservoir. But where may heat energy Q1 come from as there is no temperature gradient between gas and reservoir?


Does the Higgs boson give mass to ALL other particles?

The Higgs Field gave mass to other particles via spontaneous symmetry breaking; does this mean it gives mass to all particles that have mass - such as neutrinos, quarks or weak bosons and strong bosons (gluons)? In the articles I've seen its not clear what the criteria is for the Higgs Field to couple to particles to give mass; Anna v's answer suggest that electo-weak vertexes are required; but the linked article suggests it also couples to quarks.


frames of reference

> **Possible Duplicate:**   >  Help Me Gain an Intuitive Understanding of Lorentz Contraction Frames k and k' are inertial frames. Frame k' is moving at a velocity of magnitude v relative to frame k in the direction of the x-axis. there are rigid rods in each frame oriented along the direction of the relative velocity. Someone in frame k measures the rod that is stationary in k as having length L1 and the rod stationary in frame k' having a length L'2. What are the lengths of the rods measured by someone in frame k'?


Why does adjoint representation matter in some field theories?

Recently I am reading a paper about monopoles. In several cases, it seems that writing fields in adjoint representation of the gauge group makes a difference. Once it leads to different group after symmetry breaking when using other representation. And I also noticed statement like this, "An important open question is whether an analogous Bogomolny monopole's mass bound can be obtained if the Higgs field is not in the adjoint representation." Can anyone kindly shed light on this. Thanks! **Update:** I reckon any field (either EM field in real space or Higgs field in internal isotopic space) be in a certain type of representation space of the symmetry group associated with the Lagrangian or action. This space also dictates some constraints on the fields, e.g., specific tensor or spinor structures ( _anything more???_ ). And what representation space you use contains physics as well, that is to say, we have to check it by experiments. Perhaps this question addresses on a particular case. Either does the explicit and concrete 2nd answer. Is this understanding correct?


Unit for expressing energy eigenvalue in infinite potential well problem

How are the energy eigenvalues expressed in a infinite potential well problem( Joules/eV)?


Rotating hoop with fixed body inside of same mass

Please help me to solve this problem. I am unable to understand which force will cause the hoop to bounce. > A small body $A$ is fixed to the inside of a thin rigid hoop of radius $R$ > and mass equal to that of the body $A$. The hoop rolls without slipping over > a horizontal plane; at the moments when the body $A$ gets into the lower > position, the center of the hoop moves with velocity $v_0$. At what values > of $v_0$ will the hoop move without bouncing? ![enter image description here](http://i.stack.imgur.com/o5S2m.gif)


Can internet speed be faster than speed of light?

We send email in order to transfer information and, over time, the technology used to send email improves to send email at faster rate. Since we use the Internet to send information from one place to another place all over the world, can information speed be faster than light speed via the Internet?


Brownian motion and physical meaning

I have read Stochastic Differential Equations by Bernt Oksendal   It constructs Brownian motion by Kolmogorov extension theorem by consider $p(t,x,y)=(2\pi t)^{-n/2} e^{- \frac{|x-y|^{2}}{2t}}$   But I can't understand what is the relation to the Brownian motion in physics.


Resonance in a 1 ft granite box

* I have a granite cube made using 6 slabs of granite 1 foot square and 1 inch thick. The top and bottom slabs have a 1 inch margin around the edge. The slabs are just set together, not notched or mortared or anything.   * I also have a concrete block with pipes running through it that generates a sonic pulse/compression wave from a valve closing. If this were a regular water system we'd all call it water hammer. This water hammer comes _out the top of the block_. It is assumed that this block is not going to self destruct from the water hammer. It pulses about 60 times per minute. There is a working example of this block that I have seen online, so I know how to build it. Now what I'm trying to figure out is what would happen if I would set my granite cube on top of the concrete block. Would the sound reverberate around in the granite box until it blew it apart? Or would it somehow go through the block somewhere else? What would happen? Would it resonate at a certain frequency and produce a hum? Would it make a difference if I took away the bottom slab?


Crushing a magnetic field

What would happen if you crushed a magnetic field to an ever decreasing size? Thanks. EDIT: How small could the field possibly go? Is there a limit on how small it could get? Is there a maximum field density based on the size?


Movement of a gyroscope with non-fixed axis

Assume one has a gyroscope rotating around an axis with both ends leaning on a dedicated semiplane as shown on the picture below. There is no friction either between the rotor and the axis or between the axis and the semiplanes. The only force is the gravity acting on the rotor. How will the gyroscope behave if one instantly removes one of the semiplanes? ![enter image description here](http://i.stack.imgur.com/pn3ZO.png)


Understanding the Wave Function and Excited States

A wave function is an infinite dimensional vector space, how can it "live" in $\mathbb{R}^3$? Given the equation that is built like: $$\Psi (x,t) = \sum ^{\infty} _{n=1} c_n \psi _n (x) e^{-i E_n t / \hbar}$$ How does one "excite" a quantum particle in the lab? The excited states simply give a different probability distribution for the particle? For the infinite square well, the wave function in excited state $n$ has exactly $n$ bases, all of which are non zero? If a particle is in its ground state, does that mean that all other bases must be zero? making the wave function dependent only on one basis?


Is dimensional analysis always sufficient to establish equivalence of quantities?

In dealing with the Biot-Savart law, it was argued that $$ q\frac{d\vec{s}}{dt}\equiv Id\vec{s} $$ using the fact that the units are equal. Does this kind of argument always work? It seems too simple to be true.


Effects of gravity on light

If gravity can bend light, why can't gravity slow light. At least momentarily? Wouldn't that give the illusion of the universe expansion speeding up?


Two axes for rotational motion

I understand that angular momentum is a vector, etc.. But, what really happens when some object, say a ball for example, is set to rotate along two axes? What would the resulting motion look like?


Why is mud muddy?

How to explain properties of mixture of sand with water? Why is it so coherent and slippery at the same time? Is it due to hydrogen bonds? Why is mud of smaller grains more slippery and incoherent and mud of bigger grains is more coherent and less slippery?


Are standard and isotropic forms of Schwarzschild metric truly equivalent?

My admittedly rudimentary understanding of physical meaning of conformal flatness - as pertaining to a stationary observer exterior to a spherically symmetric static gravitating mass $M$: Locally Euclidean, in that the proper differential volume $dV$ between two concentric spherical surfaces centered about M, having differential proper radial spacing $dR$, is given by the Euclidean formula for enclosed volume $dV$ = $AdR$, where $A$ can be taken as the mean value of the two proper surface areas, and we take the limit as $dR\rightarrow0$. Correct? And that in GR, SM (standard Schwarzschild metric) is **not** conformally flat since there $dR$ is greater by factor $\sqrt{-g_{rr}}$, as can be determined by inspection of the line element - e.g.:Wikipedia - archived revision That is, $dV = \sqrt{-g_{rr}}AdR$ for SM, $ > dV$ (Euclidean) - for a _given_ proper areal difference between shells. It's evident by inspection of the line element for ISM: here, for the equivalent differentially separated concentric shells arrangement as above, $dV = AdR$ asymptotically applies as per Euclidean formula? In other words, _by virtue of it's construction as spatially isotropic_ , ISM necessarily claims a conformally flat metric, in-principle measurably physically distinct from that of SM? How then is it that the two are claimed to be physically equivalent? Also is there a precise technical term and definition specifying departure from conformal flatness here? While the above concentric spherical shells situation is the one I was introduced to, there is surely no reason preventing it being dimensionally reduced to one of proper radial spacing between concentric great circles, and in fact then further reduced to an arbitrarily small local sector cut from such concentric circles. Meaning it must be an in- principle locally observable quantity rather than only determinable globally?


How was Avogadro's number first determined?

I read on Wikipedia how the numerical value of Avogadro's number can be found by doing an experiment, provided you have the numerical value of Faraday's constant; but it seems to me that Faraday's constant could not be known before Avogadro's number was as it's the electric charge per mole. (How could we know the charge of a single electron just by knowing the charge of a mole of electrons, without knowing the ratio of the number of particles in both?) I just want to know the method physically used, and the reasoning and calculations done by the first person who found the number $6.0221417930\times10^{23}$ (or however accurate it was first discovered to be). Note: I see on the Wikipedia page for Avogadro constant that the numerical value was first obtained by "Johann Josef Loschmidt who, in 1865, estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas;" but I can't access any of the original sources that are cited. Can somebody explain it to me, or else give an accessible link so I can read about what exactly Loschmidt did?