title: Infrared-free QED and Higgsless standard model phenomenology

text: This is one of those "what if" fantasy world type questions. I like hard sci- fi so please no "well, you changed one thing about the world so now anything goes." :) What if the Higgs had no vev? That is essentially this question and I was charmed by Ron Maimon's excellent answer to it, but I was under the impression from this statement of his: > The massless electron will lead the electromagnetic coupling (the unHiggsed > U(1) left over below the QCD scale) to logarithmically go to zero at large > distances, from the log-running of QED screening. So electromagnetism, > although it will be the same subgroup of SU(2) and U(1) as in the Higgsed > standard model, will be much weaker at macroscopic distances than it is in > our universe. > > ... > > The combination of a long-ranged attractive nuclear force and a log-running > screened electromagnetic force might give you nuclear bound galaxies, held > at fixed densities by the residual slowly screened electrostatic repulsion. > These galaxies will be penetrated by a cloud of massless electrons and > positrons constantly pair-producing from the vacuum. and recently reading about the log running in Shifman, _Advanced Topics in Quantum Field Theory_ , that massless QED would be very weak at macroscopic distances. Of course, log running is slow so this seemed a little odd as well, so I decided to calculate. The (one loop) running coupling of QED with one massless charged fermion is $$ e^2(p) = \frac{e^2(\mu)}{1-\frac{e^2(\mu)}{6\pi^2}\ln\frac{p}{\mu}}, $$ where $\mu$ is the arbitrary renormalization point and $p\sim 1/\ell$ is the scale of the probe. I took $\mu=1\ \mathrm{MeV}$ and set $e^2(\mu)=4\pi\alpha$ and got this: ![enter image description here](http://i.stack.imgur.com/fwddQ.png) Note the scale. So the log running really is _slow_. Even at the Hubble scale the effective charge is only reduced by about 6%! Including $N$ massless charged flavours multiplies the beta function (yeah?): $$ \frac{\mathrm{d}e}{\mathrm{d \ln\mu}} = N \frac{e^3}{12\pi^2}, $$ so the coupling becomes $$ e^2(p) = \frac{e^2(\mu)}{1-\frac{N e^2(\mu)}{6\pi^2}\ln\frac{p}{\mu}}. $$ For the SM $N=3$ (assuming all the charged mesons are above 1 MeV - is this true?) this increases the running, but not much: ![enter image description here](http://i.stack.imgur.com/EOot7.png) So EM is still sizable at cosmological distances if:   1. I didn't make any mistakes,   2. And the number of massless charged particles isn't too great. This was somewhat surprising to me, though perhaps only because I misunderstood the assertion. It is certainly the case that atoms blow up (Bohr radius $a\sim1/\alpha m_e\to\infty$) so life is definitely not as we know it, but EM is still an important interaction at large scales - large enough to expect matter to form neutral conglomerates much smaller than galaxies. It is not at all clear to me that the dominant effect is an electrostatic repulsion that would stabilize any kind of nuclear bound galaxy. So: What is the real phenomenology of the Higgs-less SM? Can anyone elaborate on Ron Maimon's vision?


title: How does Newtonian gravitation conflict with special relativity?

text: In the Wikipedia article Classical Field Theory (Gravitation), it says > After Newtonian gravitation was found to be inconsistent with special > relativity, . . . I don't see how Newtonian gravitation itself is inconsistent with special relativity. After all, Newton's Universal Law of Gravitation is completley analogous to Coulomb's Law, so it would seem that, if there were an analogous "gravitational magnetic field", one could formulate a theory of gravitation in exact analogy with Maxwell's Theory of Electromagnetism, and of course, this would automatically be consistent with Special Relativity. What about this approach to gravitation does not work? The only problem I could see with this is the lack of evidence for a "gravitational magnetic field". That being said, gravity is "weak" as it is, and my guess is that it would be extremely difficult to set up an experiment in which a _massive_ body were moving _fast_ enough for this "magnetic field effect" to be obsevable. EDIT: As has been pointed out to me in the answers, Newton itself is inconsistent with SR. Similarly, however, so is Coulomb's Law, yet, electromagnetism is still consistent with SR. Thus, how do we know that it is not the case that Newton's Law is the special "static" case of a more general gravitomagnetic theory exactly analogous to Maxwell's Theory: Let $\mathbf{G}$ be the gravitation field, let $\rho$ be the mass density, and $\mathbf{J}$ be the mass current density, let $\gamma _0$ be defined so that $\frac{1}{4\pi \gamma _0}=G$, the Universal Gravitation Constant, let $\nu _0$ be defined so that $\frac{1}{\sqrt{\gamma _0\nu _0}}=c$, and suppose there exists a field $\mathbf{M}$, the gravitomagnetic field, so that the following equations hold: $$ \vec{\nabla}\cdot \mathbf{G}=-\frac{\rho}{\gamma _0} $$ $$ \vec{\nabla}\cdot \mathbf{M}=0 $$ $$ \vec{\nabla}\times \mathbf{G}=-\frac{\partial \mathbf{M}}{\partial t} $$ $$ \vec{\nabla}\times \mathbf{M}=\nu _0\mathbf{J}+\gamma _0\nu _0\frac{\partial \mathbf{G}}{\partial t} $$ where theses fields would produce on a mass $m$ moving with velocity $\mathbf{v}$ in our inertial frame the Lorentz force $\mathbf{F}=m\left( \mathbf{G}+\mathbf{v}\times \mathbf{M}\right)$. This theory would automatically be consistent with SR and would reduce to Newton's Law of Gravitation for the case of gravitostatics: $\frac{\partial \mathbf{G}}{\partial t}=\frac{\partial \mathbf{M}}{\partial t}=\mathbf{J}=0$. (To be clear, you can't just set the time derivatives equal to $\mathbf{0}$ as it seems I have done. Upon doing so, you obtain the corresponding static theory, which is technically _incorrect_ (as you can easily see because it won't be relativistically invariant), but is nevertheless often a useful _approximation_.) My question can thus be phrased as: without appealing directly to GR, what is wrong with this theory?


title: Why can you assume that the angular momentum vector of a top will always track its axis of rotation?

text: My favorite physics 101 textbook (Giancoli) explains precession in terms of a spinning top whose axis is tilted from the vertical. The way the book sets things up, $L$ (angular momentum) points along the top's axis, and $\operatorname{d}\\!L$ is perpendicular and horizontal to $L$, pointing in the direction of precession (in their figure, $\operatorname{d}\\!L$ ends up pointing to the right). It then goes on to state that since $\operatorname{d}\\!L$ is always perpendicular to $L$, $L$'s magnitude is constant, and only its direction changes. Finally, it concludes: > Since $L$ points along the axis of the top, we see that this axis moves to > the right... (Giancoli, 2008) I just don't understand why you can assume that it will always be true that $L$ and the axis of the top will always lie on top of one another. The book doesn't address this, but is there only one way in which the top can move in order to produce the required motion of the angular momentum vector? If that is the case, then I guess it would make more sense? I dunno. Help me out here folks. (I know that there is a deviation in $L$ due to the precessional motion itself, but another one of the book's assumptions is that this is irrelevant as long as the top is spinning quickly enough.)


title: Relativistic Dynamical System

text: I have read in a paper that: A relativistic dynamical system must be invariant under infinitesimal inhomogeneous Lorentz transformation. A dynamical system is characterized by the ten generators, $P^\mu$ and $M^{\mu\nu}$, of the Poincare group, where $P^\mu$ is the momentum 4-vector and $M^{\mu\nu}$ is the rotation and boost operators. Here, what does 'A relativistic dynamical system' mean? Reference: http://inspirehep.net/record/514295?ln=en (page: 95)


title: How to compute the propogator for Chern-Simons on a torus?

text: I'm looking to better understand Chern-Simons theory on a torus. We are given the action $$ S(\phi) = \int_E (\partial \phi)(\overline\partial \phi) + \frac{\lambda}{6}(\partial \phi)^3 $$ which yields (apparently) the propagator $$ P(z) = \frac{1}{4\pi}\wp(z;\tau) - \frac{1}{12}E_2(\tau) $$ (at least for $z \neq 0$) What I would like to understand is the meaning of the terms in the action, as well as how the propagator is derived. Classically, the action $$ \int_E (\partial \phi)(\overline\partial\phi) $$ yields the equation of motion $$ \partial\overline\partial\phi = 0 $$ or that $\phi(z, \overline z)$ is of the form $\phi_1(z) + \phi_2(\overline z)$. This then seems suggestive that the interaction term $(\partial \phi)^3$ tells us that we are only interested in _holomorphic_ functions on $E$, which of course are going to be given by some combination of $\wp(z;\tau)$ and its derivatives. This seems reasonable, but other than an intuitive feel, I don't see why this is actually the case. My questions are:   1. Is this a reasonable interpretation of the terms in the action?   2. Since my reasoning was based on classical ideas, how does this carry over to the quantum setting?   3. Given the above, how does one use this to derive that the propagator is as given above and not, say, $$ P(z) = \wp'(z)\big(\wp(z) + E_4(\tau)\big) $$ or something else similar? I should probably specify that I am a mathematician, not a physicist.


title: details for the double slit experiment

text: In the double slit experiment with electrons, are all electrons going through the slits? If the electron gun is directed between two slits, than it should hit the central part between the slits, isn't it? So if one would count ( **not watch** the flying electrons, to not collapse the wave function) the electrons hited the central part and the screen - **would the whole number of electrons be the same number shot from the gun**? Additional question: if the part with two slits has a thickness, could an electron hit the inner surface (side) of the slit (still, no watching the electrons in the space, but only detecting the hits of the surface in the slit)? The idea behind the question: could some electrons just get lost or go through the wall between slits without hitting it?


title: Resonating frequencies of atoms

text: I have a mathematics and computer science background with very little physics. I have read that the resonating frequency of an atom of some element is always **exactly** the same as the resonating frequency of any other atom of that element. This doesn't sit too well with me, I would have thought the resonating frequency could be viewed as a continuous random variable with an arbitrarily small standard deviation, but to say the resonating frequency is **exactly** an extremely strong statement to make. Is this actually the case?


title: How the electric potential of a charged body depends on the surface area of the body?

text: I have studied in the book that electric potential of a body depend on the surface area of the body, that is as the surface area increases potential decreases keeping the charge as constant and vice versa, but no explanation for this.


title: Interpretation: probability form probability amplitude (free particle)

text: If you compute the probability amplitude of a free 1D non-relativistic particle with mass $m$, located at position $x_0$ at time $t_0$, for beeing detected at some other point $x_N$ at time $t_N$ you will find it to be given by $$ \mathcal{M} = \left\langle x_N \right| \text{e}^{-\frac{\text{i}}{\hbar} \frac{P^2}{2m}(t_N-t_0)}\left| x_0\right\rangle =\left(\frac{m}{2\pi\text{i}\hbar\ (t_N-t_0)}\right)^{1/2} \text{e}^{\frac{\text{i}}{\hbar}\frac{m}{2}\frac{(x_N-x_0)^2}{t_N-t_0}} $$ Now, if I compute the corresponding probability(density) according to $$ P = \left|\mathcal{M}\right|^2 = \mathcal{M} \mathcal{M}^* = \frac{m}{2\pi\hbar\ (t_N-t_0)} $$ it somehow strikes me that it does not depend on the distance $(x_N-x_0)$ at all. Does this mean, that the probability of detecting the particle is the SAME everywhere? I expected something like the initial (i.e. $t_N \rightarrow t_0$) delta function "melting away" like a Gaussian wave packet... Can anyone tell me what the correct interpretation of $P$ should be?


title: Information or Matter or Energy

text: **Which one is the most fundamental of the universe? What it is made of?** Physicists are searching for unique and fundamental form. The question is , information is more fundamental than energy ? According to the thermodynamic Physics **information is any kind of event that affects the state of a dynamic system that can interpret the information.** But as far as I know its a bit of energy as I heard from the Physicist Lineard Susskind's Lectures. Will you please clarify according to the article ? Actually I was confused reading the head line article.http://www.pbs.org/wgbh/nova/blogs/physics/2014/04/is-information- fundamental/ I want to know that why are they referring the information as fundamental unity? Isn't it that Information is a mathematical concept or its a bit of energy i mean quantized energy?


title: Intuition/derivation behind the probability current definition

text: The definition is: $${\bf{j}} = \frac{\hbar}{2mi} (\psi^* \nabla \psi - \psi \nabla \psi^*)$$ However: Where ever I have looked, the above "pops out of nowhere". I was wondering how can I obtain some intuition about this, and/or, can it be derived from some related definition/s?


title: Calculating stiffness of a beam of non-constant cross section

text: I am considering a paraboloid shape which is fixed at its base and is being compressed downwards. I am trying to find its stiffness so I can calculate how much it deforms. When I attempt to do this I get a result that the stiffness is zero. Can anyone point out where I have made a mistake? First I'll define more clearly what paraboloid I am talking about. Paraboloids have a shape like this: ![enter image description here](http://i.stack.imgur.com/zlkeM.png) Which can be expressed by the equation $\frac{z}{c}=\frac{x^2}{a^2}+\frac{y^2}{b^2}$ But that equation is only valid for paraboloids with the origin at their peak. The paraboloid I am considering has the origin at the base so it looks like this: ![enter image description here](http://i.stack.imgur.com/RuKSY.png) I hope that diagram is clear enough. The base is a circle so the scaling factors $a^2$ and $b^2$ are equal. The peak has been displaced by a distance $h$ so the equation becomes $\frac{h-z}{c}=\frac{x^2}{a^2}+\frac{y^2}{a^2}$ The square of the radius of the cross-section is $x^2+y^2$. At $z=0$ we know that $x^2+y^2=a^2$ Putting that information into the equation I get $\frac{h-0}{c}=\frac{a^2}{a^2}$ $c=h$ So the final equation of the paraboloid is $\frac{h-z}{h}=\frac{x^2+y^2}{a^2}$ Now, the way I will calculate the stiffness is to cut the paraboloid into slices along the axis of symmetry and sum the stiffness of all the slices. For a slice of width $l$, cross-sectional area $A$, and Young's modulus $E$; the stiffness $k$ is given by: $k=\frac{EA}{l}$ To sum $N$ slices in series I treat them like $N$ springs in series. The equivalent stiffness $k_e$ is given by the formula: $\frac{1}{k_e}= \sum_{i=1}^N \frac{1}{k_i}$ In the limit as the thickness of each slice becomes very small and $N$ tends to infinity the sum becomes an integral. The slices I am using have a width $dz$ and a cross-sectional area which is a function of $z$ so the stiffness of a slice is $k=\frac{EA(z)}{dz}$ The area is just a circle with $r=\sqrt{x^2+y^2}$ $A(z)= \pi r^2$ $A(z)= \pi (x^2+y^2)$ From the equation of the paraboloid I know that $x^2+y^2= \frac{a^2}{h}(h-z)$ $A(z)= \pi \frac{a^2}{h}(h-z)$ So the stiffness of a slice is $k= E \pi \frac{a^2}{h} \frac{h-z}{dz}$ For the integral the paraboloid extends from $z=0$ to $z=h$. Therefore, $\frac{1}{k_e}= \int_0^h \frac{h}{E \pi a^2} \frac{dz}{h-z}$ $\frac{1}{k_e}= \frac{h}{E \pi a^2} (-\ln(h-h)- -\ln(h-0))$ $\frac{1}{k_e}= \frac{h}{E \pi a^2} (-\ln(0)+ \ln(h))$ Since $\ln(0)$ is undefined or $-\infty$ in the limit the stiffness is zero in the limit. I do not understand why the integral does not converge.


1. Please describe how a vacuum flask/thermos works.    2. How does the vacuum prevent convection/conduction/radiation?    3. How does the lid with the curvy lines prevent either of the aforementioned heat transfers?    4. If there are any other parts that may prevent heat transfer, please also list them.


title: Hysteresis loop of soft iron for different field strengths?

text: When calculating the work done to magnetize a material, what is the usefulness of coercivity in that calculation? If the material $Hc = 0.5\: \mathrm{A/m}$ or $Hc = 9 \times 10^5\: \mathrm{A/m}$? I only know the area of the hysteresis loop reduced because of that, however, if a material $Hc$ is equal to $0.5$, and an exterior field of $1000\: \mathrm{A/m}$ is introduced and in another case, only a field of $100\: \mathrm{A/m}$, what would be the difference? Time?


title: Introductory derivations of Heisenberg uncertainty principle

text: I'm not an expert when it comes to quantum mechanics, so correct me wherever I'm wrong, but: I've always been a little bit bothered by introductory derivations of the Heisenberg uncertainty relations (for, for example, position and momentum) that involve carrying out an imaginary "observation" of a particle by bonking it with photons. The argument goes (at least the way I've heard it) that the more precision you want in the position measurement, the higher frequency (and so energy) the photon must have. Higher energy bonking leads to more uncertainty in the momentum afterward, and so there's a tradeoff between position and momentum precision. The derivations then manage to work out that the precisions satisfy the Heisenberg uncertainty relations. The problem I have with those kinds of derivations is that they start out assuming that a particle actually _has_ a position and momentum to speak of, and if you were lucky enough to guess them, you'd be able to predict the particle's motion exactly - it's entirely classical reasoning. The way I understand it, the position and momentum representations of the state are fourier transforms of each other, and so it's just a simple mathematical fact that as one becomes more localized, the other one becomes less localized. Another way of saying it (and please feel free to comment on the validity/value of this way of thinking about it), that I think makes it qualitatively more obvious, is that each observable corresponds to an eigenbasis. It's pretty intuitive that, in general, if one aligns the state vector closely with any one basis vector in one eigenbasis (corresponding to a nearly definite value of that observable), then the state vector _won't_ be aligned any one basis vector of the other observable, but will instead be a mixture of several basis vectors, and so will have an uncertain value of the other observable. If this sort of reasoning is correct, then it'd seem like the classical derivations of the Heisenberg uncertainty principle are complete gibberish - rather than having to do with a particular way the measurement is made, the limits on measuring simultaneous, definite values of position and momentum are a result of the fact (which the vector space representation makes plain) that a state cannot even have simultaneous definite values. If it really is true that the classical derivations of the Heisenberg uncertainty relations is whack, is there any value in them at all? Thanks!


title: Basics of Current Electricity

text: I have certain questions which confuse me a great deal. I want to have a very basic and clear idea about some concepts. Here it goes: 1) I am really confused on how a battery actually works. The very basic question that I have is whether positive ions flow in a battery? I ask this because my textbook uses phrases like 'positive ion flow'. While explaining the working of a battery, it highlights the journey of a positive ion across the circuit. I get confused because positive ions don't move in a wire. 2) I know potential difference between two points is the amount of work that needs to be done to move a positive charge from one point to the other. But when we talk about a battery, my textbook uses the phrase 'Potential difference between the electrodes'. I don't quite understand what this means. Does this mean that one electrode of the battery has an excess of electrons and the other has deficiency? What is the path of a charge through a cell? 3) Also, what does 'Potential Drop' means? Why does the potential drop across a resistor? I tried reading some resources but I don't get it. 4) What is EMF? I know the basic definition, but can you please explain with simplicity? I don't know if I'm unnecessarily confusing myself? Perhaps I should accept some things as facts. The main problem is that I really get confused while solving a problem. Clearing the questions I asked above would make me understand what I actually am doing while solving a question. Thank you!


title: Measuring parallaxes from the moon

text: If one were to measure star parallaxes from the moon, what (if any) changes would you have to make compared to someone making the calculation from earth? What about on another planet in our solar system?


title: Is everything moving at c in a c unit circle

text: I was trying to explain special relativity to a few friends in a simple way and wound up with an analogy using a c unit circle. I was using y as travelling in time, x moving in space; move in space and you are borrowing from your clock-speed. E.g. the twin paradox: Your travelling twin has borrowed clock-speed. Twins clock was slower -> twin is younger. What is the problem with representing relativity using a (c) unit circle from an observers point of view? Anything Lorentz or Minkowski would be out of the question of course, I'm looking for a layman friendly description that is close to true. The circle discussed, was in my mind a half circle $y>=0$. Where $y=0$ would be a photon.


title: Is it faster underwater to go down without air or up with air?

text: So I had a very interesting conversation between me and my friends about this topic, but we could not find the answer. **The Situation** Lets say you are in a pool and you want to touch the bottom and go up as fast as you can. You have two options - Go down without any air (suppose you can last long enough in the water...) thus creating a faster descent but longer ascent. Or you could suck as much air as possible thus creating a faster ascent but slower descent. Lets say you push yourself down with a pole connected to the pool and kick in the bottom with your legs. Suppose your hands are as strong as your legs and both the kick and the push provides the same force. And lets suppose the pool is an average 2.5 meter deep. You swim with your hands as fast as you can down and as fast as you can up, so lets suppose these also provides the same force. **The Question**   * Which option is faster? With or without air? I tend more towards "with air", because it has a minor effect on your weight but it gives you more "energy or power" to do the action.


title: What type of magnet to use?

text: I am asking this question to find out practical sizes of magnets, but this will be in a fictional setting. Say I have a person dressed in iron armor, medieval knight-style. Are there types of magnets that weigh on the order of 500 kg or so that would be strong enough to pull the armor to it? I'm not thinking of super-strength magnets like neodymium. Maybe a kg of force per kg of the magnet? Sorry, I'm not really familiar enough with magnets to know how to express their strength. What material would such a magnet be made of? Would the costs of making such a magnet be overly inhibitive, or is a magnet of that size even feasible?


title: If there turns out to be matter with negative mass, would there also be antimatter with negative mass?

text: I just heard of the concept of **negative mass**. Googling led me to see that the concept of negative mass is often contrasted with **antimatter**. This made me to wonder whether there would then also be a fourth category of **exotic matter** being **antimatter with negative mass**. Of this I can find no mention. If it turns out that we have **1)** normal matter **2)** antimatter and **3)** normal matter with negative mass, would that imply that we would also have **4)** antimatter with negative mass?


title: How many atoms does one need to get reliable crystal information with X ray or electron diffraction?

text: I know that, in theoretical derivations of X ray diffraction (XRD) or electron diffraction (ED), we always assume an infinite lattice, and, as you make the crystal smaller, edge effects start to matter more. As you make it even smaller, you start to lose information about actual orientation of the crystal and such (obviously, the diffraction from two atoms really tells you literally nothing). I know it's a continuum, so "reliable" is a little subjective, but at what point can you not get any useful information from XRD or ED? I've seen ED images inset in TEM pictures of ~10nm structures, which comes out to about 100 atoms.


title: Does a cooler, submerged in water, keep beer colder, longer?

text: Looking around the web, I see some submerged bucket-like things, without insulation, and some floating coolers, where the actual cooler is not submerged. Given that your water temperature is lower than the air temperature, would a mostly submerged, insulated cooler keep cold, inside, longer? Would the heat exchange be hastened by the conductivity of the water or slowed by the improved temperature differential between inside/outside the cooler? Summertime sea temp near Seattle is 52$^{\circ}$F. Lakes are warmer, maybe 60-65$^{\circ}$F. On a summer day, the air temp might be 65-75$^{\circ}$F. To clarify, I have a cooler with beer and ice inside, hopefully around 40$^{\circ}$F. I want to keep that beer as cold as possible, for as long as possible.


title: Friction effects on ball motion direction when crossing surfaces edges

text: For a ball rolling from a high friction coefficient surface to an adjacent low friction coefficient surface. When the ball crosses the boundary at an angle, I believe it changes angle of velocity, towards the boundary perpendicular direction.   1. Is there a name for this effect?   2. What is the equation?


title: Drag on a conductor moving in a uniform magnetic field

text: Given a conductor moving through a perfectly uniform magnetic field, what is the drag force experienced by the conductor (due to induced eddy currents, or any other magnetic interactions I may have overlooked)? If the field is non-uniform, but the conductor is small enough that the field is approximately uniform across its cross-section, can the same formula be used to calculate instantaneous drag at a given point, or is the derivative of the magnetic field important? All the resources I've been able to find on my own on this subject deal with the reverse case of a magnetic field of relative limited extent passing through an infinite 2D conductor, since that's the practical situation present in magnetic brakes. From The Design of Eddy-Current Magnet Brakes (Der-Ming Ma & Jaw-Kuen Shiau, 2010), I get the following formula (after some simplification) for that case: $ F_d = v \sigma B^2 V [1 - \frac{1}{2 \pi}(4 atan \phi + \phi ln(1+\frac{1}{\phi}^2) - \frac{1}{\phi}ln(1+\phi^2))] $ where $v$ is velocity, $\sigma$ is conductivity, $B$ is flux density, $V$ is the volume of conductor intersected by the magnetic field, and $\phi$ is the aspect ratio (length / width) of the area through which the magnetic field passes. The appendix of that same paper includes calculations of corrections to account for the finite vertical extent of the conductive rail in a magnetic brake system; this leads me to think that perhaps I could just duplicate the derivation of those corrections to account for the horizontal direction as well. I have, however, two problems with this approach: first, the given corrections are valid only for a rectangular conductor and a rectangular magnetic field projection area; second, the expressions are just Really Gnarly and gross, and my sense of elegance suggests that there must be a simpler, more direct way of calculating what I want.


title: Ricci curvature tensor, definition of symbols

text: So I know that $$R_{μν}:=R^λ_{μλν}$$ is the Ricci curvature tensor (where $R^λ_{μλν}$ is the Riemann Tensor). This is in Einstein's field equations: $$R_{μν}-\frac{1}{2}g_{μν}R=\frac{8πG}{c^4}Τ_{μν}$$ and hence I presume that μ and ν are identifies of the components of the tensors been looked at. But in this first equation what does the λ represent (I think it may just be another place identifier)? (and is may assumption about μ and ν correct?)


title: Wick rotation and the arrow of time

text: It is well known that we can switch from a statistical system to a quantum mechanical system by a Wick rotation. Has this rotation some implication on the way the time flow? namely, this is an accident or has a deep meaning?


title: A flyby of orbiting supermassive black holes

text: Consider two supermassive black holes of equal mass orbiting about their common centre of mass. Is it the case that a free-fall trajectory along the axis of rotation would be outside of either event horizon at all black hole separation distances > 0 (based on the symmetry of the situation)? To rephrase this, would you be able to navigate a rocket along a path at right angles to the orbital plane and bisecting the line between the two black holes with no ill effects whatsoever even when the black holes were very close to each other? Supplementary question: What is the shape of each of the event horizons prior to coalescence? _Note: I’m assuming that tidal forces would be small until the two singularities were extremely close. Note also that the point midway between the two BHs is the L1 Lagrangian point._


title: How reliant is the Solar System on being exactly the way it is?

text: We know that all objects with mass exert forces on all other objects of mass such that $$ F = \frac{GMm}{R^2}.$$ And as others have discussed the planets do interfere with each other gravitationally to a small degree. My question is how reliant the solar system is on its exact structure. If a planet were to change its alignment or orbit or gravitational effect on other planets, through gain of a mass through an asteroidal collision for example. Would a deviation in the structure of the solar system as it is cause it to collapse? e.g planets change orbits significantly enough to drift away from the sun or drift into it?


title: Event horizons without singularities

text: Someone answered this question by saying that black hole entropy conditions and no-hair theorems are asymptotic in nature -- the equations give an ideal solution which is approached quickly but never actually reached from the point of view of an observer outside the event horizon. Since then I've been wondering **whether singularities are ever really created** , and if not, why do we worry about naked singularities? Quick recap: to an external observer, an object falling into a black hole experiences time dilation such that it appears to take an infinite amount of time to cross the event horizon and ends up sitting frozen at the border. So here's my reasoning: the above should also apply during the formation of the black hole in the first place. The gravitational field _approaches_ infinite density as the constituent matter _approaches_ a central point, but to an outside observer, it takes an infinite amount of time for the singularity to form. In other words, _it never happens_. As I understand it, naked singularities are dismissed with hand-waving, "we'll fix it when we go quantum," but I don't see that as necessary. It seems to me that singularities never actually form, although event horizons clearly do. Does this mean that we can stop worrying? What happens in naked singularity scenarios when there is no singularity yet?


title: What is "Strong Force" & "Weak Force" in Astronomy terms?

text: What is **_"Strong Force"_** & **_"Weak Force"_** in Astronomy terms?


title: Bound states in QED

text: I am a beginner in QED and QFT. What is known (or expected to be) about bound states in QED? As far as I understand, in non-relativistic QM electron and positron can form a bound state. Should it be true in QED? Most of the basic text books on QFT I known treat QED with perturbative methods which do not help to study bound states. Is there a literature to read about it? UPDATE: According to wikipedia, electron and positron form a positronium. It is an unstable particle which can annihilate to two photons. In particular electron and positron cannot form a bound state. But still there is a logical possibility that several electrons and positrons can form a bound state (though probably once one has at least one electron and one positron, they will necessarily annihilate. Is it true?) On the other hand, if one considers QED with both electrons and muons, then electron and antimuon form muonium. Clearly they cannot annihilate to photons. However in another article in wikipedia it is claimed that muonium is unstable. Is it due to some effects of QED or due to actual presence of other, say weak, interactions?


title: Practice AP Physics B Exam Question regarding Momentum

text: I am trying to review momentum for the AP exam coming up. I will be taking the AP Physics C exam for Mechanics, but I was just practicing on any free response questions I could find and I came across this one. It is from 1983, free response number 2. It says: > _A block of mass $M$ is resting on a horizontal, frictionless surface, and > it is attached as shown above to a relaxed spring of spring constant $k$. A > second block of mass $2M$ and initial speed $v_0$ collides with and sticks > to the first block. Develop expressions for the following quantities in > terms of $M$, $k$, and $v_o$._ > > _a.) $v$, the speed of the blocks immediately after impact._ > > _b.) x, the maximum distance that the spring is compressed._ ![The diagram that came with the problem](http://i.stack.imgur.com/tP5l8.png) So I got (a) pretty easily, just by using conservation of momentum. I found the result of $$v=\frac23 v_0$$ For part b, I began by finding the change in Kinetic Energy of the 2 blocks from immediately after impact to the point where their velocity is zero as a result of the negative work that the Spring does on the blocks. I found that $$K_i=\frac12(3M)\left[\frac23v_0\right]^2 = \frac23Mv_0^2$$ and that $$K_f=0$$ I then equated this change in $K$ with the Work done by the spring and got $$-\frac23Mv_0^2 = \frac12kx_i^2 - \frac12kx_f^2 = \frac12kx_0^2 - \frac12k(x_0-x)^2$$ I then tried to solve this equation for x, which is the distance that the spring is compressed, and found that $$x=\frac12*(x_0+sqrt({x_0^2+\frac43\left(\frac{Mv_0^2}k\right)})$$ from the quadratic formula. Now, in theory, I don't really see anything wrong with this, but according to solutions I found online, people have been equating the change in K with the change in momentum, and having this equation: $$\frac23Mv_0^2 = \frac12kx^2$$ Can anyone explain why this equation would be true, or failing that, where I may have gone wrong in my own calculation? I appreciate the help.


title: Does decoherence single out a preferred frame?

text: Environmentally induced decoherence makes wave function collapse unnecessary. But the environment, usually taken to be some heat bath, introduces a preferred frame. (That in which the total (spatial) momentum vanishes.) So, doesn't then the decoherence time depend on the motion of the prepared state relative to the environment? And, doesn't the ultimate environment, all particles in the universe, introduce a preferred frame into quantum mechanics in the sense that the decoherence time is relative to this frame? And would this be measureable, at least in principle? I.e. I could go into a frame with high boost relative to the CMB restframe and notice that the decoherence time changes?


title: Free energy variations

text: In a paper, I found this: $\mathbf{h}=\mathbf{h}(\mathbf{r})$ is called molecular field and is defined as the variation field of the Frank free energy functional $F_{d}$ with respect to the polarization field $\mathbf{p}=\mathbf{p}(\mathbf{r})$: $F_{d}=\int d\mathbf{r}\left(\frac{\alpha(\rho)}{2}|\mathbf{p}|^{2}+\frac{\beta}{4}|\mathbf{p}|^{4}+\frac{K}{2}(\partial_{\alpha}p_{\beta})(\partial_{\beta}p_{\alpha})-v_{1}\frac{\rho-\rho_{0}}{\rho_{0}}\nabla\cdot\mathbf{p}+\frac{\lambda}{2}|\mathbf{p}|^{2}\nabla\cdot\mathbf{p}\right)$ $$\mathbf{h}=-\frac{\delta F_{d}}{\delta\mathbf{p}}=\left[\alpha(\rho)+\beta|\mathbf{p}|^{2}\right]\mathbf{p}+K\nabla^{2}\mathbf{p}+v_{1}\nabla\left(\frac{\rho}{\rho_{0}}\right)-\lambda\nabla|\mathbf{p}|^{2}-\lambda\mathbf{p}(\nabla\cdot\mathbf{p})$$ Now, could you explain what kind of calculation was performed here, and how can I remake it?


title: Asymptotic symmetry algebra

text: So after a lot of research, and tons and tons of papers that I've went through, I finally have some idea how to solve the equations that will give me candidates for the asymptotic symmetry group for Kerr/CFT correspondence. One has boundary conditions $h_{\mu\nu}$, and metric that behaves like $g_{\mu\nu}=\bar{g}_{\mu\nu}+h_{\mu\nu}$, where $\bar{g}_{\mu\nu}$ is the background metric (in this case it's taken as near horizon extreme Kerr metric), and $h_{\mu\nu}$ are perturbations (given). So the task is finding diffeomorphisms $\xi$ for which this metric will transform according to $$\bar{g}_{\mu\nu}+\mathcal{L}_\xi \bar{g}_{\mu\nu}=g_{\mu\nu}=\bar{g}_{\mu\nu}+h_{\mu\nu}$$ And one solves that by solving equations $$\mathcal{L}_\xi g_{\mu\nu}=\mathcal(r^m)$$ where $\mathcal{O}(r^m)$ are boundary conditions, given in terms of radial coordinates. From this, and the fact that $h_{\mu\nu}=h_{\nu\mu}$ I get ten equations. Now my issue is this: What to take as ansatz for $\xi$? In some papers, they take this: $$\xi^\mu=\xi^\mu_0(t,\theta,\phi)+r\xi^\mu_1(t,\theta,\phi)+\mathcal{O}(r^2)$$ But in certain papers I've found that authors take this form (see after eq. 4.4 here, or here eq 5.1) $$\xi^\mu=\sum\limits_{n=-1}^\infty \xi^\mu_n r^{-n}$$ such that we have subleading contributions (a falloff in radial coordinate). Now, I'm inclined to use the second one, since the diffeomorphism given in Guica et. al is given with subleading terms. I should solve this by putting a certain few terms in, and see what the boundary condition says. For instance we have $$\mathcal{L}_\xi g_{tt}=\mathcal{O}(r^2)$$ That means that all $\mathcal{O}(r^2)$ contributions will cancel, and only equations with $r$, or smaller $r$ contributions will survive. But the answer is drastically different if I take first or second ansatz. So what to take? Am I on the right track? If I take second one, what n should I start from? $n=-1$ or $n=-2$? Oh and I finally got how to solve this by looking at this article and following how they got it in appendix A **EDIT:** I've been thinking. Does the fact that in their article, the metric, and the ansatz goes with powers of $v$, means that since their equations are limited by $\mathcal{O}(v)$ onward all higher power will cancel each other? In that case, since I'm taking only subleading terms in metric, and boundary conditions (different for each of 10 terms), and if I take that my ansatz falls off as $r^{-n}$, that means that all lower order correction cancel out? The question is still: what n to take? Since it's not the same if my $\xi$ starts with $r^2$, or $r$ :\ **EDIT2:** I'll put one component to show what I'm doing. Although I think something is wrong, since I'm getting complicated equations (when things get too complicated, it's kind of a show that things might not be going in the right direction, at least that's what experience showed me) So, my metric is $g_{\mu\nu}=\bar{g}_{\mu\nu}+h_{\mu\nu}$, as explained above. The first question that comes to my mind: do I put manually $h_{\mu\nu}$ in this expression, or do I use the given boundary conditions? I could say that $h_{\mu\nu}$ is arbitrary, and my metric has to have a power fall off perturbations, so that my $tt$ component would be $$g_{tt}=-\Omega^2(\theta)(1+r^2(1-\Lambda^2(\theta)))+r^{-1}h_{tt}(t,\theta,\phi)+\mathcal{O}(r^{-2})\quad (\star)$$ I removed $2GJ$ since it's just a factor in front of the metric, not depending on any of the variables ($t,r,\theta,\phi$), and it doesn't contribute to diffeomorphisms. I will try this after I finish what I did. However, I just put the given boundary conditions. For $tt$ component I have $$\mathcal{L}_\xi g_{tt}=\mathcal{O}(r^2)=\xi^\sigma\partial_\sigma g_{tt}+g_{\sigma t}\partial_t\xi^\sigma+g_{t\sigma}\partial_t\xi^\sigma$$ Since $g_{tt}$ depends on $r$ and $\theta$, I have two components in the first argument. In the second and third arguments are the same since $g_{t\phi}=g_{\phi t}$. So I have $$\xi^\theta\partial_\theta g_{tt}+\xi^r\partial_r g_{tt}+2(g_{tt}\partial_t\xi^t+g_{t\phi}\partial_t \xi^\phi)=\mathcal{O}(r^2)$$ $$(\xi^\theta_{-1}r+\xi^\theta_0+\xi^\theta_1r^{-1}+\mathcal{O}(r^{-2}))(-2\Omega\Omega'+2\Omega(\Lambda\Lambda'\Omega-\Omega'(1-\Lambda^2))r^2+\mathcal{O}(r^2))+(\xi^r_{-1}r+\xi^r_0+\xi^r_1r^{-1}+\mathcal{O}(r^{-2}))(-2\Omega^2(1-\Lambda^2)r+\mathcal{O}(r))+2((-\Omega^2-\Omega^2(1-\Lambda^2)r^2+\mathcal{O}(r^2))(\partial_t\xi^t_{-1}r+\partial_t\xi^t_0+\mathcal{O}(r^{-1}))+(\Lambda^2\Omega^2r+\mathcal{O}(1))(\partial_t\xi^\phi_{-1}r+\partial_t\xi^\phi_0+\partial_t\xi^\phi_1 r+\mathcal{O}(r^{-2})))=\mathcal{O}(r^2)$$ After sorting all out, and saying that all the corrections of $\mathcal{O}(r^2)$ vanish, I end up with $$(\Lambda\Lambda'\Omega-\Omega'(1-\Lambda^2))\xi^\theta_{-1}-\Omega(1-\Lambda^2)\partial_t\xi^t_{-1}=0$$ But, this one is relatively ok, the other ones sometimes have six or more components ($\xi^\mu$). I'll work all of them out, and then try with $(\star)$ as an assumption and see if things simplify... **EDIT 3:** So things aren't simplifying. But one thing I've learned: I need to solve asymptotic Killing equation. My next try, the one I think is a fast and relatively good try, is to just see what the leading orders of components should be, such that they satisfy the asymptotic Killing equations, given by boundary conditions. Then I'll try to do explicit calculation. For instance (and I hope I'm on a right track) for $tt$ component I would have $$\mathcal{L}_\xi g_{tt}=\mathcal{O}(r^2)$$ $$\xi^\theta\partial_\theta g_{tt}+\xi^r\partial_r g_{tt}+2(g_{tt}\partial_t\xi^t+g_{t\phi}\partial_t \xi^\phi)=\mathcal{O}(r^2)$$ $$\xi^\theta\mathcal{O}(r^2)+\xi^r\mathcal{O}(r)+\mathcal{O}(r^2)\partial_t\xi^t+\mathcal{O}(r)\partial_t\xi^\phi=\mathcal{O}(r^2)$$ So for this to be true (LHS=RHS) I should have $$\xi^r\to\mathcal{O}(r)$$ $$\xi^\theta\to\mathcal{O}(1)$$ $$\partial_t\xi^t\to\mathcal{O}(1)$$ $$\partial_t\xi^\phi\to\mathcal{O}(r)$$ I hope I'm on a right track. I got a hint how Guica et. al did it. First we need to guess what the symmetries are and then generate boundary conditions by acting with those diffeomorphisms, and then check that the charges are finite and integrable. So it's more a guessing game than exact solving :S **EDIT 4:** So far (by solving asymptotic Killing equations) I only get the $\xi^\theta$ component right. That is I have $$\xi^\theta_0=\xi^\theta_{-1}r$$ which, when I put in the ansatz I get $$\xi^\theta=\xi^\theta_{-1}r+\xi^\theta_0+\xi^\theta_1r^{-1}+\mathcal{O}(r^{-2})$$ $$\xi^\theta=\xi^\theta_1 r^{-1}+\mathcal{O}(r^{-2})$$ which is exactly the one in the article by Guica et. al. But no luck with other components. If only there was some info on what I need to put in asymptotic Killing equation after the equal sign... **EDIT 5:** I'll write the equations I got by putting $\mathcal{L}_\xi g_{\mu\nu}=\mathcal{O}(r^n)$ where $\mathcal{O}(r^n)$ are given by boundary conditions: $$tt:\quad (\Lambda \Lambda' \Omega+(\Lambda^2-1)\Omega')\xi^\theta_{-1}+(\Lambda^2-1)\Omega \partial_t\xi^t_{-1}=0$$ $$t r:\quad (\Lambda^2-1)r(\xi^t_{-1}+\xi^t_0r^{-1})+(\Lambda^2-1)r^3(\xi^t_{-1}+\xi^t_0r^{-1}+\xi^t_1r^{-2}+\xi^t_2r^{-3})-$$ $$-r(\xi^t_{-1}+\xi^t_0r^{-1})+\Lambda^2\xi^\phi_{-1}+\Lambda^2r^2(\xi^\phi_{-1}+\xi^\phi_0r^{-1}+\xi^\phi_1r^{-2})+\partial_t\xi^r_{-1}=0$$ $$t\theta:\quad (\Lambda^2-1)r^2(\partial_\theta\xi^t_{-1}r+\partial_\theta\xi^t_0+\partial_\theta\xi^t_1r^{-1}+\partial_\theta\xi^t_2r^{-2})-(\partial_\theta\xi^t_{-1}r+\partial_\theta\xi^t_0)+$$ $$+\Lambda^2r(\partial_\theta\xi^\phi_{-1}r+\partial_\theta\xi^\phi_0+\partial_\theta\xi^\phi_2r^{-1})+(\partial_t\xi^\theta_{-1}r+\partial_t\xi^\theta_0)=0$$ $$t\phi:\quad (2\Lambda(\Lambda'\Omega+\Lambda\Omega'))(\xi^\theta_{-1}r+\xi^\theta_0)+\Lambda^2\Omega\xi^r_{-1}+$$ $$+(\Omega(\Lambda^2-1))(\partial_\phi\xi^t_{-1}r+\partial_\phi\xi^t_0+\partial_\phi\xi^t_1r^{-1})-\Omega\partial_\phi\xi^t_{-1}+$$ $$+\Lambda^2\Omega(\partial_\phi\xi^\phi_{-1}r+\partial_\phi\xi^\phi_0)+\Lambda^2\Omega(\partial_t\xi^\phi_{-1}r+\partial_t\xi^t_0)+\Lambda^2\Omega\partial_t\xi^\phi_{-1}=0$$ $$rr:\quad \xi^\theta_{-1}r+\xi^\theta_0=0$$ $$r\theta:\quad \partial_\theta\xi^r_{-1}+(\xi^\theta_{-1}r+\xi^\theta_0)=0$$ $$r\phi:\quad (\xi^t_{-1}r+\xi^t_0)+\xi^\phi_{-1}=0$$ $$\theta\theta:\quad \Omega'(\xi^\theta_{-1}r+\xi^\theta_0)+\Omega(\partial_\theta\xi^\theta_{-1}r+\partial_\theta\xi^\theta_0)=0$$ $$\theta\phi:\quad (\partial_\phi\xi^\theta_{-1}r+\partial_\phi\xi^\theta_0)+\Lambda^2r(\partial_\theta\xi^t_{-1}r+\partial_\theta\xi^t_0+\partial_\theta\xi^t_1r^{-1})+$$ $$+\Lambda^2(\partial_\theta\xi^\phi_{-1}r+\partial_\theta\xi^\phi_0)=0$$ $$\phi\phi:\quad (\Omega\Lambda'+\Lambda\Omega')\xi^\theta_{-1}r+\Lambda\Omega r(\partial_\phi\xi^t_{-1}r+\partial_\phi\xi^t_0)+$$ $$+\Lambda\Omega\partial_\phi\xi^\phi_{-1}r=0$$ The problem is, the only equation I can get some information, about how my vector should behave in components is $rr$, from which I get the general form of $\xi^\theta$ component of diffeomorphism. From $r\theta$ I get that the $\xi^r_{-1}$ term is a constant that doesn't depend on $\theta$, and $\theta\theta$ equation will just confirm that $rr$ one is correct. I guess from the fact that $\xi^r_{-1}$ is not zero I could say that the $r$ component will start at that term (like in the article). **EDIT 6:** I have added the bounty to raise awareness to this, if anyone knows if what I did so far is correct, and what to do next, please do tell :)


title: Circuit Analysis: Help getting the Thevenin equivalent

text: I am attempting to solve this problem which requires me to get the Thevenin equivalent of a circuit, and I've gotten as far as getting the equivalent resistance of the circuit (which I believe is 5 Ohms), but I am not certain as to how to solve for the voltage. Can anyone help me? I missed this day of class. The question can be found here (Question #5)


title: How much is quantum computation changing the interpretation of quantum theory, and, if at all, how?

text: At the beginning of quantum computation, David Deutsch made a strong claim that the Many Worlds interpretation of quantum theory was at the foundation of his ability to do what he did. There was a lot of interest in his claim, and Many Worlds had something of a resurgence at the time. Amongst other strong claims, I'm particularly aware that Chris Fuchs has pressed a Bayesian perspective that is rather different from the Many Worlds interpretation. My perception, however, is that quantum computation/information/communication is now much less in thrall to any particular interpretation, unless we say there is such a thing as the minimalist interpretation. It seems that most quantum computation work is reported in journals in as close to the unadorned Fock space formalism of quantum optics as possible, often cut down to a small, finite number of harmonic oscillators, in one of the many formalisms and ansätze of statistical or condensed matter Physics, or, of course, the discussion revolves around _qubits_. Nonetheless, quantum information is not called quantum _particle_ information --it's not part of _particle_ physics-- and the Bell and other inequalities that form the basis of the general rejection of classical particle physics are central instead of being as peripheral as they often seem in particle physics, so it seems, to me, that there is at least something of a change of perception, of zeitgeist, if you will. Quantum computation for a long time was a subject of keen interest in the academic quantum foundations conferences that I went to back in the day. ~~Is that interest still there?~~ As Peter Shor points out in a comment, this interest _is_ still there, but Is any of that interest felt in the wider Physics community that has relatively little practical interest in quantum foundations? [Peter Shor Answered that too --in a way that agrees with my prejudices, so it must be right-- while I was writing the EDIT below, which tries to address one way in which I think the zeitgeist is being affected.] EDIT: I suppose a significant number of Physicists will occasionally read PRL articles on quantum information that are highlighted by the editors, and it would be hard to avoid all Scientific American, New Scientist, and Nature articles on the subject. Someone considering grant sources would presumably at least briefly consider whether their work could be applied to QI (I'm bored already with the comp../inf../comm..) and occasionally talk to the QI group at their Institution (almost everybody has one of those by now, right?). Insofar as they do, then it seems inevitable that some QI viewpoints must be increasingly out there. Bell's theorem is surely more a topic of informed discussion than it was 20 years ago. To make the question more specific, and to include my bias in a more explicitly leading way, _Do people agree with the implication of my second paragraph that "particles" are less in the air than they were in the heyday of Particle Physics?_ [If you not unreasonably think that's too specific, feel free to Answer the original and more general Question of the title. The more specific Question still admits at least evidence of the sort given by Peter Shor, and shouldn't be thought of or addressed as only a Yes/No question.] Hat Tip to Roy Simpson for this Question (his is the credit, mine is the blame).


title: Equations describing the liquifaction of gases

text: I would like to find out how much energy is required to liquify gases (oxygen or nitrogen, for example). **What are some relevant equations?** I'm curious whether creating small quantities of dry ice or cryogenic fluids is feasible at home. If James Dewar was able to liquify hydrogen in 1898 surely it must not be that difficult!


title: Where does the reverse current come from in a organic semiconducting diode?

text: Unlike traditional inorganic diodes, organic semiconducting materials hold few thermally exited free carriers under room temperature, so the reverse current should be small if pinholes of the films is well avoided. However the fact is that the reverse current varies a lot between devices using different types of organic materials. Is it because there are other sources of reverse current? Or is it mostly dominated by charge transport layers which have relatively higher conductivity compare to active layer?


title: Use microwave cavity in atomic clock

text: In most of the papers regarding atomic clocks, the author talks about a microwave cavity. In this box, all the unwanted frequencies of the electromagnetic radiation are absorbed and the other frequencies are maintained. But how does this work with an atomic clock? In this case, one uses atoms rather than radiation. What is the difference between these applications of the cavity? I thought this might have to do something with the duality between atomic particles and waves, although I couldn't find any sources that could verify this.


title: What is a Free Body Diagram?

text: I have this problem: > A 10 kg box is resting on a frictionless table and someone drags it by a > string at a 30 degree angle to the horizontal with a force of 40 Newtons. > Find the acceleration of the box. Draw a free body diagram of the system. What is a free body diagram?


title: What is the correct term for the "polarity" of matter (matter vs. antimatter)? Are fractional polarities allowed?

text: What is the correct term for the "polarity" of matter (matter vs. antimatter)? Are neutral polarities allowed? (1,0,-1) Are fractional polarities allowed?


title: If electrons behave as standing waves when they are bound to an atom then how do they carry charge?

text: Today in my physics lesson we learnt that the best way of describing the behaviour of an electron that is bound to an atom is to treat it as a standing wave. I understand that this is the wave-particle duality however I was taught that in the wave-particle duality something either acts as a wave or a particle, not both at the same time. With this in mind I'm curious as to how electrons can still carry charge when they are behaving as a wave. I asked my teacher this question and he wasn't able to answer it so hopefully someone on here can explain it to me :)


title: Are there any astronomical objects at night that are dangerous to look at (through a telescope)?

text: Are there any astronomical bodies that would be dangerous to my vision to view through a telescope? Obviously the sun is dangerous, but are there other bodies at night I should avoid?


title: Physical realization scheme for quantum gates and circuit

text: This post is aimed at summing up the physical realization schemes for quantum gates and circuit, please give an brief introduction to **the one you know**. I only heard that NMR is possible and Wikipedia has given an introduction already. Please help update the question if possible. By the way, if there is a review paper already, then it may be the best answer.


title: What are the relative permeability and electrical conductivity of GaAs?

text: I am doing some simulations in COMSOL with the material GaAs. The COMSOL built-in models require me to input the relative permeability and electrical conductivity of GaAs. I have tried hard to search for these two electrical properties online, but no luck. Could anyone tell me these, or even better, tell me a place where I can look the electrical properties of a material up?


title: Dimension of gamma matrices in higher dimensional Dirac equations

text: Reading about Dirac's equation in higher dimensional space-times I have read that the gamma matrices are $2^{[D/2]}\times{}2^{[D/2]}$. So, if we have $D=11$, for example, how is this formula supposed to be understood?


title: How do messenger fields break SUSY in the MSSM?

text: I have been reading the notes on Supersymmetry by Martin. I am trying to understand gauge mediated symmetry breaking. From what I understand, there is a hidden sector where SUSY is spontaneously broken, there is a messenger superfield and there is a visible sector. There should be no direct coupling between the hidden sector and the visible sector. The spontaneous susy breaking in the hidden sector affects the messenger fields which in turn breaks susy in the visible sector keeping the soft terms. The messenger fields break susy in the visible sector only via loops. This is the bit I do not understand. In the superpotential, I don't see terms where there is an interaction between the messenger fields and the visible sector. Is this something to do with the covariant derivatives? Also why do these messenger terms only appear in loops in the visible sector?


title: Tunneling of alpha particles

text: Consider this explanation of the alpha decay: It says > The Coulomb barrier faced by an alpha particle with this energy is about 26 > MeV, so by classical physics it cannot escape at all. Quantum mechanical > tunneling gives a small probability that the alpha can penetrate the > barrier. > > ![diagram of the barrier](http://i.stack.imgur.com/RF04N.gif) The explaining sentence and the attached picture suggest that the alpha particle has to overcome the coulomb barrier in order to escape - and as is hasn't enough energy to do that, it must tunnel through it. But the Coulomb force is a _repulsive_ force in this case as both the nucleus and the alpha particle are positively charged. So why is there any Coulomb barrier at all, shouldn't the Coulomb force "help" the alpha particle to escape? (The other way round, it's obvious - the particle wants to enter the nucleus, but it is hindered by the repulsive force. But when it wants to leave the nucleus, it is only retained by the nuclear force, as far as I can see.) **Why does the alpha particle have to go trough the coulomb barrier - or am I just misinterpreting the explanation and the tunneling occurs somewhere else?**


title: 2nd order variation of Hilbert-Einstein action + Gibbons-Hawking-York boundary term

text: While the first order metric variation of Hilbert-Einstein action plus Gibbons-Hawking-York boundary term is well-known and takes the form: $\delta S_{HE}+\delta S_{GHY}=-\frac{1}{16\pi G}\int d^3x \sqrt{-\gamma}~(K^{\mu\nu}-K\gamma^{\mu\nu})\delta \gamma_{\mu\nu}$ ($K_{\mu\nu}$ and $\gamma_{\mu\nu}$ are the extrinsic curvature and the projection metric), does anybody know the second order variation of this combined action? Thanks to anyone who can help me!


title: 3D SHO state transition problem

text: In this 3D SHO problem, the mass m is perturbed by \begin{align} H_{1} = Ar^{2}e^{-|t|/t_0} \end{align} The initial states has $n = n$ and $l = 0$ at $t = -\infty$. The question is what are the possible states for $t = \infty$. My attempt: So far I can get the restricted condition for the final state $l_{f}$, where $l_{f} = 0$. I achieve this by computing the following: \begin{align} <n_{f}l_{f}m_{f}|[L^{2}, r^{2}]|nlm> = 0 \end{align} After expanding the commutator term, it is not hard to get $l_{f}(l_{f}+1) = 0$ and since $ l \ge 0$, $l_{f} = 0$. However, I am not sure how to get the restrictive condition on $n_f$. All I know is, for a 3D SHO, the radial component is in terms of Laguerre polynomial, and the angular component is $Y^{m}_{l}$. Since $l=l_{f}=0$, $Y^{m}_{l}=Y^{m_f}_{l_f}=Y^{0}_{0}$. Therefore, I can use orthogonality of get rid of invalid $n$. From this webpage: http://planetmath.org/orthogonalityoflaguerrepolynomials the orthogonality of Laguerre polynomial is \begin{align} \int_0^\infty\\!e^{-x}L_m(x)L_n(x)\,dx \;=\; 0 \qquad (m \;\neq\; n), \end{align} and \begin{align} \int_0^\infty\\!e^{-x}[L_n(x)]^2\,dx \;=\; (-1)^n\\!\int_0^\infty\\!e^{-x}x^nL_n(x)\,ds \;=\; (n!)^2. \end{align} In this sense, the only possible final state has equal to its original state in order not to be deleted from the orthogonality? Which means $n_f=n$? I don't think this is right. Can someone tell me why I am wrong and how to apply orthogonality of Laguerre polynomial correctly?


title: "Dark" quantities

text: I don't know much about the so-called dark matter, apart from what has been described in popular descriptions of the reasons for it being postulated. My question is, is there dark momentum, dark charge, dark angular momentum? Also would these fit into the Standard Model (with modifications)?


title: Integral over a product of two Green's functions

text: Need some help here on a frequently encountered integral in Green's function formalism. Forgive me since I am a junior student. I have an integral/summation as a product of a retarded and advanced Green's functions, looks simply like $$\sum_{p^{\prime}}\frac{1}{p^{2}-{p^{\prime}}^{2}-i\epsilon}\frac{1}{p^{2}-{p^{\prime}}^{2}+i\epsilon}$$ where I have omitted the mass $m$ to make the notation simple; $\epsilon$ is a positive infinitesimal. I can convert the summation to an integral over momentum $p$ or energy, this is standard. Then I follow the complex analysis and identify 4 poles (if the integration is over momentum) and further apply the residue theorem. But, what I get is an expression proportional to $\frac{1}{\epsilon}$. This means it is divergent since $\epsilon\rightarrow 0$. Could any one please point out to me what have I missed in this calculation? What mistakes did I make? Many many thanks.


title: Who discovered momentum?

text: I read some text about momentum in Wikipedia, but I didn't find any information who discovered momentum. Is the momentum a philosophic principle?


title: How do we perceive hotness or coldness of an object?

text: Some objects, especially metallic ones, feel cold on touching and others like wood, etc. feel warm on touching. Both are exposed to same environment and are in their stable state, so some kind of equilibrium must be being reached. What is this equilibrium? And how do we perceive hotness or coldness of an object? Does skin have some kind of heat sensors, etc., which transmit signals to brain? Like, how do the eye transmit/convey an image formed on the retina to brain?


title: How long does it take to weigh an uncooperative mass?

text: (This is curiosity, not a practical question. It was inspired by standing still for a digital scale, and considering whether it would be possible to make a scale that could handle being jumped on, juggled on, etc.) Setup: An impermeable rigid box with arbitrary contents on top of (fixed to) an ideal scale, in a known uniform gravitational field and no electromagnetic field. Assume classical mechanics (i.e. no relativistic effects or uncertainty). Question: How long must data (i.e. the force on the scale) be collected in order to know the mass of the box and contents, given that the contents of the box are _doing their best to make it difficult_ (which I think can only consist of accelerating masses vertically)? I think that it is not possible to get an exact answer after a finite time; for example, consider if the box contains a mass being accelerated downward arbitrarily slowly — thus reducing the total weight by a small fraction, until it touches bottom. Is there an upper bound on the error, given a time interval and some property of the collected data (e.g. the maximum or mean force)?


title: How can indeterminacy in quantum mechanics be derived from lack of ability to observe a cause?

text: I don't get this part of quantum mechanics. I get the part that you can't observe particles and not affect their behavior because you are shooting photons to them while you are observing them, but how can this show that while you are not observing them, they behave in indeterministically and that's a feature of nature.


title: Holonomy twisting

text: There is Witten's topological twist of standard SUSY QFTs with enough SUSY into Witten-type TQFTs. What is a holonomy twist?


title: Ricci tensor of the orthogonal space

text: While reading this article I got stuck with Eq.$(54)$. I've been trying to derive it but I can't get their result. I believe my problem is in understanding their hints. They say that they get the result from the Gauss embedding equation and the Ricci identities for the 4-velocity, $u^a$. Is the Gauss equation they refer the one in the wiki article? Looking at the terms that appear in their equation it looks like the Raychaudhuri equation or the Einstein field equations are to be used in the derivation in order to get the density and the cosmological constant, but even though I realize this I can't really get their result. Can anyone point me in the right direction? $Note:$The reason why I'm trying so hard to prove their result is because I wanted to know if it would still be valid if the orthogonal space were 2 dimensional (aside some constants). It appears to be the case but to be sure I needed to be able to prove it.


title: Evolution of black holes ensemble

text: **Background:** I’ve read many times that arrow of time can be explained from extremely low entropy of the Universe at the Big Bang (http://preposterousuniverse.com/eternitytohere/faq.html). The argument goes that initially the Universe was very smooth. As time passed, matter gathered together in clusters due to gravitation, until eventually we got stars, galaxies and super massive black holes. There is a notion of entropy, related to gravitation. In classical statistical physics without taking into account gravity the gas spreads evenly in the volume. If gravity is taken into account than the most probable state of the system is when all gas forms a large black hole. However I don’t see how Hawking evaporation is taken into this picture. From this I conclude that somewhere there must be a textbook-level theory of entropy that takes into account gravity, Hawking radiation and expansion of the Universe. In general, we may consider a toy model – the Universe, consisting entirely of black holes of different sizes and velocities, see how it evolves and get the most probable state (or states). **Question:** If the Universe contained only black holes with a certain mass and velocity distribution, how would it evolve over time? Is it enough to know the mass/velocity distribution to predict the general evolution of such Universe? Is it possible to predict the spectrum of background radiation in such a Universe at any moment of time?


title: Observables - what are they?

text: I often read in books that an observable is represented by an Hermitean operator. But it is deceiving as operator isn't the observable. As far as I've read the observable is denoted like $\langle \psi|\hat{x}|\psi\rangle$ which is equivalent of $\langle \psi |\hat{x} \psi\rangle$ or $\langle \hat{x}^\dagger\psi| \psi \rangle$. So I would say that an observable is represented by an inner product of a (1st) wavefunction with (2nd) an operator acted on a wavefunction. _(If I look the second equation)_. Is this even correct? What do you think about this?


title: Wigner characteristic function

text: I came across the "representation of a Gaussian state by its Wigner characteristic function". I don't know what Wigner characteristic function is and google results are not precise enough. Neither have I been able to find this in some quantum mechanics book. It will be great if you could explain what it means, but even better would be citing a source from where I could read it up. I came across this term in this paper: "Inseparability criterion for continuous variable systems". Duan, Giedke, Chirac and Zoller. Physical Review Letters (year 2000)


title: What is the difference between scale invariance and self-similarity?

text: I always thought that these two terms are some kind of synonyms, meaning that if you have a self-similar or scale invariant system, you can zoom in or out as you like and you will always see the same picture (physics). But now I have just read in the context of a lattice of spins model for example, that if the system is at its critical point and therefore scale invariant, it does not mean that it is self-similar as naively discribed in the first paragraph of this question. The author of the paper I am reading even calls it a false picture on p. 9. Later on on p. 24 he explains that poles on the positive real axis on the so called Borel plane break self- similarity because lead to tha fact that to obtain the effective action (for a $\lambda\phi^4$ bare action) the scale dependent non perturbative power correction terms have to be kept. So if scale invariance and self-similarity are not exactly the same, the explanation for breaking of scale invariance should be (slightly and subtly?) different? Now I am confused and my question simply is: what exactly is the difference between scale invariance and self-similarity (if any ...)?


title: Short-duration forces

text: In **circular motion** , it is said that the centripetal force acts only for a very very short period of time, hence is able to only change the direction but not magnitude of the velocity. Similarly in a collision, the impulsive-collision forces act for a very short period of time, but they are able to change the direction as well as magnitude of velocity, considering an inelastic collision. The collision lasts for a very short period of time, almost instantaneous (with reference to Newtonian mechanics, not considering Einstein's special relativity). *Why is that Why is collision force able to change magnitude when it acts for a short period of time as well? The reasoning that collision forces have a very high magnitude won't work here, as say they have a magnitude $100,000\text{ N}$, then imagine the circular motion to be of a mass $1\text{ kg}$ and speed $100,000\text{ ms}^{-1}$ and radius $1\text{ m}$, now we have both centripetal and collision forces equal but still centripetal force is able to only change direction. Similarly we can always adjust both the forces and circle's radii accordingly, so that **impulse** provided by **both the forces** , centripetal and collision forces are **always equal**. > we calculate impulse provided by the centripetal force in circular motion to > be such that for the differential time $dt$ , we evaluate impulse for ,the > force remains constant in terms of both   >  magnitude and direction and according to continuity of time , there are > infinite of such instances giving us a non-zero length span of such a time . The reasoning that centripetal force acts perpendicular to direction of motion also won't work since then problem will be asking that momentum doesn't change even in the direction of the force which is perpendicular to path, even in the perpendicular direction there is no impulse and if there's impulse, it may lead to violation of Energy conservation, which can't happen. These two mode of reasoning, I have tried and they fail here. **All conditions are sort of idealistic here, following all of Newton's and Euler's laws.** **All masses are to be considered to be point masses.** Impulse is $\int^{t_2} _{t_1} Fdt$ where $F$ is the force and $t_2-t_1$ is the span of time of finite length we considered. Also please provide an intuitive answer as well.


title: Do restrictions on quantum mechanical measurement always just work out to avoid contradictions?

text: Classically it was said that measurement leads to a collapse of the wave function. However, if there wouldn't be any limit on the process on measurement itself, strange things can happen, e.g. a particle that is confined to a small region by a very strong potential could by measuring its momentum with high precision be made to be spread out instanteneously all over space. Likewise, if a particle is detected at one location, then its momentum is measured with very high precision, at any moment after that it can be detected arbitrarily far away. In Feynman's lectures on physics, he goes into the explicit measurement process in the double slit experiment, where light is used to detect which slit the electron passed through. As long as the photons can detect the slit the electron went through, the interference pattern is destroyed. When the frequency of the light is reduced to diminish the impact, the interference pattern keeps being disturbed, up to the moment when the wavelength of the photons is so large that they are not able to determine which slit the electron passed through. Likewise, in this answer by John Rennie to the question how it can be that if you measure the momentum of a particle with very high precision its uncertainty may extend over one light year, he explains why (doing this with light at least) a measurement with that precision would take a year. As another example, in this answer by DanielSank to the part of my question where it was asked how it could be that a measurement of a particle in a box with infinite walls could be made to tunnel out by making a measurement, it was suggested that there is a fundamental limitation on the precision of the measurement. In all three examples it looks like the restrictions on the measurement process are exactly conspiring to avoid any undesired behaviour to occur. Is there any fundamental reason for that? Thanks!


title: Experiment - Measuring final velocity of a parachute

text: I'm working on a project that involves a scale parachute. It is vital for the project to get a good measurement of the speed it has when it lands. We still haven't built the parachute, but we need a way to know the speed it has when it touches the ground. We have thought about using a cellphone as the body tied to the parachute and write an app that collects the accelerometer data, then use this data to calculate the velocity. Another option was to use two lasers very close to each other and photoresistors with arduino. Then, given that we know the distance between the lasers, the lasers would give us the time it takes the object to travel this (very small) distance and we would get an approximation of the speed at that moment. The problem here is that the parachute may move horizontally as well, and land at some point where our laser can't detect it. We are not sure if these are good ideas or if there is any better approach. What do you suggest?


title: Integer physics

text: Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.


title: Constrained-search formulation of DFT: by Levy or by Levy-Lieb

text: I'm a bit puzzled about how to give the right references for the constrained- search formulation of DFT. Till now, I only heard it being called "Levy constrained-search" but came about some papers and presentations that called it "Levy-Lieb constrained-search". The seminal papers in question are the following: Levy: M.Levy, _Proc.Natl.Acad.Sci.U.S.A._ **76** , 6062 (1979) Lieb: E.Lieb, _Int. Jour. Quant. Chem._ **24** , 243-277 (1983) The dates are quite a long way away from each other, but the author of this paper claims that Levy and Lieb developed the constrained search formulation in parallel. So, I would like to know, what is the relation between the works of these two authors (I unfortunately don't have access to the papers)? Did both of them do the same or did Lieb extend the work of Levy or do both papers contain different formulations entirely? Should I quote both papers and call it "Levy-Lieb" or would the "Levy"-only version be better suited?


title: Practical uses of antimatter in the present

text: I recently found out that a PET scan stands for a positron emission tomography. Are there any other practical uses of antimatter in the present?


title: Polar vs non-polar fluid

text: In the book "Vectors, Tensors, and the Basic Equations of Fluid Mechanics" by Rutherford Aris I read the following: > If the fluid is such that the torques within it arise only as the moments of > direct forces we shall call it nonpolar. A polar fluid is one that is > capable of transmitting stress couples and being subjected to body torques, > as in polyatomic and certain non-Newtonian fluids. Can someone help me understand this? Say by giving me another definition of polar and nonpolar fluids. Thanks.


title: How cold does it need to be for spit to freeze before hitting the ground?

text: What is the dominant form of heat transfer between warm water and cold air? If a $100 mg$ drop of water falls through $-40 C$ air, how quickly could it freeze? Is it credible that in very cold weather spit freezes in the half a second it takes to reach the ground?


title: Why is it suffice to show Tensorial identity on a tensor composed of two vectors?

text: I've encounter many proves of Tensorail identity that begin with assuming our tensor can be written in form of: $T^{\alpha\beta}=u^{\alpha}v^{\beta}$ . As helpful is it might be, I'm not sure if its a valid assumption, and if there are $\alpha\times\beta$ Independent components.


title: How long will the Universe's hydrogen reserves last for?

text: I recently became really interested in learning about physics and cosmology, but I still know very little. Hopefully someone with more knowledge will be able to shed some light on my questions. Here are my presumptions (please correct me if I'm mistaken):   * $t_{0}$: Big Bang.   * The Universe expands (and thus cools) sufficiently to allow the formation of atoms.   * The early Universe mostly consists of Hydrogen and is not uniform in its geometry.   * Gravity pushes lumps of matter together until their density (temperature) is so high that nuclear fusion kicks off. The first giant stars are born.   * Some heavy elements are created in these stars and when they explode, sufficient temperatures are reached to form heavier elements still.   * All of the successive stars and planets are the product of these original stars. My questions:   * If the amount of Hydrogen is finite in the Universe and each successive generation of stars use up most of their Hydrogen, what is the theoretical maximum number of generations of stars that our Universe can support? A ballpark figure in terms of years is fine too. ;)   * Are there some special physical processes that occur in the Universe on a large enough scale that are able to break up heavy elements (i.e., Helium) into lighter elements (i.e., Hydrogen)? Kind of like a cosmic recycling operation.   * If we discount the possibility of a Big Crunch, is the Universe pretty much headed into a time when there will be no more stars and only a bunch of black holes, planets, and other debris?


title: What's the temperature distribution of a plane wall insulated on one side with no internal heat gen.?

text: Let's say we have a plane wall that is insulated on one side, exposed to a fluid on the other side, and has no internal heat generation. Would the shape of the temperature distribution be a constant? I ask because I dont think it would be but a derivation says otherwise so I would like someone to tell me if I am doing this wrong. The general temperature distribution is created from the heat diffusion equation $$\frac{d^{2}T}{dx^{2}}=0$$ $$\frac{dT}{dx}=C_{1}$$ $$T(x)=C_{1}x+C_{2}$$ I would assume that at the insulation (x=0), the insulation is a adiabatic surface $$\frac{dT}{dx}\bigg|_{x=0}=0$$ So $C_{1}=0$ and $T(x)=C_{2}$ where C2 is the temperature of the surface exposed to the fluid. This is saying that the temperature throughout the wall is the same as the temperature at the surface, but this intuitively doesnt seem right.


title: Force from point charge on perfect dipole

text: Have a point charge and a perfect dipole $\vec{p}$ a distance $r$ away. Angle between $\vec{p}$ and $\hat{r}$ is $\theta$. Want to find force on dipole. I'm having more than a little difficulty identifying where I'm going wrong. If I do this problem in cartesian coordinates, I get the right answer, so apparently I am not understanding something about spherical coordinates. We have $F = q\Delta E$ for dipoles in a nonuniform electric field. If $d$ in dipole is small, then I can use $$\Delta E \approx \nabla E \cdot \Delta\vec{r}$$ Below I derive the expression in spherical coordinates. So, first of all, $$E = \frac{q}{4 \pi \epsilon_0 r^2} \hat{r}$$ So $$E_r = \frac{q}{4 \pi \epsilon_0 r^2}$$ and $$\Delta E_r = \nabla E_r \cdot \Delta \vec{r}$$ where $\Delta \vec{r} = \bigl(\Delta r, r\Delta \theta, r\sin\theta\Delta \phi \bigr)$. $$\nabla E_r = \biggl(\frac{-2q}{4 \pi \epsilon_0 r^3},0,0\biggr)$$ Therefore, $$q\Delta E_r = \frac{-2qp\cos\theta}{4 \pi \epsilon_0 r^3}$$ and $$\Delta E_{\theta} = \Delta E_{\phi} = 0$$ as $E_{\theta} = E_{\phi} = 0$. So $$F = q\Delta E_r = \frac{-2qp\cos\theta}{4 \pi \epsilon_0 r^3} \hat{r}$$ But should be $$F = \frac{-2qp\cos\theta}{4 \pi \epsilon_0 r^3} \hat{r} - \frac{qp\sin\theta}{4 \pi \epsilon_0 r^3} \hat{\theta}$$ So $\Delta E_{\theta}$ must be nonzero but I don't see how.


title: How do we know that nonperturbative canonical quantum gravity is wrong?

text: In these forums and elsewhere it is routinely agreed that "we do not have a theory of quantum gravity." My question is, how do we know that canonical quantum gravity is "wrong"? I understand that the theory is perturbatively nonrenormalizable, but doesn't that just mean that we can't apply perturbation theory to it? It seems the theory is nonperturbatively renormalizable. A theory being nonperturbative doesn't make it "wrong". My understanding is that in modern QFT nonrenormalizability is not anymore considered such a big deal, and that even the Standard Model is expected to be an effective theory modified by nonrenormalizable terms appearing at higher energies. So barring practical considerations, why is canonical quantum gravity considered "not a theory of quantum gravity?" EDIT: I am not sure that the term "Canonical Quantum Gravity" is correct. I am referring to what is called "Quantum Einstein Gravity" in this paper. If someone knows better please help me correct my terminology. I was not meaning to imply anything about LQG because I thought that LQG "brought more to the table" than just a nonperturbative approach to the same QFT, but I could be wrong about that.


title: Wavelength of photon changes as it rises from a planet's surface(acc. to this equation)?

text: The setup assumes a large mass(Earth?) an a photon launched from its surface initially. The wavelength of the photon on launch is known. Then the new energy of the photon is compared with energy it traveled a distance $d$.      Initially, $$E_1 = \frac{GMm}{R} + \frac{1}{2}mv^2$$ where m- mass of photon, M is mass of earth, R is radius. Finally $$E_2 = \frac{GMx}{R+d} + \frac{1}{2}xv^2$$ where $x$ is new mass of the photon. Putting $m = \frac{h}{Lc}$, $L$ is wavelength Leet the new wavelength be $W$. we can equate the 2: $$\frac{GMh}{RLc} + \frac{1}{2}\left(\frac{h}{L}\right)^2 = \frac{GMh}{(R+d)Wc} + \frac{1}{2}\left(\frac{h}{W}\right)^2$$ Solving and putting $\frac{1}{W} = y$, we'll get,      $$\frac{h^2}{2}y^2 + \frac{GMhy}{(R+d)c} = \frac{GMh}{RcL} + \frac{1}{2}\left(\frac{h}{L}\right)^2$$ So this follows a quadratic equation $ax^2 + bx + c =0$ So that would mean that $y$ would keep decreasing as $d$ increases. Then it would mean that the mass of the photon increases as it rises. Is this logic correct or am I making a really blockheaded mistake here?


title: What states of matter are possible at lowest temperature?

text: Near absolute zero, some materials are superconductors. Other materials are superfluids. Others are Bose-Einstein Condensates. Is there a complete list of possibilities? Or is this still a research topic?


title: What is current of electric circuit which has only one component - a battery (or cell)?

text: What is current of electric circuit which has only one component a battery (or cell)? Explain why.


title: Which areas in physics overlap with those of social network theory for the analysis of the graphs?

text: I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in physics which overlap in the essence of their problems with those of small world networks. Which natural phenomena exhibit these kind of features similar to small world networks? I would like to know that, so maybe I can look at those problems to get inspiration that can be taken to social network theory.


title: What reasons are there to suspect string theory may be an incorrect theory?

text: It's a truism that in science it is at least as important to state the reasons why a theory or idea might be wrong, as to state the reasons why it is might be correct. For example, early renormalization methods made experimental predictions that were very accurate, but the inventor's famously worried for decades about the conceptual problems of divergences; and many of their papers/articles/books on the subject include a long discussion about how acutely worried they were that their method for handling divergences was deeply flawed somehow. My intention with this post is not to engage any user in a debate about whether string theory is true or not. I think anyone who takes string theory seriously should be happy to acknowledge as clearly as possible all the potential theoretical issues/problems with the theory. Therefore I would like to ask, what are the major theoretical problems which would lead a reasonable person to be worried that string theory is not an accurate theory? I am excluding the fact that string theory has made no (major) predictions that have been confirmed, I am only interested in conceptual and theoretical ideas which might discredit the theory. Please keep all answers to one issue per post.


title: Force on a coil inside of a voice coil

text: as a homework exercise we were given the following question: Given the following voice coil: ![enter image description here](http://i.stack.imgur.com/YVzsu.png) With depth = 20 mm Permanent magnets with B = 1.23 T, Ur = 1.1 The coils has 20 turns, I = 1 Ampere. a) Calculate the force on the coil (the Lorentz force) using reluctance method ... However, we could not figure out how this may form a voice coil and where to actually start. We are aware of the fact that calculating the reluctance may be done by using: $R = \frac{l}{\mu_0 \mu_r A}$ And consequently, the lorentz force may be calculated using: $F = NBIl$ However, we are unsure of how the power circulates the system (i.e. how to convert this model into an equivalent circuit with power source and resistance/reluctance components). I am hoping someone of you may be able to give us more insight on how to approach this problem. Thanks in advance.


title: Current division in ideal inductors?

text: The Question is:- > Find the current distribution in the inductors at steady state (i.e. > assuming $t\rightarrow \infty$ after the switch is closed and circuit > established and consider the inductors without any resistance and ideal). ![enter image description here](http://i.stack.imgur.com/noa0t.jpg) **My Efforts**   Since both of the are in parallel, the equations for current at any time $t$ after establishing the circuit is given by ($i_1$=corrent in $5mH$ inductor and $i_2$ in the other, and the total current $i$):- $$i(t)=i_1(t)+i_2(t)=4(1-e^{-\frac{5t}{L_{net}}})$$ where $L_{net}=\frac{10}{3}mH$. But I do not know how this current divides into two in the inductances at any time $t$ or in the steady state. Had the inductors not been ideal, i.e. if they had different resistances, the current could divide in the ration of their resistances in the final steady state, but since they are ideal, this method won't work. How can I solve this? the answers given are $\frac83A$ in the $50mH$ inductor and $\frac43A$ in the other.


title: Why can't we see clouds everywhere around us?

text: ![enter image description here](http://i.stack.imgur.com/zZNlk.jpg) We see clouds at a particular height,and not everywhere near the ground.I am not really well versed in the concept of cloud,but I felt the clouds would be lighter by the way they look.So,they should have been at the bottom instead of being at the top.   **I will be waiting to know the reason for clouds being only at the top and not anywhere else around us at the ground.**


title: Can we tell from periodic table that which materials are ferromagnetic?

text: I want to know that because I want to see whether ferromagnetic materials relate to the number of outer most electrons. If there is no direct relationship, could you please give me a list of the materials that are ferromagnetic? Thanks


The matrix elements of the momentum operator in position representation are: $$\langle x | \hat{p} | x' \rangle = -i \hbar \frac{\partial \delta(x-x')}{\partial x}$$ Does this imply that $\langle x | \hat{p} | x' \rangle = 0 $ whenever $x \neq x'$? Is the momentum operator diagonal in position representation? I know that the momentum operator shouldn't be diagonal in position representation (otherwise solving for the eigenergies and eigenfunctions of most Hamiltonians would be trivial). I am obviously confused here. I need more than just yes/no answers to these questions. I need some explanation, or some intuition.


title: On a bicycle, why does my back tyre wear so much more quickly than the front?

text: This question _is_ cross-posted from Bicycles.SE, but it is really one for those that know a bit about physics. Why does the back tyre of a bicycle wear out quicker than the front tyre? I have my uneducated suspicions but I would appreciate an educated answer.


title: Why is the binding energy per nucleon not zero for hydrogen atom?

text: The lone proton has not to be worked on against any electrostatic force. So where does the energy come from? What is mass defect for a hydrogen nucleus?


title: Kerr geodesics differential equations in equatorial plane

text: With friend, we are writing an interactive educational simulation of particle falling into a black hole. Currently we use Schwarzschild geodesics. However, we want to generalize it to the case of rotating (and perhaps rotating and charged) black hole. We are mostly interested in the equatorial plane, as then we can plot it on a 2D tablet. So, **what are the differential equations for a particle (with given initial position and velocity) falling in the Kerr (or Kerr-Newman) metrics in the equatorial plane?** I'm interested in an explicit form ( **plug & play** \- should work after insertion of the black hole parameters (i.e. $M, L, Q$) and the initial contitions (i.e. $\vec{x}, \vec{v}, q$); $Q$ and $q$ are optional, as Kerr metrics is nice by itself). Side notes: Yes, I know the general procedure. Just I'm short of time (so now I'm even no longer coding it). So I may self-answer, but rather later than sooner. It's almost in Chapter 20 of something: Geodesic motion in Kerr spacetime (i.e. (20.25) and (20.31) for the equations of motion; (20.18) and (20.19) for energy and angular momentum). However, some parameters are not introduced (perhaps there are in the previous chapters...).


title: Determine the Dependence of S (Entropy) on V and T

text: Why can the equation $$dS= \frac{1}{T} dU + \frac{P}{T} dV$$ be expressed as $$dS= \left. \frac{\partial S}{\partial T} \right|_V dT + \left. \frac{\partial S}{\partial V} \right|_T dV \quad?$$


title: Is edge state of topological insulator really robust？

text: I am a little confused! Some people are arguing that the gapless edge state of Topological insulator is robust as long as the time reversal symmetry is not broken，while other people say that it is not stable for lack of topological order。Please help me out！


title: Determining the probability of a particular site having a particular spin in an Ising model

text: Given an Ising model, we have the energy formula: $E= - \sum_i h_i S_i - \sum_{i \neq j} J_{ij} S_i S_j$ and we have the probability of a given state, given the energy of that state and the temperature: $P(\\{S\\}) \sim e^{-E(\\{S\\})/kT}$ (where the normalization constant is the partition function). The question I am interested in is if there is a computationally efficient way to determine (or at least estimate) the probability (for a given temperature) that a _particular_ site $i$ has a spin of, say, $+1$. (In other words I want the sum of the probabilities of all the states where $S_i = +1$.) I understand that a method that is frequently used to solve these types of problems is to do a Monte Carlo simulation of the evolution of the state. However in this problem since I am only interested in one particular site, it seems like simulating the entire state is not necessarily computationally efficient.   * Is this a problem that is generally solvable analytically? What is known about its complexity (is it NP-hard?)   * If it is not solvable analytically, what techniques are normally used to approximate it? (If this topic is too broad for a single answer, then links to references where I could learn more would also be useful.)


title: What else does the fabric of space-time do?

text: I know that, the fabric of space is bended so there is a path for another planet to follow to cause gravity I.E. the sun and the earth ( i think) Is htere any othe rthing's the fabric of space-time does to the universe? i heard some were about that it make's it so that all light travel's at the speed of light, is this true and is there anythign else it does.


title: How does the weight force distribute in roughly kite like kinematic to determine torques

text: I have a kinematic model like the simplified following image. Assume that all points are fixed. I'm interested in how the force $\vec{m}$ distributes across $a_2$ and $b_2$ up to $a_1$ and $b_1$. Finally I'm interested in the torques that result in $A_1$ and $B_1$. ![enter image description here](http://i.stack.imgur.com/OwW0c.png) I know that the kinematic as presented is not stable. The stabilizing part was omitted for simplicity. Simply assume the kinematik is in a stable state and I simply want the forces/torques. Some notational stuff (edit if you need more): $$ c := \overline{A_1B_1}, \quad d := \overline{A_3B_3}, \quad M := \frac12(A_3+B_3), \quad A_3B_3 || A_1B_1 $$ The mass of the kinematic itself is neglectable.


title: Integral in $n$−dimensional euclidean space

text: I've asked this question in Mathematics Stack Exchange, but unfortunately there is no answer yet. I repost it because this integral comes from QFT and maybe someone here did it before or could help me. I merely copy this post. > I want to calculate this integral in $n$-dimensional euclidean space. > > $$I(x)=\int_{\mathbb{R}^n}\frac{d^n k}{(2\pi)^n}\frac{e^{i(k\cdot > x)}}{k^2+a^2},$$ where $k^2=(k\cdot k)$, > $k=(k_1,\ldots,k_n)\in\mathbb{R}^n$, > $x=(x_1,\ldots,x_n)\in\mathbb{R}^n$,$a\in \mathbb{R}$. > > I've done this integral for $n=3$ by spherical coordinates and residue > theorem. I have > > $$I(r)=\frac{1}{4\pi r}e^{-ar},$$ where $r=|x|$ > > But in $n$-dimensions I failed in using spherical coordinates, because I > have never done it before. Also I see that this integral is Fourier > transform of $\frac{1}{k^2+a^2}$, but I failed here too, because I can't > find Fourier pair in my reference books. > > If someone could guide me in this integration it would be great.


title: What is the physical meaning of the terms in the multipole expansion?

text: I have a few questions on multipole expansions and I have read about the topic in many places but could not find an answer to my questions, so please be patient with me. The electrostatic potential due to an arbitrary charge distribution $\rho(\textbf{r`})$ at a given point $\textbf{r}$ is given by (up to a factor of $1/4\pi\epsilon_0$) $\displaystyle V(\textbf{r})=\int_{V~`}\frac{\rho(\textbf{r`})}{|\textbf{r}-\textbf{r`}|} dV`$ In case where $r>>r`$, $V(\textbf{r})$ can be multipole expanded to give $\displaystyle V(\textbf{r})=V(\textbf{r})_\text{mon}+V(\textbf{r})_\text{dip}+V(\textbf{r})_\text{quad}+...$ where $\displaystyle V(\textbf{r})_\text{mon}=\frac{1}{r}\int_{V~`}\rho(\textbf{r`}) dV`$ , $\displaystyle V(\textbf{r})_\text{dip}=\frac{1}{r^2}\int_{V~`}\rho(\textbf{r`}) ~\hat{\textbf{r}}.\textbf{r`}dV`$ , $\displaystyle V(\textbf{r})_\text{quad}=\frac{1}{r^3}\int_{V~`}\rho(\textbf{r`}) ~\left(3(\hat{\textbf{r}}.\textbf{r`})^2-r`^2\right)dV`$ , etc... Now here are my questions: **1-** Is there an intuitive meaning of every one of these terms ? for example I can make sense of the monopole term in the following way: to the 1st approximation the charge distribution will look like a point charge sitting at the origin which mathematically corresponds to what is called a monopole term, which is nothing but $Q/r$ Is this correct? **2-** Now what is the meaning of the dipole term? I know that the word dipole comes from having 2 opposite charges, and the potential due to that configuration, if the charges are aligned along the z axis symmetrically say, goes like $\displaystyle\frac{\cos\theta}{r^2}$. But from the multipole expansion there is a nonzero dipole term even in the case of a **single** charge sitting at some distance from the origin say. Why is it called a dipole term then? Is there a way to make sense of this term in the same way I made sense of the monopole term? **3-** What is the intuitive meaning of the quadropole term? **4-** Is the multipole expansion an expansion in powers of 1/r only? or of $\cos\theta$ too? **5-** May be this is not an independent question but I am wondering if there is something like a geometrical/pictorial meaning of every term in the multipole expansion.


title: Relativistic transformation of the wave packet length

text: Let us suppose we have an excited atom at rest. It has a certain mean lifetime $\tau_0$. If we wait sufficiently long time $t>>\tau_0$, we will find a deactivated atom and a (spherical) electromagnetic wave function of photon with about $\tau_0\cdot c$ long layer with non zero probability to find a photon within. Something like a fast expanding probability "ring" with a $\tau_0\cdot c$ width of the ring. Now, let us consider this system in a moving reference frame. It seems to me that this width $\tau_0\cdot c$ is relativistic invariant: it is a difference between two "fronts" of electromagnetic wave rather than a length of a material body subjected to the Lorentz contraction. Is it correct? In other words, whether this picture relativistic invariant? ![Wave function evolution](http://i.stack.imgur.com/vtenD.jpg)


title: Is the Copenhagen interpretation merely an approximation to quantum mechanics?

text: So, I'm reading Max Tegmark's _Our Mathematical Universe_ (Knopf edition, p. 229). He's discussing Everett/MWI for a bit and I'm not really paying attention and then I wake up to this: > [I]t's time to update the quantum textbooks to mention decoherence (many > still don't) and to make clear that the Copenhagen interpretation is better > thought of as the _Copenhagen approximation:_ even though the wave function > probably doesn't collapse, it's a very useful approximation to do the > calculations as if it does collapse when you make an observation. Now, I believe I have read (elsewhere, e.g., on this site) that these interpretations do not make any difference _whatsoever_ * when it comes to predictions. But here, apparently (at least that is how I read the above), it is claimed that MWI and Copenhagen actually _differ_ in predictions (and that MWI has the _right_ predictions). **Is that correct?** (This would make it slightly more difficult to be agnostic about choosing your favourite interpretation for the time of day, right?) NB: I'm not specifically asking whether the wavefunction collapses or not. *As in: zip, nada, zilch, _exactly_ $0$.


title: Does graphene actually remain strong for macroworld engineering?

text: I heard that people envision strong structural materials made out of graphene, but I heard it may weaken when being stack in layers. Is graphene viable for macroworld structural engineering or is it only suitable for electronics and similar applications?