title: What grounds the difference between space and time?

text: We experience space and time very differently. From the point of view of physics, what fundamentally grounds this difference? Dimensionality (the fact that there are three spatial dimensions but only one temporal) surely cannot be sufficient, as there are tentative proposals among string theories for models with multiple spatial dimensions, and _two_ time dimensions. One of the most lauded answers in the philosophy of spacetime has to do with the fact that our laws predict temporally, rather than spatially. That is to say, if we are given enough information about the state of the world at one moment, we can predict (quantum considerations aside) the future state of the world. However if we reverse the roles of time and space here, and instead give information about a single point of space for all of time, it seems we cannot predict spatially. Are there equations in physics that can be considered to predict across space (for a given time)?


title: Generic Born stability criteria

text: The tensorial form of Hooke's law for the strain-stress relationship in a crystal is (in the Voigt notation): ![Hooke's law](http://i.stack.imgur.com/wrorL.png) where $\sigma$ is the strain, $\epsilon$ is the stress and C is the stiffness tensor: ![stiffness tensor](http://i.stack.imgur.com/mBGDV.png) For a crystalline system of the cubic symmetry class, the stiffness tensor reduces to: ![enter image description here](http://i.stack.imgur.com/lMiFw.png) The Born criterion for the stability of an unstrained crystal is that free energy must be represented by a positive defined quadratic form. In the case of a cubic crystal, it is known that this is equivalent to the following three conditions on the elastic constants: $$C_{11} - C_{12} > 0$$ $$ C_{44} > 0$$ $$ C_{11} + 2 C_{12} > 0$$ But what about lower symmetry classes? **What is the generic Born criterion for stability of a crystal?** I have quite convinced myself that _all the eigenvalues of $C$ must be positive_ , but I cannot find confirmation of that anywhere. Is it right? Is there a reference on that topic?


title: Transfer functions of active filters

text: I've been looking for some straightforward method or trick to obtain the transfer functions of active filters (like the Sallen-Key filter, the butterworth or Cauer topology etc...) since KCL or KVL requires a lot of algebraic manipulations. I've heard that SFG (signal flow graphs) could be very helpful, but with my minimum of experience I can not found any worth reference that treat the subject, so what I am looking for is some brief explanation of SFG with introductory applications to the basic models and topologies of active filters and thanks.


title: Does the measurement on a subatomic particle give its mass value?

text: No doubt I am wondering about the Young's double slit phenomena. If we observe or measure the properties of a subatomic particle, we are able to know its mass, velocity and it comes to existence. So is it true for our natural world? Like we all the form of wave functions and when we interact with an object with our sensors like eye, ear, tongue, touch and smell we give it the shape, mass etc. Otherwise the objects does not exist and form of pure energy.


title: Online magnetic field solver

text: Is there a site that allows you to give the approximate specs of a set of magnets and then it produces the graph of the magnetic field for you? Here is a situation I try to understand: I have a set of rectangular magnets about 1*0.75*.25 inches with north and south on large faces. The magnets are glued in two long lines (like dominoes) about 1 inch apart, all north sides are up. In the area between the magnets there is a strong magnetic field, as if a magnet with opposite polarity is in that places (as if a south pole is there). Why does that happen?


title: Gravity Question Can this be reopened?

text: Anyway what I am trying to figure out is something I have been thinking about for many years. The dinosaurs didn’t die from a big explosion or anything just that the earths gravity increased and made them less competitive to smaller creatures. I have heard bone mass decreases for astronauts so I am think it must increase if gravity increased. Also I am not looking for a number but an understanding of what a creature would weigh with the increase of matter that has been hitting the earth over time. The 37,000# number is what I found on the internet as a theory to what is being added to the earth ever year so over 60 million years there must by an increaseHope someone can help


title: Interacting particles

text: We are familiar with the grand partition function for the grand canonical ensemble. This makes me wonder: what kinds of modifications would be required if the particles interacted? Thanks.


title: Why does kinetic energy increase quadratically, not linearly, with speed?

text: As Wikipedia says: > _[...] the kinetic energy of a non-rotating object of mass $m$ traveling at > a speed $v$ is $mv^2/2$._ Why does this not increase linearly with speed? Why does it take so much more energy to go from 1 m/s to 2 m/s than it does to go from 0 m/s to 1 m/s? My intuition is wrong here, please help it out!


title: Is acceleration quadratic or linear outside of a gravity field?

text: So as I understand it: If you hit a wall at twice the speed you hit four times as hard? I often ask people this and everyone says "at twice the speed you hit twice as hard". $K=\frac{1}{2}mv^2$ is very counter intuitive. I have read an explanation that seems to say gravity is acceleration and that's where the squared comes from. Do we have anyway of knowing if the kinetic energy of an object outside of a gravity field is linear or quadratic? Could the gravity field somehow match the acceleration to give the $v^2$ Bonus question: If you get pulled over for speeding should you ever ask the policeman why kinetic energy is quadratic instead of linear? $K=\frac{1}{2}mv^2=$($300) dollar fine where I live.


title: How - The force of a 60 mph crash is not just twice as great as a 30 mph crash; it’s four times as great!

text: The DMV manual says that > _The faster you go, the less time you have to avoid a hazard or collision. > The force of a 60 mph crash is not just twice as great as a 30 mph crash; > it’s four times as great!_ My physics is quite rusty, so I could not figure it out. I guess the above statement is correct, but how do we prove it? **Edit** I figured this out myself, but alternative methods or new ways of understanding are still welcome.


title: Newton's Third Law of Motion

text: I want to start off by saying that I've looked around for other explanations, but I've not really found any satisfying ones. My question is basically the whole "Why can anything move at all?" question, with a little twist. Refer to this picture: ![](http://i.stack.imgur.com/bmhkv.png) Now I understand that opposite forces act on different objects, so in the top one, the rocket would have a net force of a 100 N to the right, and accelerate, as per Newton's Second Law. However, in the bottom example, wouldn't the box push back on the rocket, equal and opposite, as the rocket pushes on the box, therefore cancelling the forward push from the exhaust, making the rocket not move at all, whilst the box gets a net force of a 100 N? This isn't true obviously, but why not? Also, in this earlier Phys.SE post there is a great answer depicting a finger and a matchbox. Now this post is very related to mine. I'm wondering why in that picture, the force of the finger pushing on the matches doesn't equal the force of the muscles pushing forwards in the finger? Surely when I'm having a force pushing the finger forwards, that same force applies to the matches?


title: Where the fine structure constant $\alpha$ is speed parameter of electron $\beta_e$, How can it be a constant?

text: The fine structure constant $\alpha$ actually is speed parameter of electron $\beta_e$, moving around proton in hydrogen atom. $v_n=\frac {\alpha_c}{n}=c\frac {\alpha}{n}=c\frac {\beta_e}{n}$ How can it be a constant!? ![photo atom](http://cac07science.wikispaces.com/file/view/atom.jpg/32645403/atom.jpg) invariance is not a synonym for being a constant


title: Are there any clear and expressive plainword sense of metric tensor components?

text: Can the following groups of components of metric tensor can assigned a clear sense? ![](https://docs.google.com/drawings/pub?id=1kVqkN1gT-a2fDy2S851l9iQKaMfaatCDo517OSZBHEo&w=467&h=228) https://docs.google.com/drawings/pub?id=1kVqkN1gT-a2fDy2S851l9iQKaMfaatCDo517OSZBHEo&w=467&h=228 I have marked gray component as "newtonian gravitation", blue components as "space curving", green as "gravielectricity" and pink as "gravimagnetism". I understand that this is wrong, since "gravitoelectrivity" should be newtonian gravitation. Also I understand, that components of this tensor are closer to electromagnetic potential rather than to field intensity components. But provided this picture as starting point for explanation.


title: How to calculate the Gibbs free energy out of a given Entropy?

text: I'm stuck in a small calculation. I try to solve a small exercise. You should calculate for a given entropy the Gibbs free energy, where the entropy is given as $S\left(U,V\right) = \frac{4}{3}\left(\alpha V U^3\right)^{1/4} \qquad\dots\qquad U$ is the internal energy, $V$ is the volume and $\alpha > 0, \text{const}$ The exercise say something like "you get a surprisingly expression for the Gibbs free energy". * * * Basically I have to use the definition of the Gibbs free energy: $$ \begin{equation} G\left(T,p\right) = U\left(S,V\right) - T\cdot S + p \cdot V \label{eqn:gibbs} \end{equation} $$ The question is now, how can we exchange the volume $V$ and the entropy $S$ in the equation above. My idea was to calculate $p=p\left(T,V\right)$ and transpose it to $V=V\left(p,T\right)$. The thing is, that I get for the pressure $p$ something like: $p = \frac{\alpha}{3}T^4$, which is not $p = p\left(T,V\right)$ and it's not possible to find a relation for $V=V\left(p,T\right)$. I thing, I'm making some mistake. Can someone help me?


title: What's worse, a full frontal impact or an impact at an offset?

text: Modern car designs have a crumple zone that absorbs most of the impact in a collision, and a strong "safety cell" in the passenger compartment that protects the passengers. These designs are put to the test in crash tests. Currently there are two ways frontal crash tests are performed, a full-wrap frontal collision against a rigid barrier, and a 40% offset test against a deformable barrier, which simulates a car. The full frontal version of the test is usually conducted at a slightly lower speed. ![enter image description here](http://i.stack.imgur.com/vY4Os.png) **Videos:Full wrap, 40% Offset** Using the same car, which one of these would result in more injuries to the dummies? I fully expect the full wrap test to cause more injuries despite the reduce speed, because of a greater deacceleration, resulting in more force applied to the cars and the dummies. Notice how in the offset test the car doesn't come to a full stop immediately after the collision, it pulls to the side and continues slightly ahead. This, coupled with the fact that the barrier is deformable, gives the car more time and distance to deaccelerate. However, some argue that in the offset test there's 60% less area in the car to absorb the impact, and thus poses a greater risk to the car's structural integrity. And with that, it's more dangerous to the passengers inside. Which is true, or are they just not comparable? Are there any papers on this subject?


title: Calculating the force of a mass bearing down on an object

text: I need to calculate the force of a weight bearing down on a smaller object, constraining it from expansion. The weight bearing down has a much bigger surface area than the smaller object. I know the mass of the weight. I know the surface area of the smaller object. What else do I need to know in order to calculate the force bearing down on the small object? What I mean is, what do I need to know in order to calculate what the force bearing down on that smaller object is? I think I might need to know about the acceleration of gravity (9.8 m s^-2), but I'm not sure how that applies if I don't know the dimensions of the larger object. I know that F=ma, but I can't visualise how that applies to an object bearing down on an object with a smaller surface area.


title: Electric field at a point inside a capacitor

text: Let's say I have a parallel plate capacitor. How would I find the electric field at a certain point INSIDE the capacitor (inside the dielectric let's say). From what I understand, the flux of the electric field will be constant everywhere (even if there is more than 1 different dielectric), but the electric field varies. Is this correct?


title: Michelson–Morley @ Home

text: The Michelson-Morley experiment seems to have taken many years, resources and a nervous breakdown to complete. Is it possible to recreate a variation of this experiment at home for say, under $1000, given the technological advances of the last 126 years? The 1887 experiment was looking for a variation of 29 km/s along the surface of the Earth. I'd like to look for a variation of 11 km/s perpendicular to the surface of the Earth. The expected fringe shift of the MMX was: $$ n≈\frac{2Lv^2}{\lambda c^2}≈\frac{2(11m)(29km/s)^2}{(500nm) c^2}≈0.44 $$ In this case the fringe shift would be: $$ n≈\frac{2(11m)(11km/s)^2}{(500nm) c^2}≈0.06 $$ It also appears that their apparatus could rotate $360^\circ$ (by being floated on a pool of mercury), so that they could compare the phase shifts. Is it necessary to reproduce this rotation (in the vertical direction) or is there a modern way to achieve the same measurement using a fixed apparatus? Oh yeah and also, has this been done in the past?


title: Is Dirac's description of a photon in a split beam still seen as correct today?

text: This comes from the _Interference of Photons_ section in the book _The Principles of Quantum Mechanics_ by P Dirac: > We shall discuss the description which quantum mechanics provides of the > interference. Suppose we have a beam of light which is passed through some > kind of interferometer, so that it gets split up into two components and the > two components are subsequently made to interfere. We may, as in the > preceding section, take an incident beam consisting of only a single photon > and inquire what will happen to it as it goes through the apparatus. This > will present to us the difficulty of the conflict between the wave and > corpuscular theories of light in an acute form. > > Corresponding to the description that he had in the case of the > polarization, we must now describe the photon as going partly into each of > the two components into which the incident beam is split. The photon is > then, as we may say, in a translational state given by the superposition of > the two translational states associated with the two components. We are thus > lead to a generalization of the term "translational state" applied to a > photon. For a photon to be in a definite translational state it need not be > associated with one single beam of light, but may be associated with two or > more beams of light which are the components into which one original beam > has been split. In the accurate mathematical theory each translational state > is associated with one of the wave functions of ordinary wave optics, which > wave function may describe either a single beam or two or more beams into > which one original beam has been split. Translational states are thus > superposable in a similar way to wave functions.   1. Is this the view held by leading physicists today?   2. Can we really talk of the incident and exiting photon in the beam splitter being the same photon?   3. Is Dirac saying that the photon is partly in the two split beams, but no where else in space?


title: Probability distribution in phase space and Liouville's theorem?

text: We can define a probability distribution over phase space (say 1D) $\rho(x,p)$ such that, for example, $$\langle x\rangle = \int x \rho(x,p) dxdp$$ etc. It can be shown here that such a distribution satisfies (analogously to fluid dynamics) $$\frac{d\rho}{dt} = 0$$ and therefore $$\frac{\partial \rho}{\partial t} = - \\{\rho, H\\} $$ where the term on the right is a Poisson bracket and $H$ is the Hamiltonian. Now, shouldn't $\frac{d\rho}{dt} = 0$ imply that $\rho=$ constant? But surely $\rho$ must have some sort of time/spatial dependence to satisfy the second equation?


title: Can the rate of virtual pair production from vacuum be computed?

text: Consider for instance the QED Lagrangian. Is it possible to compute the rate of virtual electron-positron creation from the vacuum?


title: Why is there no Gravitational Magnetic Field?

text: We think that the electric field and gravitational field operate similarly with their corresponding charges/masses. With just a difference that the electric field is sometimes attractive and sometimes repulsive. Now I have read that when a charged particle moves the electric field lines associated with it, it is distorted in one way because of the finite time required to get propagated, and this is the cause of the existence of the magnetic field (if calculus is used it can be proven mathematically). So why is it not the same with the gravitational field? Why is there nothing like a Gravitational Magnetic Field?


title: Is an electric lamp a transducer?

text: Silly thought. A transducer, by definition, is a device that converts variations in one form of energy to another. An electric lamp converts electricity into visible light - the brightness may vary depending upon the electric potential applied. Is it correct to state an Electric Lamp is a transducer?


title: Physical interpretation of Probability Current vanishing inside Potential Barrier

text: In a Tunneling problem, if the $E_o<V$, we can show that the scattering wavefunction inside a rectangular barrier is a decaying exponential. The solution being real implies that the probability current $J$ is zero at every point inside the barrier. From equation of continuity, $\frac{\partial|\psi|^2}{\partial t}=0$ Does this mean that the probability density at each point inside the barrier is fixed? (Clearly it can't be so). How exactly is this to be interpreted?


title: What is the performance of a silicon crystal that makes it an essential component to computing

text: I'm on a thread of interest in the precise physics that allow the creation of the computing process. It began as a question posted in search of an understandable explanation of what physical form exactly does the code instruction information take on a hard drive that _instructs_ , and thus allows, a computer to produce its processor results that we can understand in human terms as _visualized intelligence_ in response to instructions, be it in dynamic graphic, word, or image. The answer was the directional orientation expressed by the magnetic polarities of a physical electromagnetic medium that the electromagnetic hard drive heads reads as the digital language of what is portrayed to us as 1's & 0's, but the machine has no language, per se, but can only interpret something as being on or off which is also a _misleading_ explanation. The only thing they actually read, on a physics level, is that of an electromagnetic pole's one of only 2 possible _orientations,_ which we term as _digital_ machine language instructional patterns. Now I wish to understand precisely how, from a physics perspective, silicon crystals allow this process so predominantly so many times per cycle and thus how they came to be chosen as the material of choice that make computer processes possible.


title: what property of steam makes it the preferable motive fluid in jet ejectors? why not air or nitrogen?

text: I want to know what properties of steam make it the fluid of choice in   1. steam turbines   2. jet ejectors. I want to understand the mechanism of energy conversion in these equipment and hence understand why steam is the preferred choice. Please leave out economic factors for now and keep your responses rooted only in physics/thermodynamics.


title: Lev Landau's proof of molecular motion at absolute zero?

text: I am reading the book "The man they wouldn't let die" by Alexander Dorozynski, which is an biography of Russian theoretical physicist Lev Landau, and I have encountered this passage > Absolute zero is considered as the lowest possible temperature for any > element: $-273.16^{\circ}$ C. It was long assumed that at absolute zero all > molecular motion would cease; Landau was one of the first to prove this > assumption incorrect. What proof is the writer talking about here? Does anyone know about the (corresponding) original paper?


title: Dual particle-wave behavior

text: If electrons and photons, and possibly more particles, exhibit dual character, why don't physicists create a new classification for them? Why describe them as both waves and particles. Why not rather create a new classification, which accurately describes their behavior?


title: What can be seen with a 114mm Aperture 675x Zoom Telescope?

text: I choose to post this question on the physics exchange seeing there would be a bigger audience for answers than the astronomy exchange still in BETA. But i'm looking to buy a telescope and was wondering what i could see with a 114mm Aperture 675x Zoom Telescope? The type of things would be interested in would be our planets their moons, comets hopefully and even very bright galaxy's if possible.


title: Is the field generated by an electromagnet always proportional to its current?

text: Imagine that I use a long wire to create an electromagnet. Let's also assume that the current flowing along the wire is constant, and that the wire is winded on the vacuumm. Is the magnetic field generated by this electromagnet (current flowing over an arbitrary path on a finite volume) proportional to the current?


title: Question about orthonormal decompositions over unitary operators

text: I'm teaching myself quantum information theory using Nielson and Chuang's "Quantum Computation and Quantum Information" and I'm at a point in the book where the formalism is starting to make my eyes bleed. > Exercise 2.56 Use the spectral decomposition to show that $K \equiv > -i\log(U)$ is Hermitian for an unitary $U$, and thus $U=\exp(iK)$ for some > Hermitian $K$. Using the defition of Hermitian e.g. $[A^\dagger]^\dagger=A$, I plugged the product $-i\log(U)$ and am now stuck. The problem for me is that I've been using these definitions in the context of matrix computations, but now the book is no longer connecting the operators to matrices as explicitly, expecting me to find the connections for myself.


title: Evaporation of water content from a solid material by applying low pressure

text: I have a raw material which melts at $96\ ^\circ C$. My aim is to make water content evaporate at temperature below this temperature. I can apply vaccume oven for this. I want to know at what pressure the water evaporates by keeping low temperature so that the material doesn't melt.


title: Semiconductors and localization of the electrons

text: When looking at the band diagram of a semi-conductor, direct conclusion of the invariance under discrete translations, for a filled state with an electron, one does know precisely it's momentum, so my question is: does it imply, by Heisenberg, uncertainty that this electron is spread over the whole lattice? Is it the case of all the other electrons?


title: Ideal distance of eye from a lens

text: I observed that when I keep constant distance between object and lens but I move my eye, I get different magnification. When I am closer to lens I can see large image of the object. But if I go away from the lens I can see inverted image. So while making my own binocular/telescope (for practical purpose only) what consideration should I keep in mind about ideal distance between eye and lens (eyepiece).


title: Term for "atmospheric ricochet" due to wrong "angle-of-attack"

text: I watched "Apollo 13" yesterday, and they had the "angle-of-attack" problem that had to be manually solved, to prevent the ship from " _ricochet[ing] off the atmosphere like a rock skipping off a pond_ ". I found and read this, but couldn't manage the term to further learn about this "ricochet". **Is there a term that reflects this "ricochet"?**


title: How can KVL & KCL be derived from Maxwell equations?

text: How can KVL (Kirchhoff's Voltage Law) & KCL (Kirchhoff's Current law) be derived from Maxwell equations in lumped circuits?(Lumped network : if $d$is the largest dimension of the network and $\lambda$ is the wavelength of the signal,a lumped network satisfies the condition $d<<\lambda$ where $\lambda=c/f$) Note:1) KVL & KCL works for lumped circuits(not for every circuits).trying to derive KVL and KCl from Maxwell equations without using lumped assumption(Lumped assumption:assuming that the circuit is lumped)is wrong.actually 4 $Maxwell$ $equations +lumped$ $assumption ==>$2 $Circuits$ $laws$ (KVL & KCL) 2)The other thing we can assume is that there are no incoming energy from outside,such as external magnetic field.


title: What is the first non-vanishing multipole moment of this configuration?

text: Imagine that you have a triangle where each side has the length $a$ and a charge $q$ sitting at every vertex. Additionally, we have a charge $-3q$ sitting in the center of the triangle. What is the first non-vanishing multipole moment? I thought that there cannot be a net charge or dipole moment, but I was uncertain about the quadrupole moment?


title: Implications of rotational invariance

text: The state $$|\psi\rangle ={1\over \sqrt 2}(|+\rangle|-\rangle-|-\rangle|+\rangle)$$ of system made up of 2 spin-$1\over 2$ particles is invariant under the operator $$\exp{i\theta S_y}.$$ What implications/relations does this have relating to the angular momentum properties of the system?


title: A question about Pauli’s exclusion principle and electron orbital

text: According to Pauli’s exclusion principle, $s$ orbital contains at most two electrons with the opposite spin(up and down). Why can't $s$ orbital contain a third electron whose state is the linear combination of spin up and down?


title: Frequency of the sound when blowing in a bottle

text: I'm sure you have tried sometime to make a sound by blowing in an empty bottle. Of course, the tone/frequency of the sound modifies if the bottle changes its shape, volume, etc. I am interested in understanding how the tone/frequency of this sound can be (approximately) calculated from the shape of the bottle. Is there some formula? If you have any references about this please post them in your answers. Being a mathematician I keep hearing that the principal tone is given by the first eigenvalue of the Laplace operator, and I'd like to understand the physical explanation.


title: Effect of Current on spring

text: When Current passes thru a spring , some books mention that it gets compressed. However, I think due to the heating effect of current, molecules will increase kinetic energy and the spring should get elongated. What is the physical mechanism for the compression instead of elongation?


title: Bouncing Ball Pattern

text: If a ball is simply dropped, each time a ball bounces, it's height decreases in what appears to be an exponential rate. Let's suppose that the ball is thrown horizontally instead of being simply dropped. How does the horizontal distance travelled change after each bounce? Context behind question: I read a question involving a ball that travels horizontally 1m during the first bounce, 0.5m during the second bounce, 0.25 during the third bounce etc. I was wondering if this model is physically valid?


title: A pedestrian explanation of conformal blocks

text: I would be very happy if someone could take a stab at conveying what conformal blocks are and how they are used in conformal field theory (CFT). I'm finally getting the glimmerings of understanding from reading Moore and Read's wonderful paper. But I think/hope this site has people who can explain the notions involved in a simpler and more intuitive manner. * * * Edit: Here is a simple example, taken from pg 8 of the reference cited above ... In a 2D CFT we have correlation functions of fields $ \phi_i(z,\bar z) $, (where $ z = x+\imath y$) at various points on the complex plane. The n-point correlation function can be expanded as: $$ \left \langle \prod_{a=1}^n \phi_{i_a}(z_a,\bar z_a) \right \rangle = \sum_p | F_{p\; i_{1} \dots i_n}(z_{1} \dots z_n)|^2 $$ Here $p$ labels members of a basis of functions $ F_{p\; i_1 \dots i_n}(z_{1} \dots z_n) $ which span a vector space for each n-tuple $(z_{1} \dots z_n)$ These functions $F_p$ are known as conformal blocks, and appear to give a "fourier" decomposition of the correlation functions. This is what I've gathered so far. If someone could elaborate with more examples that would be wonderful ! * * * Edit: It is proving very difficult to decide which answer is the "correct" one. I will give it a few more days. Perhaps the situation will change ! * * * The "correct" answer goes to (drum-roll): David Zavlasky. Well they are all great answers. I chose David's for the extra five points because his is the simplest, IMHO. He also mentions the "cross-ratio" which is a building block of CFT.


title: What is the difference between induced and motional emf?

text: At least from their names, it seems motional emf is induced, so what's the difference?


title: Experimental samples with rare earth metal

text: Many experiments, such as optical, superconductivity, etc, use the samples that involve rare earth metals and transition metals. Why are they used that often. Is the main reasons:   1. They have the required electronic structure in its d- and f- orbital so that we can create the required spin-spin interaction.   2. They provide the required structure of the crystal   3. They provide the required energy band gap Any elaboration? **Edit** : Here the samples I mean is the usual YBCO, or some papers, say Gd5Si2Ge2, that I do not have any idea. I am also curious about why they decide to investigate a particular compound in the first place?


title: Where can we find information of International Physics/Astrophysics conferences?

text: Where do you check and put them usually? Let's make a wiki ~


title: Object that causes spacetime to expand?

text: Is there any thing that will cause spacetime to expand, so that particles are pushed away from them rather than pulled towards it. I know things such as black holes and planets causes dips and curve in spacetime, but is it possible that a celestial object will stretch spacetime?


title: Long string model of black hole

text: I wonder if anyone can advise me literature about "long string model" of black hole. I've tried Google, and of course arXiv.org. Still I couldn't find anything about this theme. I would be also very pleased if someone could tell me any information about calculation of correlation functions of massive scalar field living on the circle.


title: What is the difference between negative acceleration and decreasing acceleration?

text: According to Reisnick and Halliday, retardation is the acceleration in the negative direction of time axis ie. opposite to the motion. Decreasing accleretion is the decrease in the magnitude of time rate of change of velocity. Am I correct or not? What is the $v$-$t$ graph with retardation and decreasing acceleration? [I don't think they are same.]


title: Why is Entropy expressed in terms of Enthalpy?

text: Why does ${\Delta}S_{m(fusion)} = \frac{{\Delta}H_{m(fusion)}}{T}$ ? I always thought ${\Delta}S = \frac{dQ}{T}$ In this case does it mean $dQ = {\Delta}H$ ?? Why is it so?


title: Potential step solution is not normalizable

text: If you try to integrate the solution of the potential step, http://en.wikipedia.org/wiki/Solution_of_Schr%C3%B6dinger_equation_for_a_step_potential#Solution you will notice that it diverges! Doesn't that mean that the solution is physically incorrect?


title: Total positive charge in the Universe

text: In their last homework, some of my students miscalculated a charge to be $10^{20}$ C over a squared meter and I was wondering if there was as much positive charges in the entire Universe. It would do the trick if I could simply estimate the total number of protons (including those in nucleus) in the entire Universe but how to do so in a simple way ?


title: Accelerating an elevator

text: A person is standing on a weighing scale in an elevator in upward acceleration. Let $N$ be normal reaction force exerted by the weighing scale to the person (upward). It is known that the person will experience a normal reaction force ($N$) larger than his own weight (larger reading on the weighing scale). While $N$ is equal, but in opposite direction, to the force that the person exerts to the weighing scale due to action-reaction pair (the person and the weighing scale). That means other than the person's weight, there should be an extra force exerting to the weighing scale downward ($A$). So $-N$ (upward)$ = mg + A$ (downward). I can't figure out where does $A$ come from?


title: How does a photon leave trace of its polarization state in a photon detector but not trace of which direction it came in?

text: Some quantum erasure experiments involve polarization of photons. In one such experiment with a double slit, a horizontal polarizer is used in front of one slit, and a vertical polarizer is used for the second slit and the idea is that then horizontal or vertical polarization of the photon coming out of the double slit "marks" which path it took and so interference pattern disappears. Then the experimenter goes on to erase that which-path information in some way to restore interference. So it seems to me that a photon detector by itself does not work as an eraser and that a horizontally polarized photon entering a photon detector leaves something very different in the detector or the environment than a vertically polarized photon entering the same detector. How is it that a detector that usually cannot tell apart different incoming directions of photons can somehow tell apart different polarization?


title: What are relativistic and radiative effects (in quantum simulation)?

text: I'm reading about Quantum Monte Carlo, and I see that some people are trying to calculate hydrogen and helium energies as accurately as possible. QMC with Green's function or Diffusion QMC seem to be the best ways to converge on the "exact" solution to Schrodinger's equation. However, if one wants to be very exact, then the Born-Oppenheimer approximation must be removed. A lot of papers mention that the results are still not exact enough, and must be corrected for relativistic and radiative effects. I'm pretty sure I know what relativistic effects are -- the non-relative Schrodinger's equation cannot account for GR as particles approach the speed of light (or even small but measurable effects at lower speeds). But what are radiative effects? And I would think you would include these two things into your QMC calculation instead of applying a post-simulation correction factor if you wanted to be ultra-precise (e.g. use the Dirac equation instead for relativistic effects). So why don't most researchers do this? Does it raise the calculation time by orders of magnitude for an additional 4th decimal place of accuracy? Finally, is there anything at a "deeper" level than relativistic and radiative effects? In other words, if I left a supercomputer running for years to compute helium's energies without the BO approximation, and with relativistic and radiative effects included in the MC calculations, would this converge on the _exact_ experimental values? (Actually, I just thought of one such left-out factor -- gravity ... and might you have to simulate the quarks within the protons individually? Anything else?)


title: Find Angular Momentum about any point

text: How do I find the angular momentum of a body about any point?   We know that $L=I\omega$ for a body rotating in space, where $L$ denotes the angular momentum, $I$ denotes the moment of inertia and $\omega$ denotes the angular velocity. However, this is **only applicable** for **Fixed Axis of Rotation, Instantaneous Axis of Rotation and Center of Mass**.   Can somebody state and prove the value of the angular momentum of a body about any point? (If a formula for that exists).   Thanks!


title: Mathematically challenging areas in Quantum information theory and quantum cryptography

text: I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? From what I saw in the books, most topics was just simple linear algebra. I am looking for an area which is mathematically more rich, and uses maybe more concepts from theoretical computer science, number theory, discrete maths, algebra etc. Classical cryptography is an area on the interface of maths and TCS which uses many areas of maths such as number theory, algebra, ellptical curves. Is the quantum cryptography also rich in mathematics? What are the prerequisites? If not, please could you suggest some areas that I are mathematically rich in QIT?


title: Theory that gets rid of dark matter/energy

text: 1. Is there any physics theory that either groups together gravity and dark energy/dark matter or eliminates dark energy/dark matter by modifying standard understanding of gravity or any force? If so, is there any theory that still matches with all correct predictions of standard physics theories?


1. Does quantum field theory accept gravitational wave? As quantum field theory is flat spacetime theory, I wonder whether gravitational wave would be true.   2. Does contemporary string theory variants accept gravitational wave?


title: Does an uneven and/or moving surface affect quality when using a solar filter?

text: I have chosen to make my own solar filter using Baader as opposed to Mylar or anything else based on these: http://physics.stackexchange.com/a/25204/6805 and http://irwincur.tripod.com/mylar_vs__baader.htm and others. My last solar filter was the product which is no longer available direct from Celestron (I'm not even sure what it was made with). **My questions** : Does "flapping in the wind" baader effect image quality? See the images below to understand what I mean... Is it possible to achieve a better taut fitting when making my own? As seen here ![enter image description here](http://i.stack.imgur.com/BcsMd.jpg) it is not flat or tight like this glass one is ![enter image description here](http://i.stack.imgur.com/EHj3t.jpg)


title: What happens when a lightning rod is not earthed?

text: A Lightning rod is fixed to the building and it is not given earthing then what happens? How does the lightning reach the ground through the building?


title: Constraining two-point functions of boundary operators on the disk

text: I'm trying to understand the constraints on the disk CFT correlation function $\langle O_1(y_1)O_2(y_2)\rangle$, where the $O_i$'s are boundary operators that are not necessarily primary. It's a well-known fact that the corresponding sphere correlator is determined up to an overall constant, but I seem to be getting two independent constants in the case of the disk. Let me just quickly give the argument that I've come up with. For $y_{1}>y_2$, we can make the $PSL(2,R)$ transformation $y'=(y_1-y_2)y+y_2$, under which $(\infty,1,0)\mapsto(\infty,y_1,y_2)$. This gives \begin{align*} \langle O_1(y_1)O_2(y_2)\rangle=(y_1-y_2)^{-2(h_1+h_2)}\langle O_1(1)O_2(0)\rangle. \end{align*} For $y_2>y_1$, we instead transform $y'=(y_2-y_1)y+y_1$, giving \begin{align*} \langle O_1(y_1)O_2(y_2)\rangle=(y_2-y_1)^{-2(h_1+h_2)}\langle O_1(0)O_2(1)\rangle. \end{align*} Putting them together, \begin{align*} \langle O_1(y_1)O_2(y_2)\rangle=|y_1-y_2|^{-2(h_1+h_2)}(\langle O_1(1)O_2(0)\rangle\theta(y_1-y_2)+\langle O_1(0)O_2(1)\rangle\theta(y_2-y_1)). \end{align*} Now, for primary operators it's straightforward to show that $\langle O_1(1)O_2(0)\rangle=\langle O_1(0)O_2(1)\rangle$, but I don't see why (or if) this is true for nonprimaries. Are there just two independent constants in this case? Thanks for your help!


title: Energy transferring question

text: If I have a spring being compressed by two bodies, A and B, with different masses, how much energy would be transferred to each one when they are released and the spring expanded?


title: Moving conducting bar in (changing) magnetic field

text: In my exam today I've been given this problem, yet even with the results at hand I simply can't warp my head around it; Given the picture below, a bar is placed on two conducting rails with a resistor (in the form of a single thin wire) at the left. Now at t=0 the magnetic field changes which causes the bar to move. (and a current flows through the "circuit"). The current can easily be found by Lenz's law: $$ \mathscr{E} = -\frac{\mathrm{d}\Phi_b}{\mathrm{d}t} = -\ell\frac{\mathrm{d}\left( Bx \right )}{\mathrm{d}t} = -\ell x\frac{\mathrm{d} B }{\mathrm{d}t} -\ell B v $$ ![enter image description here](http://i.stack.imgur.com/TnAlF.png) Now this is follow up text for the problem > It may be assumed that the conducting bar **has a negligible mass and > friction** , so it will immediately move to a position $x$ in which there is > no force exerted on it. > > b) Explain why the relation between the actual position $x$ and the actual > value of the magnetic field $B$ is given by $Bx = B_0x_0$. What did the prof try to explain here? No force means constant speed, so not a "position" at all right?   Well the result sheet shows: > No force means $\frac{\mathrm{d}(Bx)}{\mathrm{d}t} = 0$ Hence $Bx$ is > constant ..... what???? Sorry but maybe it stems from the fact that I already didn't understand what "no force" meant in the text but I can't understand this.


title: Physical Interpretation of EM Field Lagrangian

text: Using differential forms and their picture interpretations, I wonder if it's possible to give a nice geometric & physical motivation for the form of the Electromagnetic Lagrangian density? The Lagrangian for the electromagnetic field without current sources in terms of differential forms is $F \wedge * F$, where $F$ is the exterior derivative of a 4-potential $A$. Another way to say this is that $F$ is the four- dimensional curl of a 4-potential $A$, i.e. the anti-symmetric part of the flow of the determinant of the Jacobian of a vector field $A$, and since we can physically interpret the curl of a vector field as the instantaneous rotation of the elements of volume that $A$ acts on, it seems as though we can interpret varying $F \wedge * F$ as saying that we are trying to minimize the instantaneous four-dimensional volume of rotation of the electromagnetic field (since the Hodge dual on 2-forms gives 2-forms 'perpendicular' to our original ones, wedging a form with it's dual gives us a 4-d volume, so here we are getting the rotation of a volume element in spacetime). Is that correct? There is also the issue of defining the same action just in different spaces, using $F_{ij}F^{ij}$ and so a similar interpretation must exist... If I interpret $F_{ab}$ as I've interpreted $F$ above, i.e. a 4-d curl, and $F^{cd}$ similarly just in the dual space, then in order to get a scalar from these I have to take the trace of the matrix product $F_{ab}F^{cd}$, which seems to me as though it can be interpreted as the divergence of the volume of rotation, thus minimizing the action seems to be saying that we are minimizing the flow of rotation per unit volume. Is this correct? If these interpretations are in any way valid, can anyone suggest a similar interpretation for the $A_idx^i$ term in the Lagrangian, either when we're getting the Lorentz force law or the other Maxwell equations? Vaguely thinking about interpreting this term in terms of current and getting Maxwell's equations hints at what I've written above to have at least some validity! Interestingly, if correct I would imagine all of this has a fantastic global interpretation in terms of fiber bundles, if anybody sees a relationship that would be interesting. (Page 9 of this pdf are where I'm getting this interpretation of divergence and curl via the Jacobian, and I'm mixing it with the geometric interpretation of differential forms ala MTW's Gravitation) I understand Landau's mathematical derivation of the $F_{ij}$ field tensor, Lorentz invariant scalar w.r.t. to the Minkowski inner product, linearity of the EOM, and eliminating direct dependence on the potentials, but physical motivation for it's form is lacking. Since one can loosely interpret minimizing $\mathcal{L} = T - V$ as minimizing the excess of kinetic over potential energy over the path of a particle, and for a free particle as simply minimizing the energy, I don't see why a loose interpretation of the EM Lagrangian can't be given. Any thoughts are welcome. References:   1. Math 733: Vector Fields, Differential Forms, and Cohomology, Lecture notes, R. Jason Parsley   2. Warnick, Selfridge, Arnold - Teaching Electromagnetic Field Theory Using Differential Forms


How do we know for certain that space is expanding? Let's say that in the year 1950, we observe that galaxy 1 is 5 billion light years away from us and galaxy 2 is 10 billion light years away from us, putting both galaxies at a distance of 5 billion light years from each other. Then in 2013, we observe that they are now 7 billion light years away from each other so we conclude space is expanding. We see that galaxies are move away from each other but how does that prove that space is expanding? Could this illusion of expanding space simply be due to something larger in mass pulling the farther galaxy 2 away from galaxy 1? This larger mass could be accelerating the velocity of galaxy 2 faster then it's accelerating the velocity of galaxy 1.


title: Why does my eardrum feel strange inside a car?

text: When I was riding a car (I was not the driver), my eardrum felt a little similar to the case when I was in a plane that was taking off, and little loss of hearing. Nothing was played inside. The feeling was gone, when I left the car. This don't happen often when I ride a car. So I wonder what might be the reason? Thanks! That happened when the car was moving on a plain. at normal speed on a road in a city in NY. The weather was normal. I didn't sneeze. Perhaps swallowing helped a little. Windows were closed probably. Is this not good to health?


title: Dispersion relation and Heat Capacity

text: I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation $\omega = c_sk$. It is said that for temperatures much less than the Debye temperature, the heat capacity at constant volume $$C_V\sim T^3$$. Now I want to show that for bosons with dispersion relation $\omega\sim A\sqrt k$ has heat capacity $$C_V\sim T^4$$ for $T\ll T_{Debye}$. In the case studies I have read, I can't find where the dispersion relation comes into play. I have no idea how to see this. Please help! * * * Perhaps I could get a response if I change the question to: How does the dispersion relation come into the calculations for the Debye model? Links to notes or an answer would be very much appreciated!! * * * @MarkMitchison kindly pointed out that the density of state depends on the dispersion relation. What are the general definitions of $$E, p$$ in terms of $$\omega, k$$? E.g. for the first case $E=\hbar \omega$ and $p=\hbar k$. So the question is: what are the respective values for $E,p$ in general?


title: Is normalization consistent with Schrodinger's Equation?

text: Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's Equation.


title: Algebraic formulation of QFT and unbounded operators

text: In AQFT one specifies the structure of the observables as a $C^*$-algebra. This seems to excludes algebras that don't have a norm, such as the Heisenberg algebra. Fortunately for this case one turns to Weyl algebra. Is that trick always possible? _Additional material:_   * Related to this Phys.SE post.   * In Haag's book "Local quantum physics" p.5, he says that one can always come down to the study of bounded operators as discussed in I.E. Segal "Postulate for general quantum mechanics" 1947. However I don't see the answer to that question in this paper.   * It seems that from an self adjoint operator in a Hilbert space one can always define a unitary operator, Reed & Simon Thm VIII.7.


title: How do I convert tangential speed to angular speed in an elliptic orbit?

text: I am running an animation of a satellite in an elliptic orbit (defined by a parametric equation for $x$ and $y$ as a function of $t$) and want to make sure the spacecraft is traveling at the right speeds at different points in its orbit. That is, it should go slower at is apoapsis and much faster at its periapsis. I can easily calculate the _tangential_ speed of the satellite using this equation: $v=\sqrt{GM(\cfrac{2}{r}-\cfrac{1}{a})}$ How do I convert this to the _angular_ speed of the satellite at this point? I've done extensive research (hours and hours) but haven't found anything of value. The closest thing was this expression of Kepler's Third Law: $\cfrac{dA}{dt}=\cfrac{1}{2}r^2\omega$ Since $\cfrac{dA}{dt}$ is a rate (area swept out per second) I rewrote this equation as $\cfrac{A}{P}=\cfrac{1}{2}r^2\omega$ where $A$ is the area of the elliptic orbit (given by $A=\pi ab$ where $a$ and $b$ are the semi-major and semi-minor axes of the ellipse, respectively), and $P$ is the period of the elliptic orbit (given by $P=2 \pi \sqrt{\cfrac{a^3}{GM}}$). Solving this for $\omega$ yields: $\omega=\cfrac{2A}{Pr^2}$ For each time step in my simulation I use the satellite's current position in this equation to compute $\omega$ and then use the result to update the current $\theta$. This updated $\theta$ is then plugged into the parametric equation mentioned above to get the satellite's $x$ and $y$ position. I can't find my mistake anywhere and would really appreciate it if someone could point it out to me.


title: AdS/CFT not dependent on validity of string theory

text: I have been told that the AdS/CFT correspondence proof does not rely on the validity of string theory. To be honest I don't know what to make of this. The idea of taking seriously the results of applying the techniques of this correspondence is appealing, but before I head in that direction, I need some help finding any references that actually make clear the fact that such a correspondence is independent of the validity of string theory. I am also curious as to the original explicit derivation of the correspondence. I just want to be able to really learn and truly believe the results myself before considering working applying its results. I'm not contesting results of any kind, I just want to know this stuff well.


title: Specific problems with the quadrupole formulation of gravitational radiation

text: the quadrupole formula has some counterintuitive consequences, when analysing the power output averaged over a period $$ P = \langle \frac{d^3 Q_{ij}}{dt^3} \frac{d^3 Q_{ij}}{dt^3} \rangle $$ Specifically, if two separated sources are considered inside the radiation zone, $\rho_1$ and $\rho_2$, and assume that each orbit around separate centers $C_1$ and $C_2$ by a length $R$, the quadrupole moment of the pair is going to be (around the common center $C_1 + \frac{R}{2} = C_2 - \frac{R}{2}$) $$ \int ( \rho_1(x) + \rho_2(x) ) x^j x^k d^3x = \int \rho_1(x) (x_1 - \frac{R}{2})^j (x_1 - \frac{R}{2})^k d^3x + \int \rho_2(x) (x_2 + \frac{R}{2})^j (x_2 + \frac{R}{2})^k d^3x = \int \rho_1(x) x_1^j x_1^k d^3x - \frac{R^j}{2} \int \rho_1(x) x_1^k d^3x - \frac{R^k}{2} \int \rho_1(x) x_1^j d^3x \+ \int \rho_2(x) x_2^j x_2^k d^3x + \frac{R^j}{2} \int \rho_2(x) x_2^k d^3x + \frac{R^k}{2} \int \rho_2(x) x_2^j d^3x$$ $$ = \int \rho_1(x) x_1^j x_1^k d^3x + \int \rho_2(x) x_2^j x_2^k d^3x + \frac{R^j}{2}( \int \rho_2(x) x_2^k d^3x - \int \rho_1(x) x_1^k d^3x ) + \frac{R^k}{2}( \int \rho_2(x) x_2^j d^3x - \int \rho_1(x) x_1^j d^3x )$$ plus some other terms that are constant over time that are not needed However, the terms $\frac{R^k}{2} \int \rho_c(x) x_c^j d^3x$ will have nonzero third time derivatives in general, so they will contribute to the overall power, even though they depend on an arbitrary choice of a center over which the quadrupole moments are calculated? What is wrong with this expression, and how to obtain a power output from the quadrupolar moment that doesn't depend over what origin of coordinates is chosen for the calculation?


title: Resolution of the EPR paradox using relativity of simultaneity

text: **A simple explanation for photon entanglement experiments** Example: Quantum teleportation La Palma-Teneriffa in 2012 (distance 143 km) - Photons were entangled in such a way that when measuring polarization of one of the photons (obtaining a random result) the other photon will show a perfectly correlated polarization. Both measuring events may even happen at a timelike interval. Today we know that there is nothing "spooky" about it, no information is transmitted at more than speed of light. But is there a realistic and local explanation how both events may happen at a timelike interval? My proposal: Apply relativity of simultaneity to photons in the same way as to any other object moving in space. In order to determine simultaneity of events of any object moving in space,   1. I make my observations about the movement of the object (speed, time, distance)   2. I enter my observations into my own (observer's) Minkowski diagram (Edit: in order to simplify this question I suppose that there is only one space dimension so that my Minkowski diagram is similar to a sheet of paper)   3. Than I apply the factor 1/γ ( _reciprocal Lorentz factor_ ) to all values (speed, time, distance) in order to know about what is simultaneous for the object. But for entangled photons, scientists are doing exactly the contrary: Distances and traveling time of photons are always measured on the basis of light speed c (300.000 km/sec.). Simultaneity of 2 events is determined accordingly. However, according to time dilation formulas of special relativity (T'=T/γ) these measured values are no **real** values, but only **observed** values, observed by any observer, which are not permitting so say something about simultaneity of events of a photon. An application of these formulas (and more precisely: of the factor _reciprocal gamma_ ) yields that the **real** speed of light is **not defined** (zero-by-zero division) and the distances and times are shrinking down to **zero**. As a result it seems clear that all events of photons are taking place simultaneously, and thus photons may be here and there simultaneously - thus no paradox at all! I learned already that possibly relativity and time dilation do not apply to particles moving at light speed. But what is the sound reason for such an exception if on the other hand this is prohibiting a resolution of the EPR paradox? It is also important that not only reference frames are subject to the factor reciprocal gamma: The factor is part of my (observer's) diagram, and even any fictive movements or any average of two movements is subject to the fact that their real movement is **not** the observed movement. _Edit: Further current errors to related issues:_ 1.The Lorentz factor does not derive from Lorentz transformation but directly from the two SR postulates - see light clock thought experiment introduced in 1909 by Gilbert Newton Lewis und Richard C. Tolman. By contrast, it is correct that Lorentz transformation uses the Lorentz factor. 2.Accordingly, not only reference frames may be observed and submitted to reciprocal Lorentz factor. **Example:** We observe an object which is moving over a distance of 100 light years (in our reference frame). We measure its speed (according to our reference frame). If its speed is respectively 0.6c/ 0.8c/ 0.9c/ 0.99c /0.9999c or 1.0c, the reciprocal Lorentz factor yields for 100 light years a proper distance of respectively 80/ 60/ 44/ 17/ 1.4 and 0 light years. My question refers to the fact that these 0 light years are currently replaced by the **observed** 100 light years. This would mean a leap in a curve which is tending towards zero 3.There is no "proper speed of light". When proper time and proper distance are reduced to zero by reciprocal gamma, the result is that speed is **undefined** (zero by zero division).


title: Intuitive explanation for superfluidity?

text: I know that superfluidity is caused by the fluid having zero viscosity. This only happens at very low temperature, so the fluid (e.g. Helium-4) is a Bose- Einstein condensate. I also know that in a Bose-Einstein condensate all the particles are in the ground state. Now, that said: How can this explain superfluidity? Many websites say that _the particles behave as a sigle giant matter wave,_ but what is this due to and what does it mean physically?


title: Gibbs equation and reversibility

text: The equation $$TdS=dU+PdV$$ is a combination of $$dQ=dU+PdV$$ and $$TdS=dQ.$$ But in some process that is very irreversible, $TdS>dQ$, should we write $$TdS>dU+PdV$$ instead of the first equation? I guess the equation is different for reversible and irreversible process.


title: Why does black get heated the most?

text: I found out black heats up the most and white the least, as I expected. The question I had is that despite black reflecting all the wavelengths of the visible spectrum, and hence giving the black material its colour, why is it not the coolest? I mean, even blue. It's reflecting the higher frequencies, which are at a higher energy acc. to E=h*f (f is frequency), why does it get heated more than red?


title: Why are "quadratures" called this way?

text: In quantum optics (and hence also cv quantum information), given the annihilation and creation operators of the electromagnetic fields $a$ and $a^{\dagger}$, the "position" and "momentum" operators that we can construct in analogue with the harmonic oscillator, i.e. $$ x:=\frac{1}{\sqrt2}(a^{\dagger}+a) \quad\text{and}\quad p:=\frac{1}{\sqrt2}(a^{\dagger}-a)$$ are called _quadratures_. The name suggests a deeper meaning (or a mental picture - like the annihilation and creation operators suggest particle creation and annihilation), but I haven't found any. Can anyone give a suggestion?


title: Is there a good experiment to demonstrate Gauss's Law for Magnetism?

text: I'm trying to come up with a simple experiment that can demonstrate the properties of Gauss's Law for Magnetism. I am aware that it is a mathematical representation of the fact that magnetic monopoles don't exist (at least as far as we know), but are there any simple experiments that I could set up that a high schooler would be able to understand (without any higher level physics)?


title: Where is the particle during a tunneling event?

text: If, say, a particle with energy $E<V_0$, approaches a finite potential barrier with height $V_0$, and happens to tunnel through, where would the particle be during the time period when it is to the left of the potential barrier and to the right of the potential barrier? Surely there must be a finite amount of time for it to travel through to the other side, unless it simply teleports there? If it travels through with energy less than $V_0$, however, doesn't that mean it cannot enter in the region of the potential barrier?


title: Detection of W and Z bosons

text: What specific behaviour confirmed the existence of the W and Z bosons at the UA1 and UA2 experiments? Thanks!


title: Determine the point at which the electric field is equal to zero?

text: Two point charges, -2.5 micro coulombs and 6 micro coulombs, are separated by a distance of 1m (with the -2.5 charge on the left and 6 on the right). What is the point where the electric field is zero? This seems exceptionally easy, but I can't figure it out. I can calculate the answer if both charges are negative/positive easily, but the fact that they're different is confusing me. Thanks!


title: Phase Accumulation of Hankel-waves upon propagation

text: Hankel functions are solutions to the scalar Helmholtz-equation $$\Delta\psi + k_e^2\psi = 0$$ in cylindrical and spherical geometry (with respect to a separated angular dependence). Thus, they are very important describing **spherical** and **cylindrical** waves. Here is an example of such a propagation in the spherical case taken from Franz Zotter: ![animation](http://i.stack.imgur.com/GSClW.gif) I am searching for a reference that states the **phase accumulation** of Hankel waves of the form $$F_H^{\mathrm{out/in}}(\mathbf{r}) = H_m^{1/2}(k\rho)\ .$$ Assumed is stationarity with an $e^{-\mathrm{i}\omega t}$ time dependence fixing the meaning of the two different Hankel-waves as outgoing/incoming. For **plane waves** one finds that the accumulated phase of a wave in $x$-direction, $$F_p=e^{\mathrm{i}kx}$$ is simply related to its argument, $$\phi_{\mathrm{acc}}(x_1,x_2)=\mathrm{Arg}(F_p(x_2))-\mathrm{Arg}(F_p(x_1)) = k(x_2 - x_1)$$ and it is **natural** to just use this formula in the Hankel- case, e.g. $$\phi_{\mathrm{acc}}(\rho_1,\rho_2)=\mathrm{Arg}(F_H^{\mathrm{out/in}}(\rho_2))-\mathrm{Arg}(F_H^{\mathrm{out/in}}(\rho_1))$$ However, I was not able to find a **suitable reference**. Hence my question: > ### Is there a reference defining the phase accumulation of Hankel waves? **Thank you** in advance.


title: Would a bicycle stay upright if moving on a treadmill and why?

text: I suspect not, because moving forward (or backwards for that matter) is an important part, but I would like to confirm. **UPDATE** : Clearly it's possible Can someone explain why?


title: Is assuming spacetime to have |2^N| points overkill?

text: The physical continuum is commonly assumed to have a mathematical continuum of points, that is, with a cardinality equinumerous with the Power Set of the set of natural numbers. However, since [ZFC + "there exists an inaccessible cardinal"] suffices to model analysis, and [ZFC + "there exists an inaccessible cardinal"+ the negation of the continuum hypothesis] is equiconsistent with the former, but that the existence of aleph-one is a useful assumption (Borel sets, etc.),   wouldn't it be more appropriate to assume only that space-time has (at least) a cardinality of aleph-one?


title: Planetary Systems

text: How does one know the correct position of planets in relation to the sun when viewing the solar system from different angles makes the appearance of the planets different? I would think that it would require a satellite to orbit in a circular pattern above and below the entire solar system to get correct bearings.


title: How should I simulate the electric potential field from a wavefunction?

text: I was interested in making what I thought would be a simple simulation of an electron encountering a positron by numerically solving the Schrodinger equation over several time steps, but I've run into 1 problem: the potential used in most textbooks (to solve the hydrogen atom for example) are still of a classical point particle, rather than a wavefunction. How do I generate the potential field from two real, moving and interacting wavefunctions?


title: How to get the cosine of a waveform?

text: I have a set of samples that represents a waveform. This waveform resembles a frequency modulated sinusoidal wave (only it is not). I would like to invert this waveform or ~~shift it by $2\pi$~~ shift it by $\pi$. of course taking the cosine of samples as they are without preprocessing is wrong. What should I do to achieve this? Thank you.


title: Is there a method for differentiating fractional quantum Hall states aside from finding Chern numbers?

text: The ground state for a quantum Hall system on a torus with fractional filling factor can be classified by the Chern number, which is why the Hall conductance is quantized. Is there another method or classification one can use to distinguish states?


title: speed of sound relative to density of medium through which sound travels

text: I know that sound travels faster in water compared to air and say faster in steel than in what're so What would the density have to be to cause sound to approach the speed of light


title: Introductions to discrete space-time

text: It's comparatively easy (cum grano salis) to grasp the following concepts:   * Euclidean space-time _(continous space and continuous time)_   * classical mechanics _(discretely distributed matter in continous space and continuous time)_   * Minkowskian space _(continously intermingled space and time)_   * special relativistic mechanics _(discretely distributed matter in continously intermingled space and time)_   * classical electrodynamics   * classical quantum mechanics _(discrete energies, continuously distributed matter in continous space and continuous time)_   * quantum electrodynamics   * general relativity _(continously intermingled space-time and matter)_ Accordingly, there are lots of introductory texts and text-books. It's also easy to grasp   * numerical simulations _(on artificially - and mostly unphysically - discretized spaces, times, and space-times)_   * cellular automata _(on unphysical regular spatial grids)_ It's definitely hard to grasp (for somehow graspable reasons)   * quantum gravity I do not know whether there are empirical evidences for a discrete space-time or only theoretical desiderata, anyhow I cannot figure a discrete space and/or time out. Why is it so hard to introduce and explain the concept of a physical discrete space-time? Why are there no easy to understand introductory texts or text-books on definitions, concepts, models, pros and cons of discrete space, time, and - finally - space-time? Respectively: _Where are they?_ Are the reasons for this maybe related to the reasons why quantum gravity is so hard to grasp?


title: Orbit through L4 and L5

text: I was reading the Wikipedia article on Lagrangian points and doing the requisite wiki walk through the various quasi-satellites of Earth when a question occurred to me: > Could there be a stable or Lissajous orbit around the minor body > perpendicular to the ecliptic that passes through or near L4 and L5?


title: Resistance of superconducting wire in parrallel with standard wire

text: The formula for parrallel resistors is $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$ But how can you use this formula when one of the branches is a superconductor, eg: ![image description](http://i.stack.imgur.com/ltS11.png) Where the red resistor represents a wire with some resistance and the blue line represents a superconducting wire, how can the above equation be used to find the resistance between A and B, as it would mean dividing by zero?


title: What is the difference between quantum cryptography and quantum teleportation?

text: > Generate two entangled photons, send one to a message sender and the other > to the intended receiver. Both the sender and the receiver recover the same > piece of quantum information from the photons, then the sender scrambles the > message to be sent by some reversible function determined by the quantum > information, and send this scrambled data to the receiver who is now capable > of unscrambling it thanks to having the quantum information that was used > for the scrambling procedure. This description as far as I can tell would be a valid simplified explanation of both quantum cryptography and quantum teleportation. What exactly is the difference between the two terms?


title: $2+1$ dimensional physics theory of our universe?

text: Is there any physics theory that depicts our universe as $2+1$ dimensional? I heard that black holes seem to suggest that the world might be $2+1$ dimensional, so I am curious whether such theory exists? Just for curiosity.


title: How can we know the size of a dimension?

text: > **Possible Duplicate:**   >  Measuring extra-dimensions I was watching a layman's documentary and it said: "The 11th dimension is incredibly small, like a long tube about $10^-30m$ in diameter". How can we know the general sizes of extra dimensions?


title: Experiments proving/disproving extra dimensions

text: I have been recently reading quite a little about Kaluza Klein theories. I am still far from mastering this but I am curious if any experiment that may disprove or give hints of the existence of extra spatial dimensions is to be expected to be performed relatively soon. This page of CERN, for example, says that the LHC might give some clues, but it doesn't really dive into much detail. So, in some detail, which experiments might say something about this, and when might they be expected?


title: The definition of $f_{NL}$ and transfer function

text: To me there seems to be quite a few different definitions of $f_{NL}$ in cosmology and I would like to know if or how they are equivalent. Let me cite at least 3 such,   * One can see the equation 6.71 on page 100 of the book "The Primordial Density Perturbation" by Liddle and Lyth. The closest one can make 6.71 look like the following two is through equations 25.21 and 25.22 - but it still doesn't really become equal to the following.   * One can see equation 2 (page 3) of this paper. In this equation I am hoping that the quantity $\Phi(x)$ called the "Bardeen's curvature perturbation" really what is called $\xi$ in the Liidle and Lyth book or in Dodelson's.    * One can see the definition at the bottom of page 1 in this very famous paper. Here curiously though the equation looks exactly the same as in the paper above, the quantity $\Phi(x)$ is called the "gravitational potential in the matter era" I wonder if one can hope to somewhat translate between the last two definitions by using the relation $\xi = \frac{2}{3}\Phi \vert_{post\text{ }inflation}$ - but even then the last two definitions are not really "equal". Further this "discrepancy" between the definitions of $f_{NL}$ seem to be kind of related to the same problem with the definition of the ``transfer function" ($T(k)$),   * In the first paper cited above, one sees a definition of $T(k)$ in equation 9 and 10.   * But the closest one can get to the above is if one eliminates $\Phi(\vec{k},a)$ between equation 7.7 and 7.5 in Dodelson and then replaces $\Phi_p$ as $\Phi \vert_{post\text{ }inflation}$ and converts that into $\xi$ through $\xi = \frac{2}{3}\Phi \vert_{post\text{ }inflation}$ (..and hope that $\Phi$ in equation 2 and 9 of of the paper is actually $\xi$..) But still the two definitions of transfer function don't match!   * And the above two definitions are anyway still very far from the definition of $T(k)$ as in equation 8.52 (page 125) of the above cited book by Liddle and Lyth. It would be very helpful if someone can help reconcile the above!


title: What really is the future about the Standard Model

text: The fact that the bosons of the weak force have mass is something that I think technically poses many problems. To avoid this and other problems with the masses of the particles devised a mechanism within the standart model $SM$ of particle physics $"smpf"$ called "the Higgs field." This field is transmitted by a boson and the passage of particles interacting with him for the generated field causes an inertia that is what we perceive as "mass". The Higgs mechanism is accepted as part of SMPF, but can not be verified until we find the corresponding Higgs boson in a particle accelerator. Higgs boson we think we know that its mass is between $115 Gev$ and $200 Gev$, so it is expected to locate in the new collider at CERN: the LHC (Large Hadron Collider). As it is believed, has not been able to fit the force of gravity with quantum mechanics. A partial unification of the force would be the existence of a boson which would transmit the gravitational force, which we call graviton. If there was such a graviton. The graviton would be a hypothetical particle that many physicists believe. The $smpf$ presents the problem that for the 20 core values to build a coherent theory need a very fine adjustment. String theory and other developments raise the possibility that this model is part of a collection larger particles called supersymmetry. If supersymmetry were valid, this would require fine-tuning the values of the particles. Supersymmetry is the existence of a correspondence between fermions and bosons in the that every fermion has a boson superpartner similar characteristics, and each one boson fermion superpartner. The problem is that the fermions and bosons we know there is neither a single case of correspondence. That is, if supersymmetry is correct, we should still find the superpartners of all particles in the model. The hypothetical fermions superpartners of bosons be called photino, winos, gluinos, etc.. And the superpartners of fermions bosons be called Selectron, sneutrino, squark, etc.. Is it possible perhaps that the existence of these superpartners dramatically change the established concept of the standard model and open the door to a group of new models that do not understand, or hardly understand?


title: For what rare events was the LHC built?

text: I understand that for low cross-section events a very high luminosity is necessary in order to obtain enough data to produce meaningful statistics. That is why the LHC was built. But which are these event which we are interested in? What are the events which would hint at new physics or would confirm theoretical models?


title: Is there a map of the particles in outer space?

text: Since outer space is not quite a vacuum, and the distribution of various heavenly bodies is locally inhomogeneous, it seems reasonable to expect that the density and variety of particles 'contaminating' the vacuum varies with time and space. Are there any maps or data sets which detail this variation?


title: Is quantity a dimension?

text: We believe that time is a dimension and that $x$,$ y$, $z$ are dimensions in space. Is quantity a dimension like these? And if not, how do we have dimensionless numbers (like $e$, $\pi$ etc.)?


title: General relativity: gauge fixing

text: In his lectures professor Hamber said that the metric tensor is not unique, just like the 4 vector potential is not unique for a unique field in electrodynamics. Since the metric tensor is symmetric, only ten components of the metric tensor are unique. However, as the covariant divergence of the Einstein's tensor is zero, 4 more constraints are imposed and hence the number of independent components of metric tensor now has come down to 6. Finally he says that only two are unique. How did he arrive at the final result of 2 unique components of metric tensor. Can you please explain tis me ? Also, what is the physical difference between Ricci tensor and Reimann tensor ?


title: Moving a bar magnet towards a freely hanging coil

text: "A bar magnet is moved towards a freely hanging coil. Determine if the coil stays stationary or not. If it moves, determine if it moves away or towards the magnet." My hypothesis: From Lenz's law an e.m.f will be induced in the coil to oppose the change in magnetic flux due to the relative approach of the bar magnet. The resultant current in the coil produces a force on the coil equal to the Lorentz force due to the approach of the bar magnet, and in the opposite direction. As such, the forces should cancel out, causing the magnet to remain stationary. I suspect that there are some flaws in my hypothesis. Are my deductions correct, and is there a better explanation? (note: I'm not sure if the coil will move or not)


title: Does the distance to the cosmic horizon Lorentz-contract? Does the universe Lorentz-contract?

text: Our universe has a finite size. It is often called the "radius of the universe", or "distance of the cosmic horizon". If we would fly with relativistic speed at the position of our Earth, would this finite size Lorentz-contract? Or would it stay the same? In simple words: Does the universe Lorentz-contract? Would be observe the same size for the universe whatever our speed with respect to the reference frame defined by the average mass in the universe?


title: Why does laser light not affect glowing materials?

text: I have this childrens rubber ball which glows in the dark after it's exposed to light. I "charge" it with a flash light then play with my dogs at night. I thought to try a very intense green laser, and see how the ball reacted. The laser light had no effect on the balls ability to glow. So I'm left wondering, why does laser light not allow luminescence (maybe not the right word) materials to glow? EDIT In Response to Answer. So I tried a little modification. I tried exciting the ball with three different light sources; a "super bright" Red LED, a very very "super bright" white LED and a blue LED of unknown specs (no package, bottom of my kit). I held the ball to each light source (driven with the same current) for the same approximate amount of time and compared the results. The red LED had no effect. The white had a bit of an effect, enough to see dimly in normal room lighting. The blue led had a significant effect, causing a bright glow. This was interesting as the blue LED was the least bright visually. Yay science!


title: Mathematically, how do we deduce that angular momentum is bounded?

text: So, how do we know $J_{+}|j,(m=j)\rangle =|0\rangle$? I.e. that m is bounded by j. We know that $J_{+}|j,(m=j)\rangle =C|j, j+1\rangle$, but how do I know that gives zero? Is it by looking at its norm-square?


title: Cable TV version of infinite ladder network

text: This is a problem in a college physics textbook, and its bugging me that I can't get it. The figure shows a circuit model for the transmission of an electrical signal, such as cable TV, to a large number of subscribers. Each subscriber connects a load resistance RL between the transmission line and the ground. The ground is assumed to be at zero potential and able to carry any current between any ground connections with negligible resistance. The resistance of the transmission line itself between the connection points of different subscribers is modeled as the constant resistance RT. **Prove the the equivilent resistance as seen by the cable tv company is the equation at the top of the image.** I found this suggestion: Because the number of subscribers is large, the equivalent resistance would not change noticably if the first subscriber cancelled his service. Consequently, the equivalent resistance of the section of the circuit to the right of the first load resistor is nearly equal to Req. ![enter image description here](http://i.stack.imgur.com/EGFya.gif)


title: magnetic scalar potential far above a magnetic film

text: The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that far above the plate, the field should approach the dipolar field which scales as $1/r^3$. However my numerical calculations are yielding $1/r^4$. I am using Jackson's book (3rd ed.) as a guide. I assume discontinuous magnetization at the surface so I can use Jackson's Eq. 5.100 which is the magnetic scalar potential: $\Phi_M (\bf{x}) = \frac{1}{4 \pi} \oint_S \frac{\bf{n}' \cdot \bf{M}(\bf{x}')}{|\bf{x}-\bf{x}'|}da'$ assuming that the magnetization $\bf{M}(\bf{x}')$ is uniform within the volume. The top and bottom surfaces of the film will contribute to the potential. If I focus just on the top surface and assume a normalized magnetization $\bf{M} = M \hat{z}$: $\Phi_M (\bf{x}) = \frac{1}{4 \pi} \oint_{top} \frac{ M}{|\bf{x}-\bf{x}'|}da'$. I do not see where to go from here or how the expected $1/r^2$ dependence will arise.


title: Exotic coupling

text: I have encountered the minimal coupling between a field and charges before $$H = \frac{1}{2m}(p-qA)^2,$$ whereby I am considering the classical case. The description minimal leads me to ask if there exist exotic couplings (non- minimal)? Could some examples of such couplings be discussed?


title: How did gunsmiths create revolver cylinders in 1850's without the use of electrical drill?

text: How did gunsmiths create revolver cylinders holes in 1850's without the use of electrical drill? Which referces/ books specialize providing knowledge in similar molding method?


title: Nuclear transition notation

text: I have a question which asks me to determine what x is for the following nuclear transition $$^{29}Si(\alpha, n)X$$ But I don't have any idea what this notation implies. Another example: $$^{111}Cd(n,x)^{112}Cd$$


title: Can I prove boundedness of an operator without checking it for its whole domain?

text: (I don't have a direct reference so this is a little fishy and I'll delete it if nobody recognises what I'm talking about, but I though for starters I'll ask anyway) I've heard at university that if you have a operator (linear Hilbert space operator?) which is bounded on a restricted (compact?) domain, then it's bounded on the whole space. Put differently, to prove that an operator is bounded, you don't actually need to show it in the whole space. However, if you restrict the domain of the position operator it becomes unbouned right? That's a contradiction. In a finite dimensional example I see that you just have to check eigenvalues and hence consider the action on the base. The domain of the position operator is the function space with deltas as its base right? does restricting the domain here mean cut of $\delta(x-a)$ after $a\in \mathbb{R}$ has reached a certain value? I.e. considering only functions of compact support?


title: How does the atmospheric UVB attenuation of terrestrial planets compare?

text: On Earth, UVB (280nm - 315nm or 320nm depending on the source) undergoes extensive attenuation through the atmosphere, when observed at the planet's surface, as illustrated below: ![enter image description here](http://i.stack.imgur.com/utbcZ.png) Image source This is primarily due to the ozone layer, a feature unique to Earth amongst the terrestrial planets (Venus, Earth and Mars). Given the different atmospheric chemistries and differences in distances from the Sun of Venus and Mars, what UVB attenuation has been observed or simulated for Venus and Mars? Additionally, what UVB attenuation has been observed (or simulated in this case) on Titan? Any peer reviewed resources would be appreciated here.


title: Effect of strength of magnetic field on the height of a levitating superconductor?

text: Quantum levitation, flux pinning -- basically, when a superconductor floats above a permanent magnet, is really fascinating. But does the strength of the magnetic field influence the superconductor's height? And what relationship/formula suggests this? For example, if I had a coil wrapped around a metal object and then ran a small current through it, a small magnetic field would be generated and a superconductor exposed to it would float about it at some height that I put it on. But what if I increased the current, so that the magnetic field also increased? What happens to the superconductor? Does its height change? Or does it just get harder to "pull out" of its levitating state?


title: Pumping water from a closed column. Will the column get empty or just circualte?

text: As a picture is worth a thousand words, here is my problem: ![Picture here](http://s21.postimage.org/rv7a0t8br/problem_pressure.png) It is a closed water column with a bit of air in the top section. If I run the pump and make the water flow from IN to OUT,   1. Will the level stay the same and the water circulate indefinitely? or   2. Will slowly start to go down in the column and and the left side rise until it overflow?


title: friction on atomic scale

text: I am getting into friction on an atomic scale. For instance, take two rigid layers of atoms of the kind A that are placed on top of each other, just like putting two boards of wood on top of each other. Then place some atoms or molecules of the kind B between those two rigid layers, i.e. put some pebbles between the two wooden boards. Now start pushing one of the rigid layers horizontally, i.e. start pushing the wooden board on top. On the macroscopic scale, we will be able to treat this system with Newtonian Mechanics and (relatively) simple approximations, i.e. friction forces. How about the microscopic scale? When I google "friction microscopic scale", I get lots of results about ongoing research that is a bit above my level. Where would be a good place to start reading about this in general? I plan to dive into this, bearing in mind to maybe go on and model such systems computationally.


title: Absolute zero and Heisenberg uncertainty principle

text: I got to read Feynman vol I and there was written that at absolute zero, molecular motion doesn't cease at all, because if so happens, we will be able to make precise determination of position and momentum of the atom. But we do know that Heisenberg uncertainty principle holds for microscopic particle IN MOTION....then what is wrong to consider that all molecular motion ceases at absolute zero...need some help!


title: Probability of measuring two observables in a mixed state

text: Lets say i have density Matrix on the usual base $$ \rho = \left( \begin{array}{cccc} \frac{3}{14} & \frac{3}{14} & 0 & 0 \\\ \frac{3}{14} & \frac{3}{14} & 0 & 0 \\\ 0 & 0 & 0 & 0 \\\ 0 & 0 & 0 & \frac{4}{7} \\\ \end{array} \right) $$ from this two states $$|v_1\rangle=\frac{1}{\sqrt{2}}\left( \begin{array}{c} 1\\\ 1 \\\ 0 \\\ 0 \\\ \end{array} \right);|v_2\rangle=\left( \begin{array}{c} 0\\\ 0 \\\ 0 \\\ 1 \\\ \end{array} \right)$$ with weights $\frac{3}{7}$ and $\frac{4}{7}$ respectively And two observables A and B $$A=\left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\\ 0 & 1 & 0 & 0 \\\ 0 & 0 & 2 & 0 \\\ 0 & 0 & 0 & 2 \\\ \end{array} \right) $$ $$B=\left( \begin{array}{cccc} 3 & 0 & 0 & 0 \\\ 0 & 4 & 0 & 0 \\\ 0 & 0 & 3 & 0 \\\ 0 & 0 & 0 & 4 \\\ \end{array} \right) $$ If you measure $A$ and $B$ at the same time, what you are doing is measuring $A$ with some state and measuring $B$ with not necessarily the same state but it may be the same. So if I am trying to measure probability of measuring 2 and 4, that is $p(2)\times p(4)$ ? Thats $p(2) = \frac{4}{7} $ and $p(4) = \frac{11}{14}$ then obtaining the two at the same time is $ \frac{4}{7}\times\frac{11}{14} = \frac{22}{49}$ What confuses me is, why is lower than $\frac{4}{7}$, since $|v_2\rangle$ has that chance of being measured, the other state just adds chances of measuring 4 with B. Whats really going on here?


title: $E=mc^2$ and particles

text: This is a simple question. Does the Energy create both Fermion and Boson particles ? or just only the Fermion particles?


title: Orienational order parameter in isotropic systems

text: I have what may be a dummy question. In NMR or in the study of liquid crystals for example, an order parameter $S$ is often used: $$ S=\left\langle\frac{1}{2}\left(3\cos^2\theta−1\right)\right\rangle $$ with $\theta$ the angle of the molecule with a "director" (the magnetic field in NMR, the normal to a membrane for lipids, the global direction in a nematic phase etc). $S$ corresponds to a second-order Legendre polynomial. I have often read that in an isotropic environment, $S=0$ whereas when all the molecules are well aligned with the reference vector (director), $S=1$. I understand why $S=1$ as $\theta=0$° but I can't find why $S=0$ when all the orientations are random. Can anyone help me? Liam


title: Are isolated many-particle quantum systems always in a pure state?

text: I am trying to understand pure and mixed states better. If I have N quantum particles in an isolated system. The many-particle state is a superposition of the product of single-particle states by the appropriate statistics (bosons, fermions, or distinguishable). Would this state be still considered pure since there is no interaction with the environment? Does that mean isolated systems or microcanonical ensembles are always pure?


title: Can Aluminium be softened

text: I have an aluminium baking plate that I did put in a very hot oven and now it is soft, so I can bend it or almost roll it up. Why?


title: Radiated power and energy density for a black-body

text: I am having an hard time trying to understand why the radiated power per unit area $P$ of a black body is given by $$P=\frac{c}{4} u$$ in terms of the energy density $u$ and the velocity of light. I know there is a derivation in HyperPhysics, but I did not find it particularly convincing. I cannot understand the physical significance of the parameter $\theta$ and what is its relationship with the the total energy per unit time provided by a unit area. Could someone explain it better to me?


title: Non-locality and quanta

text: Quantum mechanics is non-local in that long distance correlations are present, though there is no signalling possible. But QFT is Lorentz invariant and contains quantum mechanics as a special case. I assume this is not a paradox as paradoxes do not exist but I do not understand the details. Can anyone supply a reference or satisfactory explanation?


title: Functionals of quantum states in QFT

text: Almost every book and article I can think of represents states of QFT using the Heisenberg picture of Hilbert space vectors, but Visser in "Lorentzian wormholes" does mention that you can also represent them as a functional. It is very briefly mentionned, and he does not mention any sources for it, just the result : $\Psi_0[t, \Phi(\vec{x})] \propto e^{-\frac{1}{2\hbar c}\int d^3x\Phi(\vec{x}) \sqrt{-\nabla^2} \Phi(\vec{x})} e^{-\frac{i}{\hbar}E_0t}$ With $\sqrt{-\nabla^2}$ some pseudodifferential operator. Is there any source, book or otherwise, that expands on this topic?


title: Polarization vector and bound charge

text: Why is it that the bound charge is $Q_b = - \oint_S{\mathbf{P} \cdot d\mathbf{S}}$? In particular, why is there a negative sign? Hayt's book on electromagnetism describes this as the "net increase in bound charge within the closed surface". Compared to Gauss' law $Q_{f} = \oint_S{\mathbf{D} \cdot d\mathbf{S}}$, the free charge is just the electric flux, so I don't see why the bound charge has a negative sign. Also, if the electric flux is independent of bound charge, how come the D-field changes across material boundaries? I thought the D-field was defined as $\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}$ to cancel out the effect of the bound charge (since the effect of polarization is already incorporated into the E-field). Is the D-field dependent on bound charge? Just to add to the second part of my question. I know that for a dielectric- dielectric boundary the tangential components $\frac{D_{t1}}{\epsilon_1} = \frac{D_{t2}}{\epsilon_2}$ and if $Q_{free} = 0$ on the boundary, then the normal components $D_{n1} = D_{n2}$. The tangential component will not contribute to the flux integral so for any $\epsilon_1$ and $\epsilon_2$ across a boundary the electric flux integral will evaluate to 0. It's clear that the flux is independent of the bound charge, but the the tangential component changes so the D-field is not?


title: What aspects of QFT do mathematicians find troublesome?

text: What aspects of "conventional" quantum field theory (i.e. what's used by most practicing physicists) are considered to be lacking mathematical rigor?


title: Angular Momentum Conservation

text: There's a question I've come across that I've got some confusion on. > A drum of mass $M_A$ and radius $a$ rotates freely with initial angular > speed $\omega _0$. A second drum of radius $b>a$ and mass $M_B$ is mounted > on the same axis, although it is free to rotate. A thin layer of sand $M_s$ > is evenly distributed on the inner surface of the smaller drum (drum $A$). > At $t=0$ small perforations in the inner drum are opened, and sand starts to > fly out at a rate $\dfrac{dM}{dt}=\lambda$ and sticks to the outer drum. > Find subsequent angular velocities of the two drums. Ignore the transit time > of the sand In this question, we start off with an initial angular momentum of $L_0 = I_A \omega = (M_A +M_s ) a^2 \omega _0 $ (where the moment of inertia for a drum is $I=mr^2$). If my understanding of conservation of angular momentum holds, this should mean that at all times, this system _must_ maintain this initial value of $L$. I understand that as long as there is no external torque, $\frac{dL}{dt}=0$, and hence be constant. Here's where my confusion comes in. Say we only include drum $A$ to be in our system. It's starts off with $L_0$, and as it loses mass, it must continue to rotate faster in order to keep $L_0$ constant. But if we now consider both drum $A$ and $B$ to be in our system, this can't possibly be the case. If drum $A$ continues to "compensate" for this loss in mass by having an angular acceleration, drum $B$ would have to remain stationary so that our value of $L_0$ remains stationary. In both cases, we have zero external forces, and so that means $\tau = 0$, but in the second system, we have an internal torque being applied to drum $B$ by the sand. Where's my error?


title: Taylor expansion term equals zero?

text: I have to Taylor expand an effective potential $U_{eff}$, which is given by: $$U_{eff}(r)=-\frac{Gm_{1}m_{2}}{r}+\frac{l^{2}}{2\mu r^{2}}$$ I then expand it and get: $$U_{eff}(r)=U_{eff}(r_{min})+\frac{dU_{eff}}{dr}\bigg|_{r=r_{min}}(r-r_{min}) +\frac{1}{2}\frac{d^{2}U_{eff}}{dr^{2}}\bigg|_{r=r_{min}}(r-r_{min})^{2} + \dots$$ Now, according to my book, it says that the 2nd term equals zero, or at least the derivative term of the 2nd term is. But it doesn't say why, so I'm kinda confused as why this is ? Is it some basic stuff I have forgotten, or is it something else ?


title: How can I show non-Abelian CS term is a total derivative?

text: I want to show:$$ Tr\left (F\tilde{F} \right )=\partial_{\mu}K^{\mu }=\partial_{\mu}\left (\varepsilon _{\mu \nu \rho \sigma }Tr\left ( F_{\nu \varrho }A_{\sigma }-\frac{2}{3}A_{\nu }A_{\rho }A_{\sigma} \right )\right ).$$


title: Electrodynamic multipole expansion

text: I am reading Jackson, Classical Electrodynamics, and I have a question regarding the electrodynamic multipole expansion (with page numbers I refer to the 3rd edition). So on page 409, he gives in equation 9.9 the general formula for the expansion of the vector potential: $$\lim_{kr \rightarrow \infty} \mathbf A (\mathbf x) = \frac{\mu_0}{4\pi} \frac{e^{ikr}}{r} \sum_n \frac{(-ik)^n}{n!} \int \mathbf j (\mathbf x' ) (\mathbf n \cdot \mathbf x')^n d^3 x'$$ In the following, he takes the orders $n=0$ and $n=1$ and constructs the vector potential with the "physical" multipole moments, i. e. in order $n=0$ the electric dipole moment and for $n=1$ the electric quadrupole tensor and the magnetic dipole moment. Then on p. 415 he says, that from order $n=2$ upwards, the labor becomes increasingly prohibitive to do this decomposition in physical moments again. Instead, he indicates, that a systematic expansion is much easier (what, of course, I understand). So I'm wondering now, if this decomposition has ever been done for $n=2$ (to get the electric octupole and the magnetic quadrupole tensor) or even higher orders, and if so, if is there a paper where this sophisticated task has been written down?


title: Argument for symmetry of potential of a spherical capacitor filled with dielectric

text: A spherical capacitor with inner radius $r_1$ and outer radius $r_2$ is filled with dielectric material with permittivity $\epsilon=\epsilon_0+\epsilon_1\cos^2\theta $.   $\theta$ is the polar angle. Furthermore there is a charge $Q$ on the inner surface at $r_1$ and a charge $-Q$ on the surface at $r_2$. Give reasons why the potential $\Phi(r,\theta,\varphi)$ is for all $r$ independent of $\theta$ and $\varphi$. The independence of $\varphi$ is clear as our problem is invariant under $\varphi$-rotations. I'm not able to find a valid argument why the potential is independent of $\theta$. Thanks in advance for help !


title: how to measure the age of light?

text: We measure distances in universe by the units of light year/s or parsec. Which means distance traveled by light in one year equals one light year. Thus the lights we receive from the distant stars or galaxies are coming from many light years away. So how do we know the age of the light so that we determine the distance it has traveled to reach earth ?


title: How come water in a cup won't shoot out of a straw placed inside it?

text: I've been learning about pressure and fluid dynamics, and I've stumbled onto a problem. Say you have a straw in a cup. The surface area of the water in the cup is much greater than that of the straw. So, I would expect Atm. Pressure × Large Area (of the cup) gives a _much_ greater force than Atm. Pressure × Small Area (of the straw). In fact, the force is so much larger I would expect a spectacular jet of water, which obviously does not happen. What am I missing? Thanks EDIT: So I chose a _really_ bad example. Consider any amount of fluid with two openings of different size (facing upwards). Shouldn't the force due to the atmosphere shoot the water out the smaller opening, since the force on the larger opening due to the atmosphere is greater?


title: What does f/4.6 mean in a telescope and how important is this value?

text: In some specifications for telescopes, I saw a value marked as f/4.6. What does it mean exactly, and how important is when it comes to choosing a telescope?


title: What is the lenght of the rope?

text: The $E$ string of a violin has a linear density of $0.5 g / m$ and is subjected to a $80\text{N}$ of tension, tuned for a frequency $u = 660 \text{Hz}$:   1. What is the length of the rope? I know that in order to answer the question I have manipulate the equation: $$ \nu = \sqrt\frac{\tau}{\mu} $$ Getting this equation: $$ L = \frac{m v^2}{T} $$ I have tried to find the mass but my attempts was unsucessufull. I think that i could use the equation: $$ f_1 = \frac{\sqrt\frac{T}{m/L}}{2L} $$ In order to find the lenght, but I need help to find the mass of the rope.