title: What is Higgs transition?

text: In recent publications there is a frequent mentioning of the so-called "Higgs transition" in connection with magnetic monoples. Can anybody please describe the phenomenon in simple terms? For example, it seems that here it is claimed that found a material that exhibits magnetic monople superconductivity and can sustain magnetic current. Does in mean that a cable of such material will have circular electric field around it?


title: String theory and space-time supersymmetry

text: I actually want to know whether space-time supersymmetry is important for string theory consistency? I see that NS and GS supersymmetric strings have worldsheet supersymmetry, but the first one does not have a manifest space- time SUSY while the second one has it manifest. I want to know if this space- time SUSY is really having an impact on string theory. I know the answer is Yes, but in which way it effects the consistency of string theory? (compactification?) Edit- I would like to add that the only way I think this space-time SUSY adds to string theory is the notion of a constant covariant spinor, which gives the Calabi-Yau manifold for compactification. Is this the necessity of space-time SUSY? And what else can we say about it in connection to string theory.


title: Expression for the (relativistic) mass of the photon

text: 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?


title: Exterior (covariant) derivatives and electromagnetism

text: I'm porting Maxwell's equations to curved spacetime and am having trouble reconciling the tensor and forms treatments. I think the problem boils down to a misunderstanding on my part concerning the exterior covariant derivative rather than just the exterior derivative, but that's only a guess. So in Minkowski spacetime we have $$ F_{\mu \nu} = A_{\nu,\mu}-A_{\mu,\nu}\text{, }F_{[\mu \nu , \kappa]}=0 $$ and $$ F=\text{d}A\text{, }\text{d}F=0, $$ the equivalence of which is easy to show. However, suppose we're working in curved spacetime. We get $$ F_{\mu \nu} = A_{\nu;\mu}-A_{\mu;\nu}\text{, }F_{[\mu \nu ; \kappa]}=0. $$ However, the connection coefficients in the covariant derivatives neatly cancel out, so both tensor expressions are equivalent to each other. However, suppose we attempt to bring the flat space forms expression into curved spacetime, by turning the exterior derivative into an exterior covariant derivative. We start with $$F = \text{d}_DA$$ and then (naively?) find $$ \text{d}_DF =\text{d}_D \text{d}_D A = \Omega \wedge A \neq 0 $$ where $\Omega$ is the curvature 2-form. So suddenly the tensor and forms methods seem to give differing versions of Maxwell's laws. Is one not obligated to employ the covariant exterior derivative in this situation? Maybe I am seriously missing something but it seems like the exterior covariant derivative gets much less mention than it should in relativity, if it is required to deploy forms at all on curved manifolds! The Hodge star of course contains information about the metric, but it seems here like we arrive at an inconsistency before needing to invoke it to find the other two Maxwell's equations. Thanks for any insight.


title: Definition of momentum-entangled particles

text: When we can say that two particle are momentum entangled ? I just read an article where it's said that two momentum entangled particles share the same momentum value in opposite directions no matter how far they are when it's provided a measurament ...It's a correct description?


title: What is the maximum surface charge density of aluminum?

text: I understand that the maximum free charge carrier density for aluminum has been measured using the Hall effect (in the case of electric current). However, I'm not clear how to determine the maximum surface charge density to which aluminum (or any conductor) can be charged, assuming the neighboring medium does not breakdown. Say for instance we had a parallel plate capacitor with an idealized dielectric that could withstand infinite potential across it. What is the max surface charge density that the plates could be charged to? I assume that at some point all of the surface atoms are ionized. Is this simply the volumetric free carrier density multiplied by the atomic diameter?


title: Energy in bolognese reduction - lid on or off?

text: Generally, to let my bolognese thicken, I leave the lid off in order to "let water vapor escape." I am however distracted from enjoying the taste because I'm having doubts that my physical reasoning is sound. Given a constant power output from my stove, it seems a given that having the lid on to make the contents of my pot come to a boil makes good sense: Less hot air is released to the surroundings thus more energy is left in the pot to heat the food faster. But does the same argument not apply to reducing my sauce? There's no tight seal, so I can't assume there will be an increased pressure. Where else would the energy go but with steam escaping from cracks around the lid? **Edit:** To clarify: Will my sauce reduce faster with or without the lid? Why?


title: Particle sources and particle detectors in quantum field theory

text: 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.


title: Integrals given by Landau

text: Discussion about Landau's "Theoretical Minimum" has already been posted here. Unfortunately I couldn't find much about some examples of questions he gave to students. There are three questions in the post I linked and also in the linked arXiv article. What I am mostly interested in are math exercises. There is a history of Alexei Abrikosov who after presenting himself as a 3rd year student to Landau was asked if he had a pen and then was given an integral to solve. He managed to solve it and Landau was very happy :). There are many other such anecdotes but they all lack exercise formulation. Maybe you know what this integral could be or at least of what type it was?


title: How can I solve an equation involving partial trace?

text: I am unable to find the solution to the following equation:   Tr$_{2}[U(|\psi\rangle \langle\psi|\otimes \rho)U^{\dagger}]=\rho$ Here $\psi$ is state vector representing a qubit and $\rho$ state of second qubit(the partial trace is over its subspace).   Also $U$ is a unitary operator given by $\sum |x \vee y\rangle |y\rangle \langle x| \langle y|$ where $x,y \in \\{0,1\\}$      $\vee$ stands for bit XOR and $\otimes$ for tensor product and $U$ operates on joint space of both the qubits.


title: Needed Energy For Lifting 200 kg weight

text: 1. I'd like to learn how much energy I need to lift a 200 kilograms weight on normal earth conditions?    2. For example how much electric power do we need? I'm not a physicist and not a student and this is not my hw:) I just wondering.


title: Expectation value of Hamiltonian on number state

text: Hamiltonian is defined by $H_I = \hbar \omega (\hat{a}^+ \hat{a} + 1/2)$ What is the expectation value of the energy on the number state $$\vert \psi \rangle = \frac{1}{\sqrt{2}} ( \vert 1 \rangle + \vert 2 \rangle )$$ So I think that its $$\langle E \rangle = \langle \psi \vert H_I \vert \psi \rangle$$ $$ = \hbar \omega (\langle \psi \vert \hat{a}^+ \hat{a} \vert \psi \rangle + 1/2) $$ $$ = \hbar \omega ((\langle 2 \vert + \langle 1 \vert) \hat{a}^+ \hat{a} (\vert 1 \rangle + \vert 2 \rangle) + 1/2) $$ Now we use that $\hat{n} = \hat{a}^+ \hat{a}$, and then I get confused...does the last expresion become $$ = \hbar \omega (\langle 1 \vert \hat n \vert 1 \rangle + \langle 2 \vert \hat n \vert 2 \rangle + 1/2) $$ or $$ = \hbar \omega (\langle 1 \vert \hat n \vert 1 \rangle +\langle 2 \vert \hat n \vert 2 \rangle +\langle 1 \vert \hat n \vert 2 \rangle + \langle 2 \vert \hat n \vert 1 \rangle + 1/2) $$ any advice? * * * EDIT I think I have the answer E = $$ = \hbar \omega (\langle 1 \vert \hat n \vert 1 \rangle +\langle 2 \vert \hat n \vert 2 \rangle +\langle 1 \vert \hat n \vert 2 \rangle + \langle 2 \vert \hat n \vert 1 \rangle + 1/2) $$ Where $$\langle i \vert \hat n \vert j \rangle = j \langle i \vert j \rangle = j \delta_{ij}$$ So $\langle E \rangle = \hbar \omega (3 + 1/2) = \frac{7 \hbar \omega}{2}$


title: Perceived sway difference between double-decked vs. single-decked buses?

text: Why is that when I'm standing in a moving double deck bus, my body doesn't move a lot; whereas, in a moving single deck bus, my body moves quite a bit? It seems like I swing a lot in single deck buses, much more than in double- decked buses. Why is this?


title: Regulating a particular function

text: I am interested in computing the integral of this function: \begin{align} \int_0^\infty\frac{2du(u^2+1)}{(1-e^{2\pi u})}, \end{align} which of course at first sight, does not converge. But in QFT it's usually possible to regulate such a function. Thus, the question is, does anyone know how to regulate this function?


title: Relation between holography and matrix models

text: Let's consider a 0-dimensional $N \times N$ Hermitean one matrix model. It is defined by a potential V(M). Its partition function is $Z = \int_{H_{N}} dM e^{-\frac{1}{g}V(M)}$ where $H_{N}$ is the space of $N \times N$ Hermitean matrices and g is the coupling constant. I usually think at such a matrix model as a 0+0 dimensional QFT : the matrix M is a field over a space-time reduced to a point. Let's consider the large N limit of this matrix model : $N \longrightarrow \infty$, $g \longrightarrow 0$, $\lambda = gN$ fixed. In this limit, the free energy $F= log(Z)$ has an expansion $F = \sum_{g=0}^{\infty} F_{g} \lambda^{2g-2}$. In this limit, the repartition of eigenvalues of $M$ converges to a deterministic measure with density $y(x)$ function of the eigenvalue x. The graph of this function is a real curve in the x-y plane called the (real) spectral curve. (In the simplest case where the potential V is quadratic, this curve is a half-circle, it is the well known Wigner's semicircle law). In general, the real spectral curve is defined by an algebraic equation in x,y. In particular, it is possible to consider this equation with x,y complex to obtain a non-compact Riemann surface that I call the complex spectral curve. So in the large $N$ limit, we have emergence of some geometry via the real or complex spectral curves. My question is : Is there a precise holographic description of this emergence of geometry ? In usual holography, we have a duality between a 1+(d-1) QFT and a 1+d quantum gravity theory with emergence of one space-like direction. If I look at the matrix model as a 0+0 QFT then in particular I have no time and it is not clear for me what an holographic description should be. If there is some kind of emergence of the spectral curve, is it of the real or of the complex one? Things related but which does not answer the question: The existence of a relation between matrix models and quantum gravity can be guessed from the similarity between the large N expansion of the free energy F and the genus expansion of the free energy of a string theory (the perturbative expansion of the matrix models can be written in terms of ribbon graphs, it is the same argument as the 't Hooft one on the possibility of a relation between gauge theory in the large color limit and string theory). Dijkgraak, Vafa and all have shown that starting from the complex spectral curve, it is possible to construct a non-compact Calabi-Yau 3-fold whose B-model topological string has for genus expansion the large N expansion of the matrix model. There is a long story of relations between matrix models and 2d quantum gravity, which I don't know very well (essentially, the combinatorics problems of triangulations of surfaces have a matrix model interpretation because of the ribbon graph form of the large N expansion of the matrix model). An additional question would be : Is the relation between matrix models and 2d quantum gravity an example of holography ? (Intuitively it should be but detailed formulation is not clear to me: for example, it seems we pass from 0 to 2 dimensions...)


title: De facto superluminal travel?

text: It seems that the limitation to subluminal travel can be practically circumvented (so to speak...not breaking any physical laws here) if we consider the viewpoint of the traveler, not some outside observer:   * As your ship approaches $c$ (as measured from some inertial observer) the proper time of the trip decreases. Hence, if you measured the distance to your location as 10 light years, you would reach your destination having aged less than 10 years, given that you travel at a sufficient fraction of $c$. Thus, to you, you traversed the distance faster than light. Is this a valid interpretation, or will something intervene to prevent this apparent superluminal travel?


title: Need an intermediate resistivity part/material

text: 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.


title: Counterpropagating beams in a ring cavity lasers

text: 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)


title: Space Expansion vs. Relative Motion

text: Inspired by a recent dialogue from another question: Given 2 objects moving at some velocity $v$ relative to one another, is it possible to determine whether they are moving or whether the space between them is expanding?


title: How can space expand?

text: How can space expand when it is only a perception of the separation between at least 2 objects. Isn't saying "space expands" implying it has properties?


title: How does "space" expand?

text: According to Big Bang theory and The Red shift theory "space" is "expanding". Keeping this notion of "space" as physically something in and of itself(space -time did not exist before The Big Bang); what are the supposed theoretical answers for the omnidirectional expansion of this "fabric"--noting that no matter where you are in the universe "space" is expanding away from you??


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

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


title: How to model a symmetry using Lie Groups?

text: I have been reading lately about Lie groups, and although all books keep listing the groups, and talk about Lie algebras and all that, one thing I still don't know how is it made, and I guess it's the most important question as much as my understanding goes, but most textbooks keep ignoring. My question is, **Now if I have asymmetry, and I could put it into equation** (symmetry of sea waves - simplified for example, or symmetry of planetary motion), **how to use Lie groups to express this symmetry?** How to identify which Lie group responsible for that? I am still at the very beginning but for some reason whatever I research I cannot find an answer to this question. I hope I would find help here!


title: What happens with the force of gravity when the distance between two objects is 0?

text: so I had my first approximation to the gravity equation \begin{equation} F=GmM/r^2 \end{equation} and some questions arose that my teacher couldnt respond:   if r approximates to 0 with mM being constant, then the force should tend to infinity, right? so that being true, then if we would travel to the center of the earth, we would be crushed by gravity? if so, how can there be anything right in the center of the earth? wouldnt anything there be compressed and destroyed by the infinite force? having that in mind, my next question is as gravity force is measured from the center of an object, any part of the same object which is not at the center would be affected by the same object's gravity? if so, how can we differentiate between two objects that are not in a vacuum? my question originated thinking in us standing on the earth, in contact with it, are we, in a gravitational sense, one object? this lead to the last question, if gravity is a property of matter, then how applying the same logic as before, how does it work between two neutrons?(chose neutrons because i assumed it would be more difficult obtaining gravitational force if there was electrostatic forces from charges inbetween) do two newtrons in contact count as 1 gravitational object? and how thats its own gravity affect the newtron from center and out? sorry for the big text.


title: (Botanical) branch bending under gravity

text: I'm a PhD student in maths, and attended my last physics class some 15 years ago, so you can imagine my competences in the field. My supervisor (also not a mechanist) cant tell me how to proceed either, and after having spent already way too much time on wikipedia to try to understand the elementary concepts, I am turning to you, here is my problem: Given is a discrete curve in $\mathbb{R}^3$, i.e. an ordered set of points $x_1,...,x_n$ all in $\mathbb{R}^3$, representing the branch of a (botanical) tree. $x_1$ denotes the point where the branch in question branches off from the trunk, $x_n$ is the branches ending point. This discrete curve may be curved and twisted arbitrarily. At each point $x_i$, there is a mass $M_i$ concentrated. Moreover all the branch radii, $r_i$, at point $x_i$ are known (which - I think I at least got this right - is relevant to calculate the "second moment of area"). (If it helps, I would also have a continuous version of the problem, i.e. a continuous curve $s\to g(s)$ instead of the points etc...) The discrete curve $[x_1,...,x_n]$ describes the branch without gravity being taken into account and the task is to find the new curve $[x_1'(=x_1),x_2'...,x_n']$ resulting from the original curve when taking gravity into account. (By the way the trunk itself is considered to be unaffected by the branches growth and weight, thus remains vertical). Apparently the problem is trivial if the curve is not twisted, in the way that all $x_i$ lie in one and the same plane perpendicular to the ground (discussed on the second half of page 2 of "Bending of apricot tree branches under the weight of axillary growth" by Alméras et al., in: Trees. Structure and Function, 2002.). However, I have unsuccessfully searched for a generalization for twisted branches. Could you point me in the right direction? Or, if applicable, tell me that the problem is much more complicated than I think. Thanks a lot in advance. PS: If, as it seems to me in the article mentioned, there exists a very easy way to approximate the real solution to some extend, making possibly questionable assumptions (the "small deflection assumption" seems to be of that sort), that's fine by me. I do not require an exact solution, any (halfway justified) rough approximation works perfectly for me.


title: Why does Leyden jars have a high breakdown voltage

text: I have often heared, that Leyden jars are used because they have a high breakdown voltage. For that reason the are used for example in Whimshurst machines. But what is the physical reason that they have a high breakdown voltage? And what means "high" in this context? Compared to what? How does it compare for example to a parallel plate capacitor with glass as dielectric between the plates? Why are parallel plate capacitors not used for Whimshurst machines?


title: Probability to be in a particular state

text: If I have a wavefunction $\psi = \sum_{n=0}^{\infty} a_n e^{i \phi_n} | n \rangle$ and $(|n \rangle)$ is a set of orthonormal functions. Is it correct that the probability to be in a state $|k\rangle $ is given by $|a_k|^2$?-So is it really true, that the probability to be in this state is independent of the phase factors $e^{i \phi_n}$ that is DIFFERENT for every $n$?


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

text: 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.


title: Where does elastic potential energy go after it is released?

text: Say you have two objects colliding, and there is some elasticity between them. Some of the kinetic energy of the objects will change into elastic potential energy when they collide, but when they bounce off each other again, the energy does not return to being kinetic. What happens with it? Does it stay stored as elastic potential energy, or does it change to thermal energy? Or does it perhaps do something entirely else?


title: A distributed axial load acting on a bar

text: ![enter image description here](http://i.stack.imgur.com/oc8js.png) Normally, when a distributed force is acting on a bar, if it's 'rectengular' we multiply the length with q, but I have no idea what I'm supposed to do at this situation. I first need to calculate to forces acting on C so that I can find the displacement of it by using Hooke's Law, one of the forces is 25kN and the other one comes from the distributed one, but since I can't calculate it, I'm stuck. What do I do?


title: Is there any other solar system in the universe?

text: 1. Is there any other solar system far away from ours in the universe?   2. Why don't we expect another solar system based on another star similar to sun in the universe?    3. If so, Why probably there wouldn't be some life based on those atmospheric conditions?


title: Does it take infinite energy to create a perfect vacuum?

text: 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?


title: Geometric picture behind quantum expanders

text: 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).


title: Can a charged black hole interact via electromagnetism?

text: > **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?


title: What is wrong with considering the Atwood machine as a system?

text: I am confused about a method used in the following problem. There is an arrangement as shown below. The surface is smooth, and the pulleys are light. We have to find the acceleration $a_0$ of $m_1$. ![Problem](http://i.stack.imgur.com/X1esM.png) The method I used to solve it was to consider the pulley B and masses $m_2$ and $m_3$ as a single system that goes down with the same acceleration as that of $m_1$. If this acceleration be $a_0$, then the equations of motion give $$a_0=\frac {m_2+m_3}{m_1+m_2+m_3}g$$ However, the textbook solution treats motions of all objects individually, where $m_1$ has an acceleration $a_0$, $m_2$ has an acceleration $a_0-a$ and $m_3$ has an acceleration $a_0+a$, all from the lab frame(inertial). The answer calculated thus does not match with mine. The texbook gives $$a_0=\frac {g}{1+ \frac {m_1(m_2+m_3)}{4m_2m_3}}$$ The question is, what is the problem with considering the pulley B and the masses $m_2$ and $m_3$ as a single system of mass $(m_2+m_3)$? Or do we have to take some precautions, when the system is accelerated? (The textbook solution is perfectly alright and I understood it too, but what is the problem with mine?)


title: How is this the graph of induced emf against angle for a rotating coil in a magnetic field?

text: So a coil is rotating in a magnetic field, and at $\theta=0$ the coil is perpendicular to the field lines. At $\theta=90$ the coil is parallel to the field lines. The the angle, theta, is the angle between the normal to the coil and the direction of the magnetic field lines. This implies that the magnetic flux induced in the coil will be at a maximum when $\theta=0$ and 0 when $\theta=90$. The question I was asked was to sketch a graph of induced emf, $\epsilon$, against $\theta$. Since $\epsilon=\dfrac{\Delta\phi}{\Delta t}$, where $\phi$ is the magnetic flux linkage, the induced emf should be at a maximum when the magnetic flux is a maximum. So at $\theta=0$, $\epsilon$=maximum and at $\theta=90$, $\epsilon=0$. This means that the curve sketched should look like a cosine graph, starting at the maximum value for emf induced. However, in the mark scheme for this exam question the correct answer was a sine graph. It says that at $\theta=0$, the emf induced is zero. How can this make sense? Is my logic wrong?


title: Detecting if resistances are parallel or series in complex circuits

text: I know how to detect when resistors are arranged in parallel or series arrangement and   I can also find their equivalent resistance in simple circuits or when resistances are connected in form of   triangle but what happens when the arrangement is complex like this :   ![Resistors](http://i.stack.imgur.com/MM06V.png) Which resistors are parallel and which are in series ? How can I find the equivalent resistance in such cases ? Is there rule or method for figuring this out ?


title: Dr. Masaru Emoto and Water Message

text: I have been viewing this video :   Masaru Emoto's Rice Experiment   Anybody has any physical explanation of this phenomena?


title: Neutral axis of T shaped beam?

text: I am not a mechanics or physics student but a computer science student. I came across a question related to find neutral axis of figure but I do not have slightest idea of what it is and how to find it. Can someone please tell what would be neutral axis and how is it calculated for following T shaped beam? ![For following T beam](http://i.stack.imgur.com/wcuyB.jpg)


title: Adiabatic theorem in the regime of quantum optics

text: I am wondering whether there is a version of adiabatic theorem in the regime of quantum optics. My understanding of quantum optics involves with the interaction between photon and atom. This interaction has always been almost instant. But the perturbation for adiabatic theorem needs to be as slow as possible. This is what confuses me. Is there any adiabatic theorem for quantum optics at all?


title: Newton's rings experiment

text: 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?


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

text: 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.


title: Spring with changing equilibrium

text: Suppose that we have two cars on a track, each with a different mass. Now suppose that the cars are connected with a spring. We smack one car. I would like to write down the equations of motion for this scenario and solve them but I am just a lowly mathematician who has never really studied physics. My attempt yielded this ODE $$m_1x_1''(t)-m_2x_2''(t)= -k(x_1(t)-x_2(t))-c_1x_1'(t)+c_2x_2'(t)$$ where $c_1$ and $c_2$ are the coefficients of friction, $m_1$ and $m_2$ are the masses, and $k$ the spring constant. Is this correct? How do I solve?


title: Difference between a quantum process and a thermal process?

text: 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


title: How is the current flow perpendicular to the wire?

text: 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.


title: Is the Dirac Lagrangian Hermitian?

text: 1. I'm wondering of the Dirac Lagrangian density $$\mathcal{L} =\overline{\psi}(-i\gamma^\mu \partial_\mu +m)\psi $$ is an hermitian operator, since upon complex conjugating one gets $$\mathcal{L}^\dagger =\psi^\dagger(i\gamma^0\gamma^\mu \gamma^0 \partial_\mu +m)\gamma^0\psi$$ $$ =\overline{\psi}(i\gamma^\mu \overleftarrow{\partial_\mu} +m)\psi \neq \mathcal{L}.$$   2. And should a Lagrangian always be Hermitian ? I know that a Hermitian operator has real eigenvalues, which is desirable for a operator describing observables. But here the Lagrangian isn't really an observable since it is determined modulo an total derivative.   3. I've found a related question on the site: were it is said that  > "the derivative $\partial_\mu$ in the Dirac Lagrangian is antihermitian" (Is > the Lagrangian density in field theory real?) can someone show me how to demonstrate this ?


title: Quantum Mechanical Meaning of Atomic Orbitals

text: According to quantum mechanics, for multi-electron atoms, a single electron around the nuclei can be in the state of linear combination of different eigen energy states. In that case, even the energy of the electron is not one of the eigen energies. In chemistry, we often say that an electron is in an orbital (such as 1s, 2s), another electron is in another orbital, etc. How does it make sense if an electron is in a linear combination state?


title: We create systems with different values of Energy?

text: I understand that Energy is a conserved quantity in a system. A number, that's always the same to the system. However, don't we determine such a number? I mean, we can create systems(Or study them usually) and see the amount of Energy tit can have. Correct? Because to me, Energy is a confusing concept... Why was it even created? Work is a good explanation, but what's the use of Energy? It's not something physical, isn't it our manifestation? We created that concept, to explain work? or what? What's is the importance of Energy, why do we need such a concept? It's not something real, it's just a mathematical expression taken to extremely in Physics. It's such a confusing subject... And everyone in Physics, act's as if Energy is something "given". Why? It's a number! A measurement of work! And what about E=mc^2?! How do we define Energy here? A number as well?


title: Why potential energy of a dipole in an electric field has a negative sign?

text: In the following equation $$V = -\mathbf{P}\cdot \mathbf{E}$$ why I have to take Potential Energy as negative. Is there any simple reason behind this ? I am preparing for my high school examination.


title: To what extent are the astronomically observed black hole candidates compatible with GR black holes?

text: Do they all fit Schwarzschild black holes? How people compare them with more complicate BH solutions as spinning BH solutions (even if they are not known analytically), say. I'd like more than qualitative comments, if possible.


title: Does Hawking radiation break asymptotic flatness?

text: Basically what the question says -- there is reason to expect that, if allowed to continue long enough for the radiation to reach future null infinity, the fact that the radiation will fall off at $\frac{1}{r}$ will break the set of conditions required for the enveloping metric to stay asymptotically flat, which will, in turn, combined with the fact that the spacetime is inherently neither static nor stationary, will subsequently remove most of the nice features that enabled us to derive the Hawking radiation in the first place. If this is true, why is it common for people to make claims like "The black hole will eventually completely evaporate?", and other statements relating to conditions where an appreciable proportion of the black hole's initial mass has left the horizon?


title: Why change in internal energy is zero in isothermal process

text: In isothermal process $\Delta U =0$. But I am having trouble understanding it. Say we have an ideal gas, and say my temperature is constant but I move the pressure, volume from $(P, V) \to (P-dP, V+dV) $. So the volume has expanded and system has done some work to the surrounding. So my work is non-zero. So how come $\Delta U=0$? I am really confused here.


title: Fukushima vs Thorium

text: This is **not** a question about traditional nuclear power plants vs the thorium based. But about the Fukushima plant itself and the very negative environmental effects from its meltdown of reactors 1 and 3 vs a Thorium based design under similar natural stressors. Fukushima leaking radioactive water for ‘2 years, 300 tons flowing into Pacific daily’ This is the basic outline of what happened to cause the melt down. > Immediately after the earthquake, the remaining reactors 1–3 shut down > automatically and emergency generators came online to power electronics and > coolant systems. However, the tsunami following the earthquake quickly > flooded the low-lying rooms in which the emergency generators were housed. > The flooded generators failed, cutting power to the critical pumps that must > continuously circulate coolant water through a Generation II reactor for > several days to keep it from melting down after shut down. After the pumps > stopped, the reactors overheated due to the normal high radioactive decay > heat produced in the first few days after nuclear reactor shutdown (smaller > amounts of this heat normally continue to be released for years, but are not > enough to cause fuel melting). http://en.wikipedia.org/wiki/Fukushima_Daiichi_nuclear_disaster I am just wondering if this was a Thorium reactor, would all of this had taken place in the first place? Because thorium needs to be constantly primed and not cooled. I am not an engineer nor a paid scientist so please excuse my ignorance. I am just very curious. Thanks.


title: What is the usefulness of the Wigner-Eckart theorem?

text: I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's _Modern Quantum Mechanics._ I was wondering if someone could tell me why it is useful and perhaps just help me understand a bit more about it. I have had two years of undergrad mechanics and I think I have a reasonably firm grasp of the earlier material out of Sakurai, so don't be afraid to get a little technical.


title: What causes gravity?

text: What causes gravity? Why is there attraction between masses? Is it due to time or space distortion?


title: Application of Noether's theorem

text: > Consider one parameter transformation: $y = y ( \tilde{y}, \alpha)$ such > that lagrangian satisfies: $\tilde{L}(\tilde{y}, \alpha) = L(y ( \tilde{y}, > \alpha))$. We say that equation is invariant under this transformation if: > $$\tilde{L}(\tilde{y}, \alpha) = L(\tilde{y}) + > \frac{dF(\tilde{y},\alpha)}{dt}$$ Show that: $$\int \frac{\delta L}{\delta > y_t} \frac{\partial y}{\partial \alpha} dx - \frac{\partial F}{\partial > \alpha}$$ is a constant of motion. Here $\tilde{y}$ is an old field before transformation, so is lagrangian $\tilde{L}$. Space is 2-dimensional $(x, t)$ and the exercise is listed in section concerning KdV equation. Any hints?


title: Why do physicists believe that there exist magnetic monopoles?

text: One thing I've heard stated many times is that "most" or "many" physicists believe that, despite the fact that they have not been observed, there are such things as magnetic monopoles. However, I've never really heard a good argument for why this should be the case. The explanations I've heard tend to limit themselves to saying that "it would create a beautiful symmetry within Maxwell's equations" or similar. But I don't see how the fact that "it would be beautiful" is any kind of reason for why they should exist! That doesn't sound like good science to me. So obviously there must be at least another reason apart from this to believe in the existence of natural magnetic monopoles. (I'm aware that recent research has shown that metamaterials (or something similar) can emulate magnetic monopole behaviour, but that's surely not the same thing.) Can anyone provide me with some insight?


title: Trying to model pinball physics for game AI

text: I'm working on an AI for a pinball-related video game. The ultimate goal for the system is that the AI will be able to fire a flipper at the appropriate time to aim a pinball at a particular point on the table. We are using an engine that will handle the underlying physics interactions when the ball is hit (Unreal). I'm trying to quasi-realistically model the physics for the AI's "thinking". I have a reasonable understanding of Newtonian physics but I'm going to need some help making sure I'm correct about everything I may need to account for. For the purposes of simplification, I'm considering the table to be vertical on an XY axis with gravity just being a small fraction of actual gravity accelerating down on the Y axis (yes, this means I'm ignoring friction between the ball and table, for now). By my understanding, I've got the work with the following when a ball is rolling along a flipper.   * The ball will have velocity along both X and Y axes as it rolls to the flipper.   * The flipper will have a range of motion (minimum and maximum angles) and a Torque value.   * When the flipper fires, it will apply force to the ball based on the flipper's Torque, the distance the ball is from the flipper's rotation point, and the length of the arc the contacted point on the flipper needs travel.   * The applied force will accelerate the ball back up the table following a new trajectory. My question(s) are: Am I overlooking an important interactions in this system? Or am I misinterpreting anything? Does it seem like this is a reasonable modeling for video game? Et cetera? Thanks!


title: Are there any serious alternatives to QCD nowadays?

text: 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.


title: How do you add temperatures?

text: This will probably be considered very simple, but I am just a beginner: I'm developing a software application where temperatures need to be added and subtracted. Some temperatures are in Celsius, some in Kelvin. I know how to convert to/from Kelvin (273.15), but how should one go about adding and subtracting these? Should everything be converted to Celsius first? For example:               0°C + 0°C = 0°C     0°C + 500°C = 500°C      But:               0°C + 273.15K = ?      If we put everything in Kelvin, we get:               273.15K + 273.15K = 546.3K      If we put everything in Celsius, we get:               0°C + 0°C = 0°C      But obviously, 546.3K isn't equals to 0°C. Now, you might say I can't add temperature to temperatures (but should be adding energy or something? not sure). But the reason I'm doing this is because we need to interpolate. I have a collection of key-value-pairs, like this:               973K  -> 0.0025     1073K -> 0.0042     1173K -> 0.03     1273K -> 0.03      Now I need to get the value for 828°C. So I need to interpolate, which means adding/subtracting values. I hope I'm making sense.


title: Can an electron make a transition between sub energy states of the same energy level?

text: Electrons make transition between different energy levels - say, $n =3$ to $n=2$ or $n =1$, as per the applicable selection rules. My question is: _can an electron make transitions between sub energy states of the same energy level?_ For example: if an electron is in the $n=3$ energy level, can it make a transition between different sub energy states of $n=3$ following the selection rules?


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

text: 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/


title: Newton's third Law?

text: **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?


title: Equivalence principle and acceleration vs a gravitational field

text: I picked this up on the net: _Einstein came to realize the principle of equivalence, and it states that an accelerated system is completely physically equivalent to a system inside a gravitational field._ When I am being accelerated I will pick up speed over time. This will have a noticeable effect, e.g. there will be an increasing blue-shift in the light of stars which lie in the direction of acceleration. This will not happen if I am just in a gravitational field and I could well distinguish acceleration from gravity. I suspect that being _completely physically equivalent_ may be a bit of an overstatement and is only true as long as I don't look outside? Or is the solution, that I cannot really know, whether those stars are being accelerated too? So when I feel the gravity and I see a constant blue shift, I might conclude that I am being accelerated, but all these stars are being accelerated the same as me? Or is there a way to interpret gravity as acceleration, which also leads to an increasing red/blue shift?


title: efficiency of electric cars vs gas?

text: I have been listening to my friends brag about electric cars and I can't seem to convince them that electricity is not some magic force that comes out of the wall outlet. It must be produced somewhere, in most cases by a coal fired plant, where the chemical energy of hydrocarbons are are transformed to electrical energy by a generator, which is then transmitted hundreds of miles, where it is transformed to ionic energy in a charged battery in a car, which is then converted again into mechanical energy by the engine which turns the tires. Every time the energy is converted to a different form it loses most of its potential right? Isn't it much more efficient to burn fossil fuels directly at the source - the cars engine? Unless the electrical plant powering the batteries of an electric car is nuclear or hydro, do not electric cars increase total emissions? Anyway, I'm just looking for opinions? am i crazy?


title: Is a photon "fixed in spacetime"?

text: 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?


title: How does a photon experience space and time?

text: 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.


title: How do photons experience time?

text: 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?


title: How is the universe is experienced at light speed?

text: 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?


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

text: 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?


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

text: 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.


title: Life of a photon

text: 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.


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

text: 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.


title: Highly diminished image of an Object placed at Infinity

text: ![enter image description here](http://i.stack.imgur.com/SGAoC.jpg) Consider an object at infinity. The rays coming from it are parallel to each other. Let one of the parallel rays pass through the focus $F_1$ of a thin lens, and let a second ray pass through the optical center $O$. The ray which passes through $F_1$ becomes parallel to the principal axis after refraction and the ray which passes through the optical center does not suffer any deviation. We therefore get the image as formed at $F_2$, inverted, real and highly diminished. My question is: without comparing the size of the image with the size of the object placed at the infinity, how can we say that the image is **highly diminished**?


title: Why only fully connected diagrams contribute to T matrix

text: In Peskin's introduction to QFT, he wrote: > only fully connected diagrams, in which all external lines are connected to > each other, contribute to the T matrix. I don't understand this statement. Suppose we have many particles in initial and final state, and two independent reactions take place, then we will have a diagram which contains two pieces. The initial and final statse are different, so the diagram cannot be classified in the `1` in `S matrix`. So it should be in `T matrix`. Do I have anything wrong?


title: Can a mass matrix be asymmetric?

text: I am developing a mathematical model of a mechanical device consisting basically of coupled harmonic oscillators. It turns out that the system mass matrix is asymmetric. I seem to read somewhere that a mass matrix has to be symmetric, but I am not sure. So I would like to know whether it is possible for a mass matrix in this case to be asymmetric. If it can't, what are the physical implications of an asymmetric mass matrix in this case?


title: Problem deriving displacement from accelerations

text: I have a problem deriving displacement from an accelerometer; I want a time series of displacement so I used numerical integration twice; I based my code on the trapezium rule and so did something like this to get velocity and again to get displacement; while (i However, I just tested my method and the displacement values are not sensible suggesting very small strides. Obviously there is a problem with my approach and I know that errors can be accumulated this way, any ideas of a way around this?


title: How large must the Quantum teleportation fidelity have to be in order for it to be useful?

text: This question relates and stems from my original question. Please read this one and the comments before answering this question. Quantum Teleportation Fidelity I know that for discrete variables quantum teleportation, one needs a fidelity greater than 50%, otherwise you could produce that state by classical means. For continuous variables quantum teleportation, it needs to be greater than 75% for the same reason as discrete variables. Many experiments have shown quantum teleportation in discrete and continuous variables cases, but how large must the fidelity need to be in order for it to be considered "useful"? Does it depend on application? Moreover, let me offer an example: If the "exact" quantum state of a physical system was transferred to another physical system, where the two physical systems were made out of the same particles, then it wouldn't it mean that it is "as if" the original object disappeared from one location and reappeared at another? My understanding and reasoning is that since the quantum state of a physical system is literally the only thing that allows us to distinguish quantum systems from each other, then if the quantum state is teleported to from one physical system to another physical system that's made up of the same particles, the physical system literally "becomes" the object. Branching from this, say you had 97% fidelity in teleporting the vibrational state of a diatomic molecule to another diatomic molecule. Since quantum states change all the time due to constant interactions from the environment, then transferring 97% of the the original quantum state would basically give you the real system because it too would be subjected to tons of interactions right after the transfer. What I'm saying is that comparing a 100% transfer fidelity scenario to a 97% scenario, you'd end up with the diatomic molecule basically behaving in the same way as the original because there's so many interactions that would mess up the state anyway. So, is this valid in saying that its still useful to teleport, even if technically the quantum state is not the same, but its "effectively" the same?


title: Has unnaturalness motivated new ideas in physics?

text: The cosmological constant problem arises because the natural scale of the cosmological constant is $10^{120}$ times larger than what we observe. This implies that the dimensionless constant is much smaller than one and that is considered to be unnatural (though that's a perfect logical possibility). The hierarchy problem is of a similar nature. My question is whether a similar kind of reasoning motivated by unnaturalness has been useful to physics in the past. I.e., is there any example where some constant was deemed unnatural and to resolve the issue new physics was discovered? I would like examples from settled physics rather than from speculative theories. (So supersymmetry doesn't count.)


title: Surface gravity for a rotating charged black hole

text: 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?


title: Lorentz transformation implemented by a non-unitary operator.

text: One often come across in QFT sentences like the following, for instance: > ...under a Lorentz transformation $\Lambda$ implemented by the unitary > operator $U(\Lambda)$, a Dirac field transforms as > > $$ U(\Lambda)^{-1}\Psi(x)U(\Lambda) = D(\Lambda) \Psi(\Lambda^{-1}x),$$ > where the matrix $D$... What would be the other case, i.e. implemented by a non-unitary operator? Is $N(x)$ an example of such an operator? $N(x):=\mathrm{i}x+x^2$.


title: Anderson localization in 1d, 2d and 3d

text: Why in 1d and 2d systems, all states will be localized for infinitesimal disorder, but in 3d only states with energy lower below mobility edge will be localized?


title: Determining if a semiconductor is n-type, p-type or intrinsic

text: The probability that an energy state in the conduction band is occupied by an electron is 0.001. Would this semiconductor then be n-type, p-type, or intrinsic? Notation that I use: $E_F$ represents the fermi energy level, $E_C$ represents the energy level of the conduction band, and $E_V$ represents the energy level of the valence band. $E_{Fi}$ represents the fermi level of an instrinsic semiconductor. We know that the $E_F$ is where the majority of the electrons are. Because the probability that an electron is in the conduction band is 0.001, we know that there are very few electrons in the conduction band. In that case, that means that $E_F$ is very far from $E_C$ and is instead close to $E_V$. Because $E_F$ < $E_{Fi}$, the semiconductor is p-type. The semiconductor is actually n-type. What is the flaw in my understanding?


title: Tesla to Newtons

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


title: Can symmetry be restored in high energy scattering?

text: Suppose you have a field theory with a real scalar field $\phi$ and a potential term of the form $\lambda \phi^4 - \mu \phi^2$ that breaks the symmetry $\phi \to - \phi$ in the ground state. Is this symmetry restored in a scattering with high momentum transfer in any physically meaningful way? My problem is that there is no background field for which I could take a mean field approximation, so the usual argument for phase transitions does not work. One thing that came to my mind is that the potential will have higher order corrections, so maybe one could ask which way these corrections work in the limit $\Lambda \to \infty$, where $\Lambda$ is a UV scale? I know the first order correction for small $\phi$ does actually contribute to the breaking rather than to restoration, but then that doesn't seem to be the right limit for the scattering. If you don't know the answer I'd also be grateful for a reference. (Please do not point me to references that are for in-medium effects, nuclear matter etc, as I have plenty of these and it's not addressing my problem.)


title: Have there been more distinctive names suggested for neutrino mass states $\nu_1, \nu_2, \nu_3$?

text: The different mass states of neutrinos are generally named $\nu_1, \nu_2, \nu_3$. By comparison, the names of quark mass states (`up`, `down`, `strange`, and so on) or the names of mass states of charged leptons (`electron`, `muon`, `tau(on)`) appear more distinctive, or whimsical. Have there been perhaps any suggestions of correspondingly less generic "proper names" for each of the (three distinct) neutrino mass states?


title: How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

text: I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, but knowing the momentum operator (1), how can I get the position operator (2)?


title: what are the main factors holding back magnetic energy storage systems?

text: Perhaps is it the magnet's own magnetic field that causes it to lose its superconductive state? It seems as though these systems could become incredible energy dense.


title: Walking along a moving train, we make 18 steps. Opposite: 11. How long is the train?

text: > _A man walks in the same direction as a slowly moving train ($v_{man} > > v_{train}$). He counts the train to be 18 steps long. Then he turns around > and counts the train to be 11 steps long._ > > _(Suppose both man and train are moving at a constant speed; every step is > the same length.)_ > > _How long is the train?_ * * * For some reason I always end up with two equations and four unknowns... I'd really appreciate a solution!


title: Justification for smeared fields in the Wightman axioms?

text: 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?


title: Does a light cone look the same from all reference frames?

text: If there were a light cone centered at some point $P$, and you were to look at that light cone from different reference frames, would it change its shape? I know that points inside and outside the light cone would remain inside/outside of the light cone in every frame, but does the light cone itself shift? If it does, how would it shift?


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

text: 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._


title: Does the particle number in the universe need to increase?

text: Can someone give me an example of a physical process - some (realistic) scattering process - in which one can observe that the particle number has decreased? I was wondering, because it is relatively easy to create antiparticle-particle pairs, but is there a process that in some sense makes up for that, or does the overall number of (fundamental) particles (say in the universe) just keep increasing? Edit: (I have also changed the title of my question, sorry) So far the photoelectric effect and the gluon + gluon --> Higgs process have been mentioned. So interestingly the number of gauge bosons can decrease. But are there processes for leptons or fermions where the particle number decreases or is it true that these numbers keep increasing in the universe?


title: thermal energy while calculating Langevin Forces

text: I have a quick question from thermodynamics. I remember that we take kT/2 as the kinetic energy per degree of freedom in kinetic theory of gases. But when we do langevin forces (for example in cavity dynamics), do we take the average thermal energy as kT/2 or kT ?


title: What is band filling effect?

text: 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.


title: The "stationary potential energy" condition for static equilibrium in mechanical systems

text: I've often read that, for a mechanical system which can be described by $n$ generalized coordinates $q_1,...,q_n$, a point $\mathbf{Q}=(Q_1,...,Q_n)$ is a point of equilibrium if and only if the potential energy $U$ is stationary at that point, i.e. iff $\frac{\partial U}{\partial q_i}(\mathbf{Q})=0$ for all $i$. I've only seen a proof for the unidimensional case $n=1$, that uses the Lagrangian of the system to show that if the system is in $q=Q$, with $\dot q=0$, then $\ddot{q}=0 \iff \frac{\partial U}{\partial q}(Q)=0$ (in this case it is also easy to obtain the _stable_ equilibrium condition $\partial ^2 U/\partial q^2>0$). Following this example I was trying to prove the statement for the general case, however probably some steps aren't correct for the general case. The Lagrangian is (using Einstein's notation for summations $a_ib_i\dot{=}\sum _i a_ib_i$): $$L (\mathbf{q},\mathbf{\dot q})= T(\mathbf{q},\mathbf{\dot q})-U(\mathbf{q})=\frac{1}{2}\dot {q_i} A_{ij} \dot {q_j}-U(\mathbf{q}),$$ where I've expressed the kinetical energy as a quadratic form of the generalized velocities and $A_{ij}$ are functions of $\mathbf{q}$ (as I said, I don't know if this is generally possible). Now we have:$$\frac{d}{dt}\frac{\partial \cal L}{\partial \dot{q_i}}=\frac{d}{dt}[A_{ij}\dot q_j]=\dot{q_k}\frac{\partial A_{ij}}{\partial q_k}\dot{q_j}+A_{ij}\ddot{q_j},$$ and $$\frac{\partial \cal{L}}{\partial{q_i}}=\frac{1}{2}\dot{q_k}\frac{\partial A_{kj}}{\partial q_i}\dot{q_j}-\frac{\partial U}{\partial q_i}.$$ So, if all velocities $\dot{q_j}=0$, the equations of motion are:$$A_{ij}\ddot{q_j}=-\frac{\partial U}{\partial q_i},\qquad i=1,...,n.$$ Now, I see that if the system is in equilibrium in $\mathbf{Q}$, then, for all $j$, $\ddot {q_j}=0$ and it is required that $\partial U / \partial q_j = 0$. What about the vice-versa? Does $\partial U / \partial q_j = 0 \ \forall j \implies \ddot{q_j} = 0 \ \forall j$? I see that this is equivalent to require $\det A\neq0$, where $A$'s elements are $A_{ij}$, so is there a reason why it must be so? Thank you for your time.


title: Is ch. 2, sect. 4 of The Feynman Lectures on Physics, Vol. 1 still accurate?

text: The chapter 2 section 4 of volume 1 is on nuclei and particles. Here are a few things that trouble me. Dr. Feynman says that > Another most interesting change in the ideas and philosophy of science > brought about by quantum mechanics is this: it is not possible to predict > exactly what will happen in any circumstance. For example, it is possible to > arrange an atom which is ready to emit light, and we can measure when it has > emitted light by picking up a photon particle, which we shall describe > shortly. We cannot, however, predict when it is going to emit the light or, > with several atoms, which one is going to. You may say that this is because > there are some internal "wheels" which we have not looked at closely enough. > No, there are no internal wheels; nature, as we understand it today, behaves > in such a way that it is fundamentally impossible to make a precise > prediction of exactly what will happen in a given experiment. Has this statement changed at all? He says that there are no internal wheels. At one point I also remember him mentioning that we do not know what is going on inside a nucleus. Is this still true? One more extract is this: > just like with a field of interaction between charges and photons, we made > quantumelectrodynamics, with a field of interaction between neutrons and > photons, we can make quantum'NUCLEO'dynamics He later mentioned that the calculations are going on for 20 years and are too complicated to solve. What about this theory? Has it been proven or disproven? Or are we still not capable of calculating it? The last thing that bothers me with this chapter is this: > So we are stuck with a theory [he is talking about the pion and mesons > etc.], and we do not know whether it is right or wrong, but we do know that > it is a little wrong, or at least incomplete. While we have been dawdling > around theoretically, trying to calculate the consequences of this theory, > the experimentalists have been discovering some things. For example, they > had already discovered this m-meson or muon, and we do not yet know where it > fits. Also, in cosmic rays, a large number of other "extra" particles were > found. It turns out that today we have approximately thirty particles, and > it is very difficult to understand the relationships of all these particles, > and what nature, wants them for, or what the connections are from one to > another. Is this condition still the same? Have we tied the loose ends together yet? Or do we still not know what these particles do? What is the prevailing theory currently about these particles?


title: Why is the computer useful if a chaotic system is sensitive to numeric error?

text: In every textbook on chaos, there are a lot of numerical simulations. A typical example is the Poincare section. But why is numerical simulation still meaningful if the system is very sensitive to numerical errors?


title: Voltage across an inductor contradicts Lenz's law?

text: Imagine a simple circuit consisting of an alternating current source connected to an inductor. Assume they are connected in the following fashion: AC source - terminal A - Inductor - terminal B - AC source. When the current flows from terminal A towards terminal B and is increasing, the inductor should generate electromagnetic force that opposes the increase in current (according to Lenz's law), that is terminal B should become positive with respect to terminal A. But simulation shows the opposite is true. Terminal A becomes positive with respect to terminal B. Why?


title: Two definitions of Riemann curvature tensor

text: I am relatively used to the coordinate free expression of the Riemann tensor: $$ R(X, Y)Z=\nabla_X\nabla_Y Z - \nabla_Y\nabla_X Z - \nabla_{[X, Y]} Z, $$ where $\nabla$ is the Levi-Civita connection on a (pseudo)-Riemannian manifold and $X, Y, Z$ are contravariant vector fields. This $R$ is a tensor field with $3$ covariant indices and $1$ contravariant index. Problem is, I am having a hard time figuring out why the following formula (taken from Wald, "General Relativity", §3.2) defines the same tensor field: $$ R_{abc}{}^d\omega_d=\nabla_a\nabla_b\omega_c - \nabla_b\nabla_a \omega_c,$$ where $\omega$ is an arbitrary _covariant_ vector field. (This formula uses the abstract index notation, but I think it can be safely read by interpreting indices the usual way). Can you show me how to prove equivalence or point me to some reference?


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

text: _[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


title: Should theory be the appropriate term?

text: Should theory be the appropriate term? I mean, for example, because of the quantum field theory we have been able to find the subatomic particles that it theorized and make the Standard Model. Why then is is labeled as a theory? Also wave-particle duality is widely accepted fact yet labeled as a theory. What is up with that, why call it a theory. Maybe because it promotes the fact of idealism?


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

text: 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?


title: Bose-Einstein Condensate with T>0  in Theory and Reality

text: I am interested to understand how positive entropy Bose Einstein condensation for cold atoms (say) behave. The way I think about it is as follows: We have an ideal pure state where every atom is in the same ground state which depends on a geometry of a certain trap and the atoms do not interact. Now, naively, I thought about the actual positive-entropy state looking as one of the two following alternatives: (1) Every atom get excited with some small probability p. A different picture is as follows: (2) If the type of the intended ideal state puts every atom in the same ground state A (where A, say, depends on the geometry of the trap), then the positive-entropy state is obtained by mixing this ideal state with a state which is Bose Einstein state w.r.t. a different ground state B (or many such B;s). I asked around a little and what I was told is that the T>0 theory is not part of the original theory discovered in the 1920s but rather a more recent theory that was developed in the 1990s. Moreover, the perturbation for the ideal pure state described by the T>0 state manifests pairwise interaction between the atoms, and that there are interesting singularities that occur immediately when T>0 no matter how small. I will be very thankful for some explanations and references. Most helpful for me will be non-technical explanations. **Update:** I am aware of one book on a related topic: The Poincare seminar 2003 on Bose Einstein Condensation - Entropy. (I did not get a hold of it yet but a few of the papers are here.) I will appreciate any information regarding the matter. Genneth recommend the book Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford Graduate Texts) by Anthony Leggett.


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

text: 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?


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

text: 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?


title: Black and white matters. But why and how?

text: I know black conducts heat while white reflects it. But they are colors after all. If a metal is painted black, it conducts more heat or at a rapid speed than it would do before it was coated. But, as far as I know, colors don't have any special "substance" in them, which might trigger the sudden absorption of heat or reflection of the same. What is the physics behind this? Are colors by themselves, some catalyst kinda thing?


title: Can a point source be located more accurately out-of-focus or in-focus?

text: Let's say I am taking a picture, and I know _a priori_ that the image is of a single ideal point source of light at infinity. With a perfect imaging system **in focus** , the image shows an Airy disk. I already _knew_ to expect an Airy disk, so I can do some mathematical fitting to guess the center of the Airy disk. That's my best guess for the source location. Alternatively, the imaging system might be somewhat **out of focus**. The image would show a much bigger blurry circle. Again, I can do some mathematical fitting to guess the center of the blurry circle. Again, that's my best guess for the source location. **My question is: Which approach would give me more accurate information about the location of the point source?** I can't see an obvious answer. In the out-of-focus image, you are drawing useful information from a much greater number of pixels, which is usually helpful in mathematical fitting. (Particularly if a large pixel size limits the resolution.) On the other hand, we normally say that defocusing an image simply erases its small-scale information, and I've never heard of anyone defocusing an imaging system on purpose like that!


title: Dopler Shift for Reflected Sound Waves

text: If a car was going at near mach-1 speed heading towards a wall and honked its horn. What frequency would the driver measure the reflected sound wave? I trying to think about this reasonably, but the answer I get is somewhat not what I initially expected. Here is my current thinking, correct anything you might deem wrong. First let's pretend there is no reflection but instead the wave comes from another source moving head on to the observer with equal and opposite velocity. So then we have the receiver moving towards the source, and the source moving towards the receiver. Using the Doppler shift equation, the observed frequency is upshifted by a factor of (c+v)/(c-v), where c is the speed of the sound wave, and v the speed of the car. I suppose the interesting thing is that the source and receiver are actually the same, but there is still a shift due to the reflection. Or, maybe I made a mistake in my logic.


title: what if the time is zero in one reference frame

text: 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 $$\Delta t^\prime = \gamma \Delta t$$


title: Subatomic particle mass and Benford's Law

text: Nine out of 15 subatomic particle masses begin with the digit one. Benford's Law would imply 30% with one as the leading digit. Is there any significance to this frequency distribution, such as perhaps it implies 15 undiscovered subatomic particles?


title: Spaceship split near event horizon

text: Lets say there's two astronauts, Alice and Bob, going on a space trip to a super-massive black hole. So large that they wouldn't notice any significant spaghettification forces at the event horizon. Alice is sitting on the left, and Bob on the right. They go so close to the event horizon, that Bob enters the event horizon, but Alice does not. The event horizon is splitting the spaceship. Alice's side of the spaceship is travelling at a velocity greater than the escape velocity of the black hole, so presumably will escape it's fate. What do Alice and Bob see? Bob is apparently doomed, but Alice should be able to survive, but it seems like she has to tear the spaceship apart. And what do they see? Does Alice just see Bob moving closer and closer to the event horizon but never crossing it, whereas Bob sees Alice moving further and further away from him until he crosses the even horizon and she disappears?


title: Why does light travel in a straight line through a liquid?

text: So I was reading a document that stated that when traveling through a material (I'll use a liquid here, maybe water), a photon actually always traveled at 300,000 km/s, it was just that it occasionally 'hit', was absorbed and then re-emitted by water molecules along its path. It was this absorption and re-emission that made the speed of a photon appear slower overall, but that "in between" hitting molecules it had the same 300,000 km/s speed. My questions:   * Is this a correct way of thinking about why a photon moves more slowly through water?   * If it is, how would the photon "know" to exit the water molecule heading in the exact same direction that it was heading when absorbed?


title: Relationship between torque and angular momentum

text: I want to know how to deduce the equation $\vec{\tau}=\vec{\omega} \times \vec{L}$, where $\vec{\tau}$ is the moment of force (also known as torque), $\vec{L}$ is the angular momentum, $\vec{\omega}$ is the angular velocity.


title: frequencies of light

text: Why are available frequency of light continuous ? I keep hearing that atoms absorb (and emit ) photons of particular frequency which correspond to their energy levels of their electron. Where do all other colours come from ?


title: How to express continuous values as a matrix

text: Usually a quantity of a matrix is defined as the eigenvalues of the matrix. If so, how can anyone express continuous values, as in Schrodinger picture, into a matrix?


title: What does a Field Theory mean?

text: What exactly is a field theory? How do we classify theories as field theories and non field theories? **EDIT:**   1. After reading the answers I am under the impression that almost every theory is a field theory. Is this correct?   2. What is difference between QM and QFT?


Title says it all. If hydrogen and helium are lighter than air, why won't liquid hydrogen and liquid helium defy gravity?


title: Can any rank tensor be decomposed into symmetric and anti-symmetric parts?

text: I know that rank 2 tensors can be decomposed as such. But I would like to know if this is possible for any rank tensors?


title: Is there a default notation for 4-vectors while handwriting?

text: In printed paper 3-vectors can be denoted bold italic while 4-vectors can be denote just bold. While handwriting 3-vectors are denoted by arrows above letters. Is there a similar way to denote 4-vectors? I mean except indexed Einstein notation. **UPDATE** I am just reading Misner Thorn Willer and wish to conserve their notation (p. 20): ![enter image description here](http://i.stack.imgur.com/SZbeJ.jpg)


What maintains quark spin alignments in baryons? The $uud$ proton and $udd$ neutron are both spin 1/2, implying that two of their spin 1/2 quarks are always parallel and the other is always opposed. In contrast, the $\Delta^+$ particle (which like the proton is $uud$) and the $\Delta^0$ particle (which like the neutron is $udd$) are both spin 3/2, implying presumably that the same principle keeps their internal quark spins all parallel. What principle keeps trios of quarks aligned or anti-aligned in such specific ways?


title: Inverse Square Law in Beta Radiation

text: **Setup:** A radioactive source is placed at alternating distances from a Geiger Counter. Counts per second for 10 different distances (each spaced 1 cm apart) were taken for preset times ranging from 200 to 2000 seconds (depending on how far the source is from the counter). **Objective and Question:** We are plotting counts per second vs source-to- counter distance for our sample, which emits beta radiation. We expect it to be $\frac{1}{r^2}$ dependance by the inverse square law, however we are getting less than $\frac{1}{r^2}$ dependance for larger distances (i.e) we are getting fewer counts than predicted by the inverse square law. At first we thought it was the air particles interacting with the beta particles, but that shouldn't have anything to do with it (according to the instructor), and the lab question hints it should have something to do with the geometry of the experiment. Can someone please help me understand this problem?


title: Energy transfer in elastic collision

text: In a given reference frame where object 1 (with known mass and velocity) collides elastically with object 2 (with known mass and velocity), can we identify which object loses kinetic energy? Is it always the more massive one? The faster one?


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

text: 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?


title: Is the uniqueness theorem correct in superconductivity?

text: There is an uniqueness theorem in electromagnetism. It says that the solution of Maxwell's Equations is determined uniquely by boundary conditions. We can treat superconductivity as a completely diamagnetic material with magnetic susceptibility $\chi=-1$. I think the uniqueness theorem is still correct in this case, but I am confused very much. If we think about a superconducting ring, and we know the magnetic field at infinite distance, the boundary condition at infinity, we can not be sure about the magnetic field. We don't know whether the ring have flux. If we cool down the material before adding the magnetic field, the ring will have a zero flux. If we add the magnetic field before cooling down the ring, the ring will have a non-zero flux. Does it mean that the uniqueness theorem is not correct? The solution is not determined by state of the system only, but is determined by history and state of the system. Could you answer my question? Thank you very much!


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

text: 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)?


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

text: 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.


title: Difference between periodic oscillation and periodic movement

text: I'm dealing with a problem here. I'm not sure about the answer of this question: "What is the difference between periodic oscillation and periodic movement?". -For my opinion the difference is that the periodic oscillation changes the side but the periodic movement doesn't(if it changes the side than it is an oscillation) and I also think that the periodic oscillation is a movement back and forth at a regular speed instead of periodic movement which is a motion that recurs over and over and the period of time required for each recurrence remains the same(which means that it isn't a movement back and forth). Can anybody help me? Thank you!