title: Why are the true variance of these orbits out by ~pi?

text: I have an object that is orbit around a point mass in a 2D environment with a known speed, radius and zenith. I calculate the following orbital parameters as such and can confirm that these values are correct (where $R_{p}$ is the periapsis, $R_{a}$ is the apoapsis, $e$ is the eccentricity, $a$ is the semimajor axis, $r$ is the radius, $v$ is the velocity and $GM$ is the product of the mass of the point mass and the gravitational constant): $C = \frac{2GM}{rv^{2}}$ $R_{p} = r \times \frac{-C+\sqrt{C^{2}-4(1-C)(-\sin^{2}(1-C))}}{2(1-C)}$ $R_{a} = r \times \frac{-C-\sqrt{C^{2}-4(1-C)(-\sin^{2}(1-C))}}{2(1-C)}$ $e = \left | \frac{R_{a} - R_{p}}{R_{a} + R_{p}} \right |$ $a = \frac{R_{a} + R_{p}}{2}$ I then go on to attempt to calculate the true anomaly of the orbit as follows (where $z$ is the zenith and $\theta$ is the true anomaly): $N = \frac{rv^{2}}{GM}$ $\theta = \tan^{-1} \frac{N\sin z \cos z}{(N\sin^{2} z)-1}$ This is calculates a correct value as long as the radius is greater than a value slightly less than the semiminor axis of the orbit. Adding pi to the true anomaly corrects this error, except where the radius is close in value to the length of the semiminor axis. Why is the true anomaly off by ~pi in this case?


title: What is the relative speed of two near-light speed particles headed towards each other?

text: I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem for myself: > If both particles are moving at 0.9c towards each other (according to an > observer on Earth), what speed does each particle have relative to the > other? I'm stumped since I am only familiar with Newtonian classical mechanics to solve this (which would be wrong). I am aware of Lorentz' factor $\gamma =\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ and the time dilation equation $t_m = \frac{t_o}{\sqrt{1 - \frac{v^2}{c^2}}}$, but I'm not sure how to apply it in this instance. I'm just looking for a gentle push in the right direction. Edit: My prior research:   1. This article, https://what-if.xkcd.com/1/, talks about the effect of a baseball thrown at 0.9c would have as it traveled towards a batter. This is not what I'm looking for since it doesn't explain the math behind finding the collision speed between two high velocity entities.   2. This question on Yahoo, https://answers.yahoo.com/question/index?qid=20110529201519AAxbxvm, asks a similar question to mine, but no math is involved to demonstrate the calculations behind the reasoning.   3. This question on Physics.SE, Collision between a photon and a massive particle, does not answer my question either. I have not been able to find a similar Physics.SE question which can provide me to clues to my own hypothetical question.    4. I have also Googled the following phrases: > i. "collision faster than the speed of light" > > ii. "collision of high speed particles" > > iii. "lorentz transformation in a collision" > > iv. "collision analysis at light speed"


title: Chain with mass gradient problem

text: ![This is the question](http://i.stack.imgur.com/I5qBu.jpg) This is the problem, basically. Now my question is about the approach. Mine, and my teacher's. I would like some help as to which one is correct... Mine: As the whole chain is in equilibrium, the horizontal forces must be balanced. Therefore, tension in the thread must be equal to the total horizontal Normal Reaction by the fixed sphere. Now, to calculate the $dN$ for a mass $dm$ taken at an angle of $\theta$ from the horizontal is $dm g \sin(\theta)$ and its component in horizontal direction is $dN \cos\theta$ after the integration you get (finally) $\ T = \frac{\lambda r g}{2}$ My Teacher's Approach: The differential increase in the tension in the chain due to the mass $dm $ should be $dmg \cos\theta$. Now integrate this increase in tension to get the net increase in the tension from the point where the chain looses contact to the point where it is attached to the thread. So you will get option A. According to me, the problem lies in the fact that you are integrating the $dT$ as a scalar, whereas it is a vector, but my teacher does not agree. He says that we are focusing on the magnitude, and the fact that its a vector is compensated because its magnitude is a function in $\theta$. But I think that the direction of the infinite $dT$s is ignored while integrating.


title: Klein-Gordon Canonical Commutation Relation (CCR)

text: In the complex Klein-Gordon field we regard as dynamical variables the field $\phi$, the complex conjugate of the field $\phi^*$, and the momenta $\pi$, $\pi^*$. I can't see how should arise the (equal time) canonical commutation relations, in particular: $$ \left[\phi\left(t, {\bf x}\right),\ \pi\left(t,{\bf y} \right)\right]=i\hbar\delta^3\left({\bf x}-{\bf y}\right)$$ because the momenta are time derivatives of the field, and hence a function of $(ct,{\bf x})$, so the commutator above should be zero because both are functions of the space time coordinates, $\pi$ is not a differential operator. Where am I wrong?


title: Reference for the renormalization of a scalar field's mass

text: There are a couple of interesting lectures by Leonard Susskind online, and in the first lecture on Supersymmetry & Grand Unification he explains renormalization. His example is the mass renormalization of a scalar field, and he uses a couple of dimensional analysis tricks to get his results (around 35:00). It's a nice lecture that makes you feel you understand the topic better, but at the same time it is a lot of hand waving. I'm trying to write up a bit on renormalization, along his line of argument, but I'm confused about a lot of small details. For starters, he omits a lot of factors of $\pi$ and $2$, but OK, I can live with that. I think he skipped doing an integral when calculating the one loop diagram, but I'm not sure. Then I'm confused about the different diagrams were a particle goes from $A\rightarrow B$ without any loops or branches. Which one is called the propagator: the summed one, the naked one, the naked one with an explicit mass "$\times$"? How is it related to mass? I think I understand the physics, but the terminology is confusing to me. Instead of asking a half-dozen confused questions, I'm looking for a reference, a book or a review, that explains the mass renormalization for a scalar field in a pedagogical way but without skipping the technicalities. I'd strongly prefer something citable (I'm hesitant to quote youtube in my thesis ;-)).


title: How do we perceive colors outside our gamut?

text: Let's take an CIE XYZ color space as an example. There are many colors that are outside our gamut - how do we see such a color?


title: How many quarks in a proton?

text: I am confused by different papers I have seen on the internet. Some say there are three valence quarks and an infinite of sea quarks in a proton. Others say there are 3 valence quarks but a large amount but finite number of sea quarks(quark, antiquark virtual pairs) in the proton What is the answer? are there an infinite amount of quarks in a proton at any one time? how can this make any sense?


title: Spontaneous symmetry breaking: How can the vacuum be infinitly degenerate?

text: In classical field theories, it is with no difficulty to imagine a system to have a continuum of ground states, but how can this be in the quantum case?   Suppose a continuous symmetry with charge $Q$ is spontaneously broken, that would means $Q|0\rangle\ne0$, and hence the symmetry transformation transforms continuously $|0\rangle$ into anther vacuum, but **how can a separable Hilbert space have a continuum of vacuums deferent from each other?**      I saw somewhere that says the quantum states are built upon one vacuum, and others simply doesn't belong to it, what does this mean? and **then how could $Q$ be a well defined operator** which acting on a state (the vacuum) actually gives a state (another "vacuum") out of the space considered?


title: Bat hitting a ball

text: When a bat hits a ball, consider two cases: 1) The batsman goes for a defense, and stonewalls it, to reduce its speed. 2) the batsman goes for a shot, e.g. a home-run, etc. in which case will the bat have the highest chance of breaking due to the impact? And am I right in assuming that the force on the bat due to the reaction force of the ball is the only thing that causes it to break?


title: Angular momentum of 2d harmonic oscillator

text: So, I have the problem of determining the spectrum of H and L, in terms of creation and annihilation operators of angular momentum... The problem goes along with what is happening on this page. However, my professor is asking us for the commutators of H and L with a quantity A, which is defined as $$A=\hat a_x^2+\hat a_y^2$$ When I do this out, writing H as $1+\hat a_x^{\dagger}\hat a_x+\hat a_y^{\dagger}\hat a_y$, I find that $$[H,A]=\hbar\omega(a_x^3+a_y^3)$$ I have no problem with this, except that when I want to construct an eigenket representation of $E_{nm}$in terms of the $\hat a_L^{\dagger}\text{ and } \hat a_R^{\dagger}$ and $A^{\dagger}$, I am not sure how to use this result to find this. I know that the result should be $E_{n,m}=\hbar\omega[2n+1+|m|]$ Thanks


title: Any simple reason why spin 2 polarization tensor should be symmetric in $\mu\nu$?

text: Perhaps this is obvious to the not so tired one, but is there any reason why the five spin 2 polarization tensors $\epsilon_{\mu\nu}^{a}, a=1,\dots,5$ should be symmetric in $\mu\nu$? While I'm at it, perhaps I should also ask where the tracelessness condition: $$g^{\mu\nu}\epsilon_{\mu\nu}^{a}=0.$$ For more info, see Zee page 33.


title: Kinematic, motion in 2D

text: If the kinetic energy at maximum height is 2/5 the kinetic energy at half the maximum height, find the angle of projection. In other words: K.E. at H(max) = 0.4*K.E. at 0.5*H(max) I got 60 degrees, however, my teacher told me that the answer is 30 degrees. Please solve it for me so I can see where I went wrong. Well here's my edit: Consider u to be the velocity at H(max) Consider v to be the velocity at half of H(max) Consider c to be initial velocity given Consider @ to be angle projected at sqr() means square root u^2 = 0.4v^2 u is obviously c*cos(@) v I found to be: sqr((0.5u^2)(1+(cos(@))^2) Using this, I substituted into the previous equation and solved to attain: cos@ = 0.5 So.... That gives me 60 degrees. Am I right? Or is there some sort of catch?


title: Single photon interference experiment

text: ![Original illustration by me. Use as you please](http://i.stack.imgur.com/mRDkD.png) In short: the question is, does the length of the path affect the outcome of detecting a photon? Consider the single photon beam splitter experiment. Does the probability of detecting the photon change if the distance between the detectors is unequal? Because light has a fixed velocity c. If the photon is detected at a place that is nearer (detection means absorption unless some special means are used), then it can no longer be anywhere else. This might be the case in Wheeler's delayed choice experiment: http://www.sciencenews.org/pictures/112010/essay_delayed_zoom.gif As the particle detection path is shorter when that path is chosen, the photon will always be detected there? If so, could temperature gradient on the detection plate cause unequal expansion of the plate on quantum scales affecting the outcome of detecting photon because the place where they reach on the plate first is different?


title: What the heck is negative effective mass?

text: I am reading this book:Solid State Electronic Devices by Ben G Streetman and Sanjay Kumar Banerjee.   I have some doubts in the article **3.2.2** Effective mass.   In this the aythors say that $E=\dfrac{1}{2}mv^2=\dfrac{1}{2}\dfrac{P^2}{m}=\dfrac{{\hbar} ^2}{2m}k^2$. >   * Electrons usually have thermal velocity of order $10^7$m/s. So Shouldn't > we use $E=mc^2$ rather than $E=\frac{1}{2}mv^2$. > The author further says that electron mass is related to curvature of (E,k) relationship as $\dfrac{d^2E}{dk^2}=\dfrac{\hbar^2}{m}\tag{3.2(d)}$. then the author says that the effective mass is given by $m^{*}={{\hbar^2}/{{\dfrac{d^2E}{dk^2}}}}\tag{3.3}$ >   * Is equation $3.3$ derived from equation $3.2(b)$. In equation $3.2(d)$ > we have $m$ the original mass and in eqn $3.3$ we have $m^{*}$ the effective > mass which is completely different from $m$. > In the end of the article the author says that the total force on the electron is given by $F_{tot}=ma$. After this the author says the external force applied on an electron is related to effective mass as: $F_{ext}=m^{*}a$. >   * From where this equation comes? Sometimes the effective mass $m^{*}$ is > negative then the equation implies that if we apply certain external force > on electrons in the crystal they will accelerate in the opposite direction, > how this is possible? What's going on? >


title: What breaks the symmetry between the electromagnetic and weak nuclear force?

text: I know the electromagnetic force is mediated by a photon and the weak nuclear force is mediated by two massive bosons. Are there any other insights into why the masses are so different?


title: Kinematics question

text: An electric train accelerates uniformly from rest to a speed of 20m/s which it maintains until the brakes are applied. It is then brought to rest by a uniform retardation equal in magnitude to twice its former acceleration. The total distance covered is 7.8 km and time taken is is 7 minutes. Calculate   * the time for which the train is travelling at constant speed,   * the initial acceleration in m/s^2.


title: Best shape to reduce the splash of a droplet?

text: Our coffee machine catches the last couple of droplets, after your cup is removed on a shape to reduce plash of the coffee droplets. These shapes are placed inside the spill reservoir.   The shape used by our coffee machine is shape nr 2 with the droplet falling at position 1, this works well but not perfect.   What shape would be even better for this purpose? And at which position should the droplet fall? I've included some shapes I came up with but I'm open for other suggestions. ![](http://i.stack.imgur.com/xwQHS.png) The image displays a 2D version of the shapes, the first 2 shapes are cone shaped and the last 2 would have to be open on the ends (or sides) to release the coffee into the spill reservoir.


title: Sound as a conserved quantity

text: From the first man to the present day men, all of them have made some sound. Sound is an energy, it can neither be created nor can it be destroyed. Therefore, every word spoken by each human that came into this world made some sound. Their voices might have converted into another form of energy. But, we have not lost that sound energy. Am I right?


title: What is a realistic launch speed of a grappling hook gun?

text: In The Dark Knight, at the end of the movie Batman throws the Joker off of a building and then shoots his grapple hook gun to catch him. Is 68m/s a reasonable speed for a grapple gun to shoot?


title: Deducing from the double slit experiment that electrons mostly behave like particles

text: I saw this video of a lecture by Feynman where he said that electrons behave like particles when there is a photon source to detect which slit they pass through. Does this imply that electrons mostly behave like particles, since the real world is full of such possible interactions that would destroy interference?


title: Virtual particles/quantum tunneling - conservation of energy?

text: I'm confused as to how the above phenomena can take place since arent they breaking the law of conservation of energy (even, if temporarily)?


title: Question on Type HO/HE string theory

text: The Heterotic string state is a tensoring of the bosonic string left-moving state and the Type II string right-moving state. Therefore, I expect the spectrum to be: $$\begin{array}{*{20}{c}} \hline & {{\rm{Sector}}}&{{\rm{Spectrum}}}&{{\rm{Massless fields}}}& \\\ \hline & {{\rm{Bosonic}} - {\rm{R}}}&{{\bf{1}}{{\bf{6}}_v} \otimes {{\bf{8}}_s} = {{\bf{8}}_v} \otimes {{\bf{8}}_v} \otimes {{\bf{8}}_s}}&?\\\ \hline & {{\rm{Bosonic}} - {\rm{NS}}}&{{{\bf{8}}_v} \otimes {{\bf{8}}_v} \otimes {{\bf{8}}_v}}&?& \hline \end{array}$$   1. However, how does one calculate the massless fields of the Type I string theory using the spectrum of the type I string theory?   2. Furthermore, to calculate the mass spectrum of the Heterotic string, does one simply add the number operator of the bosonic string to that of the type II string and the same for the normal ordering constant? i.e. is it true that $$\begin{array}{l} m = \sqrt {\frac{{2\pi T}}{{{c_0}}}\left( {B + {{\tilde N}_{II}} - {a_B} - {{\tilde a}_{II}}} \right)} \\\ {\rm{ }} = \sqrt {\frac{{2\pi T}}{{{c_0}}}\left( {B + {{\tilde N}_{II}} - 1 - {{\tilde a}_{II}}} \right)} \end{array}$$ **Edit: I found the answer to Question 2. Check the answers section. I have answered my own question.**


title: Relationship between Connection and Material Derivative

text: Suppose $D\subset \Bbb R^3$ contains a fluid and that $f : D\times \mathbb{R}\to \mathbb{R}$ is a time dependent function defined on the fluid region. In that case, the material derivative is defined by $$\dfrac{D}{Dt}f(a, t) = \dfrac{\partial f}{\partial t}(a, t) + (\mathbf{u}\cdot \nabla)f(a, t)$$ Where $\mathbf{u}\cdot \nabla$ is the operator defined on scalar function $g$ by $$(\mathbf{u}\cdot \nabla )g = \mathbf{u}\cdot (\nabla g) = D_{\mathbf{u}} g$$ That is the directional derivative along $\mathbf{u}$ of the function $g$. On vector fields it is defined componentwise, that is, if $\mathbf{v} = (v_1,v_2,v_3)$ then $$(\mathbf{u}\cdot \nabla)\mathbf{v} = ((\mathbf{u}\cdot \nabla)v_1, (\mathbf{u}\cdot \nabla)v_2, (\mathbf{u}\cdot \nabla)v_3) = (D_{\mathbf{u}}v_1, D_{\mathbf{u}}v_2, D_{\mathbf{u}}v_3)$$ But that latter thing is clearly the Covariant Derivative of $\mathbf{v}$ along $\mathbf{u}$ when we consider the Levi-Civita Connection on $\mathbb{R}^3$ with the usual flat metric tensor, that is $$(\mathbf{u}\cdot \nabla)\mathbf{v} = \nabla_{\mathbf{u}}\mathbf{v}$$ Now, is this conclusion right? Can we really write the material derivative as $$\dfrac{D}{Dt}\mathbf{v}(a, t) = \dfrac{\partial \mathbf{v}}{\partial t}(a, t) + \nabla_{\mathbf{u}}\mathbf{v}(a, t)$$ and if it's right is there some usefullness in this relationship? I mean, I don't know that much of connections and how they can be used on Physics, but I know they are usefull. In that case, writing the material derivative in terms of a connection gives some advantage? Would it make sense if $\nabla$ were another connection other than the Levi-Civita connection?


title: From where does the force/energy of action-reaction comes from? (Newton's Third Law of Motion)

text: I was wondering, from where does the opposite force and thus energy comes from when we apply force. For example, lets say there are two persons (P1 and P2) on the universe, and no force is applied to them. P1 applies a force to P2. P2 will start to move. P1 lost some energy to do that. Now, according to the third law of newton, P1 will also get a force from P2 as a reaction. But from who does the energy of reaction comes from? I mean, I found it hard to believe that P2 is the one who losses energy, just for the sake of reaction. So, from where does this force, and thus energy, comes from? I am not an expert, I just know the basics. So please, be tolerant :P


In the Gravity movie discussions we learn that objects accellerated towards an object in the same orbit miss it and move to a higher orbit. Objects accellerated away from an object in the same orbit move to a lower orbit. What shape would an explosion be in orbit? Edit. Compared to an explosion in space that is not in an orbit. How would the shape of the trajectories of shrapnel evolve over distance and time.


title: Friction on a conveyor belt

text: I was surfing through an Olympiad paper and I was caught with this question. > A block of mass 1 kg is stationary with respect to a conveyor belt that is > accelerating with $1\, \tfrac{m}{s^2}$ upwards at an angle of 30° as shown > in figure. Determine force of friction on block and contact force between > the block & belt. _(I don't have enough reputation to post a diagram)_ I tried to split the normal forces and proceed using the pseudo force method but am stuck on how to do so. Any other methods so as to proceed in this problem?


title: How can one predict the length of the Synodic month? Why is it irregular?

text: I'd like to write a program that uses the exact (down to the second) amount of time from one new moon (or full moon) to the next. Yet, I am told that this period is irregular. Yet, it seems to be predicted in a number of places (ie, by the navy). How do they do this? http://aa.usno.navy.mil/data/docs/MoonPhase.php


title: What's the most accepted theory for Blue Stragglers These Days?

text: I'm working on a post against a recent creationism article about blue stragglers. From when I was in undergrad, the general explanation was that they were likely second generation stars within globular clusters. More recent work seems to indicate that it's likely due to binary interactions with a sun- like star siphoning material off a companion to become a recent and short- lived blue supergiant. Since this is way outside my field, I thought I'd try my luck here and get a bronze badge because I've never asked a question. What are the most accepted theories these days for this phenomenon?


title: Is there a correlation between the mass of a supermassive black hole and the mass of its host galaxy?

text: I would love to know! I can find lots about the mass-velocity dispersion relation. There's a mass-luminosity relation (but not really tight). I hope you can include references, as I'm spending hours looking for this and not finding answers. thanks


title: the color we perceive

text: The white/yellow light hits a red case, and the red color is reflected into our eyes since other wavelengths are absorbed. My question is since both the paint on the case and the white/yellow light have wavelengths, is there any connection to the paint's wavelength and the red wavelength from the light that makes the observers see the red light? Basically, what properties of the paint material makes it absorb the red wavelength the least?


title: Calculating the minimum Lawson parameter for sustained d-d fusion

text: Calculate the minimum Lawson parameter for sustained deuterium-deuterium fusion in a plasma with an energy of 10 keV. I have been given the above question as part of a homework assignment and help would be much appreciated. The Lawson parameter is given as $$ n \tau > \frac{12 k T}{<\sigma v> Q} $$ where $\sigma$ is the fusion cross-section. I think that Q for d-d reaction is 4 MeV when a proton is produced and 3.3 MeV when a neutron is produced so I assume for the minimum Lawson parameter I should use the larger value of 4 MeV? Also if the energy of the plasma is 10 MeV should I use this to calculate the temperature of the reaction $T$ using $\frac{3}{2} k T$ or the velocity $v$ using $\frac{1}{2} m v^2$ ?


title: Why does sound travel faster in iron than mercury even though mercury has a higher density?

text: The speed of sound depends on the density of the medium in which it is travelling and increases when the density increases. For example, in solids sound travels faster than in liquid and even faster than in gas, and the density is highest in solids, lower in liquids and lowest in gas. So iron has a density of about 7,800 kg/m$^3$, while mercury has 13,600 kg/m$^3$, but the speed of sound is 1,450 m/s in mercury and 5,130 m/s in iron, so mercury has a higher density, but sound travels slower in it. Why is this?


title: Horizontal force on elevator?

text: I would like to ask the following: If an observer travels up or down in an elevator on earth, does he experience a horizontal force due to earth's rotation?


title: How to derive the spin-orbit term in Kane Mele model?

text: The Kane mele model is a famous quantum spin hall model on honeycomb lattice (C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)). The Hamiltonian is $$H = - t\sum\limits_{\left\langle {i,j} \right\rangle \alpha } {c_{i\alpha }^\dagger {c_{j\alpha }}} + i{\lambda _{SO}}\sum\limits_{\left\langle {\left\langle {i,j} \right\rangle } \right\rangle \alpha \beta } {{\nu _{ij}}c_{i\alpha }^\dagger \sigma _{\alpha \beta }^z{c_{j\beta }}} $$ The first term is just the nearest hopping term for graphene, while the second term represents the spin-orbit interaction, which seems quite peculiar to me.   1. Must it be in the z direction? Why?   2. Why does the spin-orbit term only have the second nearest hopping term, but no nearest hopping term? How does it relate to the symmetry of honeycomb lattice?   3. Is there an intuitive way to understand this term? **Can somebody tell me the derivation for the second term?**


title: What is the difference between manifest Lorentz invariance and canonical Lorentz invariance?

text: I often read that the Lorentz symmetry is manifest in the path integral formulation but is not in the canonical quantization - what does this really mean?


title: Space and Time Equality and information transfer between particles existing at different time

text: Since space and time are the same is it that whatever happens at different positions in space should take place at different time? If what I think is correct consider an electric dipole, the charges are at different positions in space then, can there be electrostatic attraction between the charges even if they are individually present in different time? To make it more clear what I’m thinking about consider the following. I have a body with charge Q1 at time t1 and then I neutralized it. At another instant of time t2 I have another body with charge Q2. Can there be electrostatic forces of attraction between the charges Q1 which was present at time t1 and Q2 which is present at time t2(remember that at time t2 there is no charge Q1 as I had neutralized the first body) i.e can there be EM force between charges that don’t exist at the same time like there can be entanglement between particles which do not exist at the same time as given in this article(http://news.sciencemag.org/sciencenow/2013/05/physicists-create- quantum-link-b.html)?


title: Black hole entangled with the cosmological horizon

text: Maldacena and Susskind recently proposed a interesting and very suggestive duality between entanglement and topological identification: http://arxiv.org/abs/1306.0533 But are such ideas applicable to horizons in general? Can I entangle a black hole horizon, with, say, a Rindler horizon as seen by an accelerated observer? Can I entangle a black hole with our cosmological horizon? Are these in principle, physically possible operations? **Note:** this question might be part of a multi-part question


title: What axiomatizations exist for special relativity?

text: Einstein 1905 gives the following axiomatization of special relativity (Perrett and Jeffery's translation):   1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.   2. Any ray of light moves in the "stationary" system of coordinates with the determined velocity $c$, whether the ray be emitted by a stationary or by a moving body. What other axiomatizations are possible? _References_ Einstein, "On the electrodynamics of moving bodies," 1905, Annalen der Physik. 17 (1905) 891; English translation by Perrett and Jeffery available at http://fourmilab.ch/etexts/einstein/specrel/www/


title: How do I prevent shattering of glass?

text: I am not an expert of physics, instead I am more good at chemistry. I just wanted to ask that how do I prevent shattering of glasses on sudden large temperature changes? Sometimes, when I have to cool hot test tubes rapidly, the test tubes break down when I place them in water for cooling. Is there any way to prevent it?


title: number of gravitons launched by a proton

text: The wikipedia article http://en.wikipedia.org/wiki/Gauge_bosons describes how in QM exchanges of gauge bosons carry force, and describes how the graviton may also be a gauge boson. If the observable universe is made of around 10^80 hydrogen atoms*, this implies each atom should be exchanging gauge bosons with 10^80 other atoms. So each atom should launch 10^80 gravitons, and a similar number of photons, gluons etc. Is this really how it works? Does one proton launch 10^80 bosons when it comes into existance? * http://www.universetoday.com/36302/atoms-in-the-universe/


title: About units and plural form

text: The plural form of physical units are always confusing me. I asked some senior students, some of them said we need to use plural form of units but some said units are always singular. For example, 1 meter is 1 meter. But it is 3 times, should it be 3 meters? I know that if we use the abbreviation form, no plural form, i.e. 3m. But if we use 'meter', for the case like 0.04 meter, should it be 0.04 meter or 0.04 meters? I think we should use 0.04 meter because it is less than or equal to 1. The last question I have is about foot and feet, when the magnitude is less than or equal to 1, I should use foot, otherwise, use feet instead, is that right?


title: How does an electron microscope work?

text: I am a physics novice. Google tells me that electron microscopes work much like their optical counterparts -- but the analogy falls apart for me when I think about what I'm "viewing." Obviously, you can _see_ light through the lenses, but what is the "image" analog for electron microscopes? Is it at-all like spraying an invisible shape with bullets and examining where collisions took place? Like if you shot at an invisible car with a tommy gun and were able to make out bullet holes -- so that the more bullets you shoot the better your image? And, just for completeness, I suspect this implies that the best resolution you can get is the bullet-size, or in this case the size of the electron. How do you map "objects" or whatever they are considered on that scale if they are smaller than an electron? Is our perception of how _small_ we can see limited by this cap?


title: What's the relationship between mass and time?

text: This question has arisen from a wish to understand an end-of-universe scenario: heat death. ### Are time and mass intrinsically linked? If so, does time "run slower" (whatever that may mean) in a universe with less mass? And ultimately, in a universe without any mass, just space and energy (photons), then the universal clock stops ticking. I.e. no further aging takes place? So does time slow down gradually as baryonic mass breaks down? If this is the case, would the rate at which time slows down also slow down - because time itself as slowed down - leading to an asymptotic decay of time. I.e. it would take forever for all the particles to decay because each particle takes longer and longer to break down due to time slowing down.


title: $t\bar{t}$ asymmetry

text: Some weeks ago, there was lots of talk about this CDF paper: Evidence for a Mass Dependent Forward-Backward Asymmetry in Top Quark Pair Production where they measured a much higher asymmetry than the one predicted in the SM. In trying to understand the paper, I had some question which I thought would fit in a discussion here. ### Experimental question When all $t\bar{t}$ events are considered, the asymmetry is merely $1.4\, \sigma$ above the SM prediction. Well, no one would be excited with such small mismatch. However, in the paper above, they separate the data in 2 bins of $t\bar{t}$ mass, above and below $450\, GeV$ and claim a $3.6\, \sigma$ difference for the high mass bin. Oh! 3.6 is **way** more exciting (most of the people said). But my question is: where did this $450\, GeV$ come from? In the paper they claim: > We find that the significance of the asymmetry at high mass is maximized > when the bin division is at $M_{t\bar{t}} = 450 GeV/c^2$ Can this be justified statistically? I mean, can you simply ignore the rest of your data and focus on the subset which gives the largest statistical evidence? Notice that I'm not necessarily questioning the CDF paper, which is well written, I'm just asking whether people should have been so excited about the significance of this "evidence". ### Theoretical question I was trying to understand where this asymmetry comes from. There is this paper: Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders which discusses, among many other things, the reason for the asymmetry. They say: > These _[the $t\bar{t}$ asymmetry]_ arise if, in the interference of one-loop > and tree-level diagrams, the top-quark fermionic line and the light-quark > fermionic line are connected by three gluons. Is that so obvious? I really don't understand the reasoning. Would someone care to explain why this is the reason in more details? They even have a Feynman diagram which, they claim, depicts the asymmetry (I thought it would be useful to have it here in case someone wants to refer to it while answering). ![](http://img834.imageshack.us/img834/92/ttbar.png)


title: Electron/Photon Scattering

text: Hey guys, I have a final tomorrow and I am going over some assignments. One of the questions from the assignment was: > A photon having 37 keV scatters from a free electron at rest. What is the > maximum energy that the electron can obtain? Now, I got the right answer (4.67 KeV) but I can't seem to figure it out now. Maybe I am just too tired. Any hints to where I should begin?


title: Is quantum field theory defined by its lattice regularization?

text: One statement I've heard many times is that QFT is "defined" by the lattice, or that the "only" definition of QFT is on the lattice (when such definition exists, e.g in pure Yang-Mills theory). I've heard that from many people I respect, but I have my doubts. Specifically - the lattice is an algorithmic definition of those quantities that can be calculated in Euclidean spacetime. As I said in my answer to this question, this is a proper subset of all physical quantities you may be interested in calculating in general, and many physical situations do not have Euclidean formulation. Is there some response to this objection I am missing, or am I being naive somehow?


title: superconductor levitating in earth's magnetic field?

text: > **Possible Duplicate:**   >  Can superconducting magnets fly (or repel the earth's core)? I've seen superconductors levitating on magnets. But is it possible for superconductors to levitate on Earth from Earth's magnetic field?


title: Relativity and the Higgs field

text: We know very well that as the velocity of an object increases, its relativistic mass also increases because of an increase in its energy which is directly equivalent to mass. We also know that the higgs field is responsible for giving mass to particles and in turn the objects make up the particles. According to our current assumption, some particles face more resistance in the higgs field and therefore end up getting more mass while some feel less resistance and end up getting a lesser mass. Now coming to the question. Can we say that when an object is accelerated to a high velocity its particles experience more resistance from the higgs field (we can think of this in terms of friction or something) and therefore the object acquires more mass?


title: Is there a stable numerical algorithm for FWHM that isn't 2.35*sigma?

text: This is a question that should have a simple answer, but which I can find no proper discussion of in the literature or on the internet. I start from the assumption that I have a noisy numerical signal with a peak in it - for example amplitude as a function of $x$, i.e. $A(x)$ - and I wish to determine its full-width at half maximum (FWHM). I am aware of two basic algorithms that may be used on numerical data:   1. Assume it's Gaussian, determine the r.m.s. value, and multiply by 2.35 ( $2\sqrt{2 \log{2}} $).   2. Determine the FWHM using a peak-finding algorithm that locates the peak $A_{max} = A(x_{peak}$), then locates the _first_ positions either side where $A(x)$ falls to $1/2 A_{max}$. Method 1 is numerically robust as you don't have to bin (i.e. smooth) the data that determines $A(x)$. However, if the peak is significantly non-Gaussian in shape you get a systematically wrong answer. Method 2 is direct, but there are plenty of numerical cases where there are multiple points in $x$ either side of the peak where $A(x)$ crosses $1/2 A_{max}$. And of course the number of crossing points depends sensitively on whether I smooth A(x) or not. My question is therefore whether there is a mathematically justifiable algorithm for determining FWHM numerically that doesn't assume the peak is Gaussian,


title: Plotting a wave function that represents a particle

text: The problem is this: > A particle is represented by the wave function $\psi = > e^{-(x-x_{0})^2/2\alpha}\sin kx$. Plot the wave function $\psi$ and the > probability distribution $|\psi(x)|^2$. This the problem 2.1 in the book _Fundamental University Physics Volume III_ by Marcelo Alonso and Edward Finn. The thing is I don't know what values $k, \alpha$ and $x_{0}$ should have. Probably I don't know what $\psi$ really represents in this case.


title: Basic mechanics problems, unsolvable by brute-force numerical integration

text: I'm looking for simple problems in theoretical mechanics that are impossible or unreasonably difficult to solve by means of "brute-force" numerical integration of Newton or Euler-lagrange equations. I'm interested in these beacuse I noticed that kind of "computer-nihilism" point of view is getting popular (at least among some students): A person says, that " _in the end we anyway doing real stuff by computer simulation_. _And for the numerical values of parameters we are usually able to numerically obtain the result with a given precision. So we just need to know how to write down the equations_ ".   And, therefore, " _there is no need to learn all that complicated stuff in theoretical mechanics_ ". Apart from obvious counter-arguments for this, I'd like to show that there are basic problems you are unable to solve without "the complicated stuff".   Let me give an example of such a problem:   **Given:**   1. A center, that creates some strange field with the potential $U(r)=-\frac{\alpha}{r^3}$. (Mysterious planet)   2. A body with mass $m$ scattering off this center. (Our space ship.)   3. A radius R, at which we want to stay as long as possible. **Find:** the impact parameter $\rho$ and the energy $E_0$ for our body, so it will stay in the "ring" $R<r<2R$ for as long as possible. The problem is easily formulated. And it is easy to solve even for "newbies" in theoretical mechanics. The specific feature of the problem -- there is no reasonable way of solving it by doing straightforward computer simulation. Can you propose other examples of problems with these properties?


title: Cooling via the quantum vacuum?

text: Suppose you had an isolated cloud of gas at a low temperature in a vacuum with no external sources of radiation (e.g. no CMB). The gas would clearly cool via the emission of low-energy photons. But where do these photons come from? The thermal energy of the gas is simply manifest as elastic collisions between atoms where no energy should be lost. Do we have to appeal to the vacuum state of the electromagnetic field? But aren’t these virtual photons which could not be transformed into thermal radiation?


title: What does second quantization mean in the context of string theory?

text: String field theory (in which string theory undergoes "second quantization") seems to reside in the backwaters of discussions of string theory. What does second quantization mean in the context of a theory that doesn't have Feynman diagrams with point-like vertices? What would a creation or annihilation operator do in the context of string field theory? Does string field theory provide a context in which (a) certain quantities are more easily calculated or (b) certain concepts become less opaque?


title: black body radiation graph

text: I got really confused about the graph of the relationship between wavelength and intensity of black body radiation. What does the peak stand for? And what does the graph tell us?How can we analyze it?


title: Which temperature to evaluate fluid properties in pipe?

text: I am always confused about which temperature to evaluate fluid properties at. Let's say I have a helical pipe and I know the inlet temperature, outlet temperature, and surface temperature and the inlet Reynold's number. I must determine the length of the pipe needed to satisfy the outlet temperature which means I must know the mass flow rate. I can do this by determining the inlet density and viscosity. When I use the inlet temperature for these properties, the length is 1.046 m When I use the average between the inlet and the surface, the length is 0.3994 m. When I use the average between the inlet and the outlet, the length is 0.5768 m. As you can see, the temperature I use drastically changes the pipe length. Also, I am always confused as to what temperature to evaluate the properties at for the Nusselt number as well.


title: Am I understanding power correctly?

text: 4 men weighing 380kg, carrying a 380kg piano up 5 meters will generate 31 watt if the load takes 20 minutes. Now this is very hard to do and saps the strength out of any human being. However, that barely powers a light bulb...Would I need more than all my strength to power a light bulb?? Thank you.


title: How can one calculate the phase difference between two quantum harmonic oscillator (Hermite-Gauss) states?

text: The analytic solutions of a quantum harmonic oscillator are given by Hermite- Gauss states, which differ in the order $n$ of the Hermite polynomials. If two such states are plotted, there will be a relative phase shift. How can that be calculated analytically?


title: Can we always apply a pure torque at arbitrary positions on an object in practice?

text: I want to apply a **pure** torque to an object, say a square box on the ground. And I also require that the torque is generated on the corner of the square, not the center of mass. Is there any way for me to do that? I know there is torque motors. But imagine this, if I attach the torque motor the a corner of the square box and turn the motor on, it's not hard to predict that the box will rotate around where I connect the motor but not the center of mass. This means that what the motor applied is not pure torque. (If it's a pure torque, the box will rotate around the center of mass) Any help and suggestions are greatly appreciated! Thank you for your attention.


title: Why and how does symmetry work in circuits?

text: Why symmetry work in circuits? In my book there is no mention explanation as such for symmetry arguments and circuits. But there are circuits that are very difficult to solve without symmetry. Also I have heard that they save a lot of time. Can anyone please tell me why symmetry works in circuits? And what are some basic arguments that we make using symmetry while analyzing circuits? If anyone can point me to any link for the same, it would be very helpful.


title: 3D: Get linear velocity from position and angular velocity

text: I want to find out the linear velocity of a point in 3D space, (Euclidean), given:   * Its position    * Its angular velocity   * The point it's rotating around (fulcrum) (This is a problem I need to solve for 3D graphics programming with a physics engine). The position of the point and position of the pivot point will be 3-value vectors, $x$, $y$ and $z$. The angular velocity will also be a 3-value vector, representing Euler angles. What operation(s) would I need to perform to calculate the linear velocity of the point? The 3d/physics engine has various high level mathematical operations including matrix, vector and quaternion operations, so hopefully what I need is among those.


title: Hamiltonian Nuclear collective model

text: Let $\mathscr{I}_3$ and $\mathscr{I}$ are the moments of inertia for rotations about symmetry axis 3 and about an axis perpendicular to it , and I is the angular momentum operator with components $I_1, I_2$ and $I_3$ along the body fixed axis(1,2,3), ,then , > **How the Hamiltonian can be written with angular momentum as**? $$H= > \sum_{i=1}^{3} \frac{\hbar ^2}{2\mathscr{I}_i}I_i^2= \sum_{i=1}^{3} > \frac{\hbar^2}{2J}(I^2 - I_3 ^2)+ \frac{\hbar}{2\mathscr{I}_3}I_3^2 $$ For the symmetric top $\mathscr{I}_1= \mathscr{I}_2 =\mathscr{I}$ * * * **Source:** Nuclear physics theory and experiment by RR Roy and BP NIGAM In system 1 the body-fixed reference frame is attached to the rotating body. The 3-axis is used as the axis of symmetry. If $\mathscr I_3$ and $\mathscr I$ are the moments of inertia for rotations about about symmetry-axis 3 and about an axis perpendicular to it, and $\mathbf I$ is the total angular momentum operator with components $I_1$, $I_2$ and $I_3$ along the body-fixed axes, the Hamiltonian is given by $$H=\sum_{i=1}^3\frac{\hbar^2}{2\mathscr I_i}I_i^2 =\frac{\hbar^2}{2\mathscr I}(\mathbf I^2 - I_3 ^2)+\frac{\hbar}{2\mathscr{I}_3}I_3^2$$ where for the symmetric top $\mathscr I_1=\mathscr I_2=\mathscr I$. ![Figure](http://i.stack.imgur.com/pUh2z.png) * * * ## Consider Let we denote the Euler angle of the spheroid by $(\theta,\phi, \psi)$. Let's define some angular momentum operator, $$I^2 D^I_{MK}=I(I+1)D^I_{MK},$$ $$I_z D^I_{MK}=MD^I_{MK},$$ $$I_3 D^I_{MK}=KD^I_{MK}.$$ Considering these relations, > **How can we write wave-function as $$\Psi^I_{MK}=|IMK\rangle= > \left[\frac{2I+1}{8 \pi^2}\right]^{1/2}D^I_{MK} (\theta, \phi, > \psi)?\tag{1}$$ Here $(\theta, \phi, \psi)$ are the Euler angles.** Now the spheroid symmetry, rotations angle are $$\theta \rightarrow \pi+ \theta , $$$$\phi \rightarrow \pi- \phi,$$$$ \psi \rightarrow \psi.$$ Then how we can rewrite the equation (1)as, $$\Psi^I_{MK}=|IMK\rangle= \left[\frac{2I+1}{8 \pi^2}\right]^{1/2} \frac{1}{\sqrt{2}}(1+R_I)D^I_{MK} (\theta, \phi, \psi)?\tag{2}$$ $$= \left[\frac{2I+1}{16 \pi^2}\right]^{1/2} \left[D^I_{MK} +(-1)^{I+K}D^I_{M,-K}\right]$$ Since, $$R_ID^I_{MK}(\theta, \phi, \psi)=e^{i\pi (I+K)}D^I_{M,-K}(\theta, \phi, \psi)$$ $$R_1^2 =1, R_1\Psi^I_{MK} = \Psi^I_{MK} $$ The question is related to the rotational Hamiltonian


title: Is my electric power cord creating magnetic field when coiled?

text: Simple question. But I was wondering, does my mac power cord create a magnetic field when its all coiled?


title: Intensive radiative heat transfer in very hot gas ( >5000K, gas core nuclear reactor related )

text: **The question:** At temperatures **above ~5000K are not stable any solid or liquid** materials or even more complex molecules (such as fullerenes and Polycyclic aromatic hydrocarbons) **which emit/absorb wide-spectral black-body radiation effectively**. Simple molecules and atoms which survive such temperatures have very narrow absorption/emission lines and small absorption/emission cross-section. => **They are transparent for thermal radiation.** **Is there anything which would emit/absorb broadband thermal radiation at temperatures >10,000 K ?** **What about plasma?** I guess plasma must be both highly ionized (~hot) and at the same time dense in order to have high opacity and absorption for thermal light (Am I right?). This is a bit contradictory. Density is inversely proportional to temperature if we are limited by pressure let's say 100MPa, while ionization is increasing with temperature. Is it possible to increase opacity/absorption of gas/plasma at ~10,000-100,000 K by **seeding with alkali metal** which release electron very easily ? **background:** Gas core nuclear reactor, and derived gas core nuclear rocket is a fission nuclear reactor theoretically able to achieve temperatures above 5000K (some proposals talk about 40,000-100,000 Kelvin ) which is important for high energy efficiency of electricity production (using MHD generators ) and high specific impulse of nuclear rocket. There is a concept of space propulsion called nuclear lightbulb rocket which should achieve high specific impulse exhausting moleculer/atomic hydrogen propellant at velocity up to 20-40 km/s which means temperature ~25,000-90,000 Kelvin. For effective function of such engine it is necessary that all the heat from gaseous nuclear core is transferred to propellant by thermal radiation. However, hydrogen propellant itself is almost transparent for thermal radiation. This would cause that the heat is transfered to the walls of rocket nozzle instead, which would melt the walls and destroy the reactor. In order to make propellant opaque it was proposed that tiny dust particles of tungsten or hafnium-tantalum carbide particles would be dispersed in propellant gas. These particles would however evaporate above ~5000K making propellant gas transparent again.


title: Hydrogen cloud at the universe's beginning?

text: What prevented all of the hydrogen at the universe's start from coalescing into one gigantic star?


title: What forces are involved in this situation?

text: > _A old massless rope of 12 meters attached to a ceiling can sustain a > maximum tension force of 1200N before breaking. An 85 kg person climbs up > the rope. What is the minimum possible time in which he can climb to the top > without breaking the rope?_ My issue is figuring out the forces involved as the person climbs up the rope.   would there be an applied force downward, because the person must push down to climb up the rope? Or is that not counted because the person always weighs the same? So would it be:   Fgravity \+ FApplied = Fmax tension?


title: My math says this is wrong, but what part of energy conservation am I violating?

text: ![enter image description here](http://i.stack.imgur.com/JMjzp.png) Basically energy of conservation says it doesn't matter what path I take, energy will be the same from before as it is after. So I took the block at the top's energy equal to the energy when it lands on the ground (when it stays still) $$E_i = mgh - \mu mg(1.3)$$ and $$E_f = 0$$, Energy is 0 because it s on ground level and not moving $mgh - \mu mg(1.3) = 0$ But I get something absurd like $h = 0.39m$ Which makes no sense at all Now if I had set it equal to the point where it doesn't fly off I get $mgh - \mu mg(1.3) = mg(1.9)$ Then I get h = 2.29m. Which is A LOT better. So what part of energy of conservation did I violate in the beginning? This isn't homework, this is just self-study


title: Trouble justifying calculation of force on a sphere due to radiation pressure

text: I know very little about electromagnetic waves and light in general so you are going to have to bear with me. I am attempting to calculate the force on a sphere in a plane wave of light where the light has intensity I. My calculations and research have concluded that, regardless of whether or not the sphere absorbs or reflects the light, that the force can be modeled as: $\frac{\pi{r}^2{I}}{c}$. This pdf document outlines what I am looking for (with $I$ replaced with $\langle{S}\rangle$) but in equation 24 it seems like a factor of $2\pi\text{r}$ appears out of nowhere. Another solution I have tried is a double integral in spherical coordinates and exploiting symmetry to find that $\text{Force} = \iint\limits_A \\! p \,\,{dA} $ where p is a function describing the pressure on an area element. Every time I calculate this pressure I find a function of one angle rather than of two angles. I find that my integral looks like: $$\int_{0}^{\pi}\\!\int_{0}^{\frac{\pi}{2}}\\!\frac{4\pi{r}^2{I}}{{c}}cos(\theta)^3sin(\theta) \, d\theta d\phi$$ which evaluates to the correct expression for force (up to the sign) but I have trouble justifying that the pressure does not depend on $\phi$ and only depends on $\theta$. In this instance, I am integrating over half of a hemisphere where $\theta$ is the polar angle and $\phi$ is the azimuthal angle or as described in this image. I feel like these calculations are incorrect and that the double integral over ${dA}$ should include an element reflecting the influence of $\phi$ as I cannot see any reason why the calculation would be independant of it.


title: Can I call additional conditions on potentials a Gauge choice?

text: Let's say I have an electromagnetics problem in a spatially varying medium. After I impose Maxwell's equations, the Lorenz gauge choice, boundary conditions, and the Sommerfeld radiation condition, I still have more unknowns than equations and the solution for (say) the magnetic vector potential is not uniquely determined by the above. This does actually happen when you formulate the equations in plane-stratified media in the plane-wave / Fourier domain. The way to proceed that I have seen is to choose that one of the cartesian components of the vector potential is zero, i.e. impose one of the following as an additional condition to ensure uniqueness of the potentials: $A_x=0$, $A_y=0$ or $A_z=0$. We could of course make up an infinite number of other conditions that leave the fields invariant. **My question is, can I call the above arbitrary choice about the vector potential a "gauge choice"?** The reason for imposing it seems to be identical to the reasons we normally impose the Lorenz or Coulomb gauge, namely that the field equations don't dictate anything about certain potential quantities, the choice makes solving the equations uniquely possible, and the physical $\mathbf{E},\mathbf{H}$ fields are invariant to the extra condition on the potentials.


title: If electromagnetic waves have magnetic fields, why beam of flashlight is not disrupted by a Magnet?

text: Wikipedia article about Electromagnetic Radiation says "As an electromagnetic wave, it has both electric and magnetic field components". And this discussion also confirms Light is EM wave. Since we know that light travels through electromagnetic waves. Does that mean when we hold a Magnet close to the beam of a flashlight, it should interact with the waves and cause funny things to happen ?


title: Does the spectrum of Sol's emission change as it ages?

text: A follow-up to my earlier question How would one navigate interstellar space? that just occurred to me; albeit on a different tack. Sol is probably in a state of continuous flux. The change of state is probably over large timescales as compared to the life-span of the average human. If one were to compare a spectrograph of Sol over a span of, say, 10 million years, would the graph be significantly & predictably different?


title: A question from Weinberg QFT text

text: In page 71 Weinberg's QFT, $$A\Psi^{\theta }_{a,b} ~=~(a\cos{(\theta )}-b\sin{(\theta )})\Psi^{\theta }_{a,b}.$$ He says that massless particles represented by $\Psi ^{\theta }_{a,b}$ are not observed to have the continuous degree of freedom $\theta$. I do not understand why. These $\Psi ^{\theta }_{a,b}$ are eigenstates of $A$ with eigenvalue $a$ where $$ U\left [ W\left ( \alpha ,\beta ,\theta \right ) \right ]~=~ 1+i\alpha A+i\beta B+i\theta J{3}. $$ $W$ is an element of the little group with a faithful representation $D(W)$.


title: Validity of the Multi-Species Navier-Stokes Equations for real gases

text: I'm wondering what are the validity limits of Multi-Species Navier-Stokes equations. I'm aware of the limit for rarefied gases. But is there any new limit that arises in the context of real gases? I hope that an answer could be found by making use of the kinetic theory.


title: Type/Valence of the stress tensor

text: In classical continuum mechanics, the stress tensor is said to be of type/valence (1,1) and I do not see why. If I am correct, its maps a vector $n$ defined in $\mathbb{R}^3$ (which is the normal to a given infinitesimal surface) to another vector $t$ (which is a force) also defined in $\mathbb{R}^3$. We can then consider a second direction $m$ defined in $\mathbb{R}^3$ so that the usual scalar product $m^\top\cdot t$ provides a real number (which is physically the projection of the force $t$ on direction $m$, _ie_ a linear combination of the stress components). Coming back to the definition of a tensor $T$ of valence (1,1), it takes two vectors $v\in V$ and $w\in V^*$ ($V^*$ being the dual of $V$) such that $T(w,v)\in\mathbb{R}$. Where I am confused in the above example comes from the fact that I do not really see $m$ as the dual of $n$ but it is probably the case through the usual scalar product I guess. Am I correct?


title: Are there dedicated instruments to measurethe viscosity of shear thinning liquids?

text: Googling around for ways to measure the viscosities of shear thinning liquids, it seems to me that most of the time viscometers are used at different settings to measure different apparent viscosities. Is this the only strategy out there, did I miss something?


title: Do composite particles that are electrically neutral but have charged constituents radiate?

text: For example an electron radiates when accelerated. So does a positron. But is the radiation emitted by accelerated positronium the sum of the radiation emitted by each separately? If not, why not? If so, does this provide a way of testing whether a given neutral particle is composite? For example, does a neutron bremsstrahlung when decelerated?


title: What evidence is there for the electroweak higgs mechanism?

text: The wikipedia article on the Higgs mechanism states that there is overwhelming evidence for the electroweak higgs mechanism, but doesn't then back this up. What evidence is there?


title: polynomial fit and uncertainty

text: I am trying to fit a polynomial function by least square method and I want to know the uncertainty on my fitting parameters. In which book can I find a clear answer?


title: Spin 1/2 particles hamiltonian, addition of angular momentum confusion

text: Suppose I want to compute $S^{1}_z -S^{2}_z$ on a singlet state $|0,0>$. (where $S^{i}_z$ are two particles' spin operators). $$|0,0> = \frac{1}{\sqrt{2}} (|\frac{1}{2},-\frac{1}{2}> \- |-\frac{1}{2},\frac{1}{2}>).$$ I don't get the correct answer by just computing and using $$S^{1}_z|m_{s1}, m_{s2}> = m_{s1}|m_{s1}, m_{s2}>.$$ I know how to get the answer by matrix representation but how can I use this operators?


title: Finding the direction of the magnetic force acting on a conducting wire

text: I have a problem in finding the direction of the force when a conducting wire is placed in a magnetic field. If I use Fleming's Right Hand rule I get a circular magnetic field, so what will be the direction of force acting on the wire. I have asked this question on other forums too, but still have no positive responses. Let me give an example: In the following question, ![enter image description here](http://i.stack.imgur.com/ZiAo4.gif) we can see a U magnet and a conducting wire. Now what is the direction of the force acting on the wire? I am confused between using the left and right hand rules.


title: Difference between "Lorentz transformation" and "proper orthochronous"

text: I'm doing an assignment and I've been given a list of $4 \times 4$ matrices and asked: > _Which of the following areLorentz transformation matrices? Which are proper > and orthochronous?_ But, as far as I can tell from my notes and internet trawling, the two are synonymous. As in, a matrix $L$ is a proper orthochronous Lorentz transformation if it satisfies:   1. $L^{t}gL=g$, where $g={\rm diag}(-1,1,1,1)$   2. $L_{0}^{0}>0$   3. $det(L)=1$ Am I missing something?


title: Followup to: The relation between energy quanta of an Einstein solid and the equipartition value of heat capacity

text: As a followup question to this question: The relation between energy quanta of an Einstein solid and the equipartition value of heat capacity and this answer http://physics.stackexchange.com/a/133053/55779: Apparently energy quanta and the equipartition values are related somehow. I'd like to approach the problem without the formula, since the problem the question is asked in is before the problem where that formula is derived. How can I know that value of $x\approx3$ without the formula ? I can't even tell that I should be looking for the half maximum. Or can I?


title: Angular momentum of a sphere moving vertically downwards

text: If a solid sphere is moving vertically down with a velocity $v$ and spinning with an angular velocity $\omega$, what is the angular momentum of the sphere about an axis through the sphere which is at a distance $ \frac{R}{2}$ vertically below the center of mass of the sphere ?


title: Fundamental Constants in a theory of everything (TOE)

text: Do physicists ever expect to be able to derive the fundamental constants of nature from theory? For example, if string theory or some other theory unites the four forces, would the theory be considered complete if it relies on these measured constants, or would a true theory of everything (TOE) require that these constants come out of the theory itself?


title: "Delayed choice" quantum imaging experiment - why wouldn't it work?

text: I was just reading a Nature news article (Entangled photons make a picture from a paradox, 27 August 2014) about a way to form an image of an object out of photons that have not interacted with the object, but which are entangled with photons that have. The article has a photograph of the image, which is of a cardboard cutout of a cat. If I understand correctly, the technique is that   1. a photon beam is split, e.g. via a semi-silvered mirror, resulting in two beams, call them A and B;    2. in each beam there is some device that turns each photon into two entangled photons. At this point there are four beams, call them A1, B1, A2 and B2.    3. The photons in beam A1 interact with the cardboard cat   4. The photons in beam A1 are allowed to interact with the photons from beam B1 in some fashion, _and then discarded_   5. The photons in beams B2 and A2 (neither of which has interacted with a photon that's interacted with the object) are combined somehow and used to produce the image. This is pretty neat - the article talks about using to image an object with very low-energy photons, while still being able to make an image on a screen using high-energy ones. However, the following occurred to me while reading about it: presumably, as with all experiments of this kind, it shouldn't in principle make any difference if we change the length of the beams. What would happen if we keep the length of beams A2 and B2 short, but we make beams A1 and B1 really long, say a few light hours? In this thought experiment the cardboard cat, along with the device for combining the photons from beams A1 and B1, is on Pluto, and the rest of the equipment is in a lab on Earth. It seems as if it should work just as well in this case as it does with everything in the same lab. But now we're seeing the image of the cat five hours before the photons interact with it - and by swapping the cat out for a different object, someone on Pluto could send us a message from the future. Presumably this can't really work, since it would be possible to construct a paradox if it did. But where is the issue? Have I misunderstood something about the setup (entirely possible since I'm getting this from the news article rather than the actual paper), or is there some fundamental reason why it would stop working if the A1/B1 beam length was much longer than the A2/B2 one? This seems similar to delayed choice quantum eraser experiments. However (if I remember correctly from looking into them years ago) in those experiments you have to combine all the beams back again to make the image in the end, so there's no way to construct a paradox. In this case the Nature news article seems quite clear that the photons are thrown away after interacting with the cardboard cat, and the image is produced _only_ from those that haven't - this seems to be a major difference.


title: Dirac Delta function

text: Although I find it mathematically dubious, we said that $\Delta \frac{1}{r} = -4\pi \delta(r)$. Now, I was wondering is there a similar relation to the delta function if we look at $\Delta \frac{1}{r^n} =?$.


title: Cycle with unspecified irreversbile transformation. Find $P,V$ in the various states.

text: I've been thinking to this for the last two hours and haven't been able to come with a solution. **Problem.** A mole of gas initially at pressure $P_A = 2 \text { atm}$ and occupying a volume $V_A=20\,\text {L}$, passes through an irreversible transformation in which it absorbs $Q=1200J$ as heat and ends with pressure $P_B=3/2 P_A$. Then it expands reversibly and in adiabatic conditions, until its pressure is again $P_A$ ($P_C=P_A$). Finally, it has an isobaric transformation that brings the volume back to $V_A$. Given that the absolute values $|W_{CA}|=300J$ and $|\Delta U _{CA}|=450J$, determine the thermodynamic coordinates $P,V,T$ in the three states $A,B,C$. I think that the only way to find the coordinates is to work in reverse: finding $V_C$ from $$W_{CA}=p_A(V_A-V_C),$$ and then $V_B$ using the adiabatic's $P|V$ law. Now, the information on the absolute values tells us that $$Q_{\text {tot}}=Q_{AB}+Q_{CA}>0,$$ since $Q_{CA}\geq-750J$ and so $W_{\text{tot}}>0$. Having noted this, I don't see how does it put a constraint on the sign of $W_{CA}$. Since the transformation $A\to B$ is totally unspecified, I think that the volume $V_B$ could be everything without any contradiction, and this affects the sign of the work in last transformation. Have any idea?


title: Naming vectors in free body diagrams

text: Is there a convention for naming the vectors? Suppose there is a box on a table. I'm going to draw the forces acting on the box. So I focus on the box and ignore forces acting on the table, the normal vector on the box is named after the box or the table? My doubt is, subscript $B$ to mean "normal vector acting on the box", or subscript $T$ to mean "normal vector, from table to the box"?


title: Is the viscous sublayer size universal?

text: We know the non-dimensionalized distance of the viscous sub-layer is 5 wall units for a turbulent boundary layer. It is common to see this in Fluid Mechanics books but seems somewhat arbitrary. I want to know if this true for all conditions or does it depend on the Reynolds number (high viscosity, high speed, etc).


A little bit of background information: I'm planning to write a little booklet or web page about CPU/computer architecture, basically for my own education, because we didn't cover it in depth in college. I feel like I should be learning a lot more about the fundamentals about how computers work, if I want to be a better programmer. The idea is to present the workings of a CPU by describing it from the ground up. Starting at simple electrical circuits, then semiconductors, transistors etc. From my school physics class I remember that I was very often left with a lot of gaps about how different concepts are linked together. I want to avoid this. So here's my question: How does an electrical field really work? How come that an electron can exert a force on another electron without physical contact? What is it in an electron that creates the field, where does the energy for doing the work come from?


title: In a spaceship, if a vessel suddently stops will an object inside the vessel keep going?

text: My question is a 2 part question. First if a vessel in space is going very fast and suddently stops (maybe it is not possible but that is not the point) will things/humans inside the vessel keep going forward or stop with the vessel? Is it the same if the cabin is oxygened or not? I know the question is pretty vague but please explain possibilities.


title: Lorentz Invariant Equation of Motion for Scalar Field

text: I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity. Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my notes a quantity of form $v^{\mu}\partial_{\mu}\phi(x)$ will not be Lorentz invariant. But explicitly doing the active transformation the quantity becomes $$\Lambda^{\mu}_{\nu} v^{\nu}(\Lambda^{-1})^{\rho}_{\mu}\partial_{\rho}\phi(y) = v^{\nu}\partial_{\nu}\phi(y)$$ where $y=\Lambda^{-1}x$ and the partial differentiation is w.r.t. $y$. This seems to suggest that the quantity is a Lorentz scalar, so could be used to construct a Lorentz invariant first order equation of motion. I'm clearly making a mistake here. But I don't see what I've done wrong. Am I wrong to think that $v$ transforms nontrivially under the active transformation? Maybe it shouldn't transform at all because it's just a vector, not a vector field? Many thanks in advance for your help!


title: Are a measured object always part of the theory?

text: Is there a notion of measurement, which doesn't correspond to a yes/no question or with the idea of the comparison of two real world objects, which produces a real number? And does at least one of the object which are compared to produce the measurement result have to be modeled within the theory? (One of my motivations for that question is that I wonder if a human can make a measurement involving light without a length measurement and it also seems to me that almost all measurements involve looking at data, which therefore effectively makes them length measurements. And then I speculate if there are even other mearuements than these. For example, I can't test the quantum wave values unless I collapse it - its reality is hidden (this question is certainly not only about QM though.) and therefore the specific configuration is not real is a strict sense. Similarly there is no time mearuesment, is there? The configuration of the clock is just infered by a mearuement of light.)


title: effective theory of graphene

text: This is a question about deriving effective mass theory for graphene. For the two sub-lattice atoms, the wave equation can be written as the massless Dirac equation: $ \displaystyle -i\hbar v_F \begin{pmatrix} 0 & \partial_x -i\partial_y \\\\\partial_x +i\partial_y & 0 \end{pmatrix} \left(\begin{array}{c} \Psi_A \\\ \Psi_B \end{array}\right)=E \left(\begin{array}{c} \Psi_A \\\ \Psi_B \end{array}\right) \ \ \ \ \ (1)$ where ${A,B}$ are two subatoms. The derivation of the equation went back to 1984, which is the paper I am trying to understand. In the article, they argued that at first order of ${\vec{\kappa}\cdot \vec{p}}$ expansion, the momentum matrix can be written in the form, under group-theoretic arguments (equation (3) in the paper): $ \displaystyle \bar{p}\begin{pmatrix} 0 & \hat{x} -i\hat{y} \\\ \hat{x} +i\hat{y} & 0 \end{pmatrix} . \ \ \ \ \ (2)$ What is the argument behind it? Is there anyone read the paper or know the answer?


title: Can the time direction of wave function collapse be reversed?

text: The laws of physics are invariant under CPT transformations reversing time, inverting space and flipping charges. Almost so. The collapse of the wave function is the odd man out. Can the time direction of the collapse of the wave function be reversed so that the collapse happened in the past? The collapse presupposed the Schroedinger picture. Can a collapse occur in the Heisenberg picture, with the projection operator $P$ replaced with $UPU^{1}$?


title: Non-unitarity of wave function collapse

text: Why the wave function collapse corresponds to a non-unitary quantum operation?


title: Why is the sun so dense?

text: Looking at the radius and mass of stars on Wikipedia, I see that the Sun is the densest of all, often many times denser than other stars. Is that because only non-dense starts are easily seen from a distance? Are there any stars of comparable luminosity to the sun that can be seen with the naked eye, and do they have a similar density as the sun? If needed I can copy-paste the mass and radius of other stars here for reference.


title: Probability current

text: Conservation of probability: Suppose a wavefunction has ${\partial \mathbb P \over \partial t} = -t f(x,t)$ and ${\partial j \over \partial x} = i f(x,t)$. How does it follow that ${\partial \mathbb P \over \partial t} = {-\partial j \over \partial x}$? Thanks.


title: Can Somebody give me Questions

text: Can someone give me questions on physics because I have my Examination tomorrow Class 9th (CBSE) topic : - Fluids(Density,buoyant Force , Archemedis Principal) , Work Power Energy(Work Basics, potential Energy, Kinetic Energy, Conservation of energy) , Sound(Sound Basics).Thanks in Advance


title: Why is it easier to glide on sharp ice skates than on dull skates?

text: There have been previous questions (e.g. here and here) on Physics.SE about the mechanism that makes ice skating possible. Reviewing these, as well external references, it seems pretty clear that the popular "pressure melting" explanation is bunk: the pressure on a pair of typical skate blades is just way too little to depress the melting point of water by any meaningful amount. The currently accepted explanation is that H2O ice at terrestrially-realistic temperatures has a persistent liquid water film that has a lubricating effect. Heat dissipated by friction might amplify this effect a bit. So, under this understanding of ice's slipperiness, why do ice skates need to be regularly sharpened? Any hockey player will tell you that attempting to get around the rink on a pair of dull blades is a major chore. This would make sense if the pressure melting explanation were true, but it's not, and so it doesn't to me. The simple model of friction (which clearly must not apply perfectly to this scenario) is that the frictional force is independent of contact area. If that were true in this case, then since the source of slipperiness is just the pre-existing water film on the ice, it ought not to matter whether one's skates were sharp or dull: it's just changing the contact area. I can suggest one possible unsatisfactory explanation: the sharp blades have to push less ice out of their way on the leading edge when they dig into the ice. I say unsatisfactory because "digging in," were it responsible, could be avoided just by spreading one's weight over an even larger area. Would skating on polished steel blocks work just as well as skating on blades? It seems a bit far-fetched. Presumably, the sharpness of the blades must correlate with the coefficient of kinetic friction between the steel and the ice/water film. What mechanism could be responsible for that?


title: Strong force, where is the seperation?

text: In class I got given a diagram like this: (albeit without the Electrostatic force line) ![](http://www.boredofstudies.org/wiki/images/b/bb/Sci_phys_quanta_strong_force.png) However the teacher told us the nucleons are typically separated when the force is zero. So as the string force crosses the x axis. (as does our textbook) However initially this did not make sense to me because electrostatic force will still be repelling (in the case of a proton-proton "bond"/interaction) and so surely the separation distance must be on the positive side to counteract the electrostatic force?


title: Whats wrong with this perpetual machine?

text: Consider a cube of mass M resting on a rough surface such that the coefficient of friction between the cube and the surface is K. So in order to just slide the cube I need to apply a minimum force of KMg, g= acceleration due to gravity. Now IF I apply a force, F which is very small as compared to KMg in magnitude then the body will not slide because the surface will exert an equal amount of friction force on the body. Now consider a sphere of same mass resting on the same surface having the same coefficient of friction. Now when I apply a force very very small in magnitude as compared to KMg, then an equal amount of frictional force will be exerted by the surface on the sphere at the point of contact. This frictional force will cause the sphere to rotate as it exerts a torque about the center of the sphere. Now as the sphere rotates the point of contact slides and hence now frictional force of magnitude KMg acts on it, pushes it forward and slowly sets the sphere on rolling motion. But This certainly constructs a perpetual motion machine and hence violates conservation of energy. May I know where was I wrong, where is the flaw in this so called perpetual motion machine?


title: Any open areas to work in non equilibrium thermodynamics for a Phd student?

text: I see that many papers written on fundamentals of thermodynamics(theory) nowadays are by some old professors somewhere(there may be exceptions). Most active young faculty don't seem to be seriously interested in reinterpreting thermodynamics like nonequlibrium thermodynamics i.e. continuing the work of Ilya Prigogine etc. So is this worth while for a graduate student starting his research career to work in this area? Any open problems a fresh graduate student can aim to solve theoretically?


title: What is the minimal set of expectation values I need in a statistical model?

text: At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ being a function of $v$. So integer powers of the generator of the function algebra $v$ are special functions. I wonder if there are other special functions whos expectation are equally useful and if so, how they depend of the system you consider. For example, let $\langle \dots \rangle_f$ be some prescrition to calculate a mean or expectation and $$\langle A \rangle_f:=\int_\Gamma A(\vec v)\ f(\vec v)\ \text d \vec v,$$ then is there e.g. a statistical significance to $\langle f \rangle_f$? Maybe this question has a "trivial" yes as answer, because there are more options than taylor series to give a basis for some function algebra of elements $f(v_1,v_2,\dots)$. However, I don't know how this changes if one considers noncomutative generators $[v_1,v_2]\ne0$. The question comes in part because I'm intimidated by relations like $$\langle T^n\rangle \equiv \int_0^\infty E^{n-1}\, e^{ - \left( {E /T } \right)^C }{\rm d}E\ = \tfrac{\Gamma \left(\tfrac{n }{ C }\right)}{C} \cdot T^n,$$ i.e. $\langle A(E) \rangle$ expectation values are apprearently trivial to compute for weights which are polynomial in functions $f_{\ T,C}(E)=e^{ - \left( {E /T } \right)^C}$.


title: Relationship between angles

text: > Question: Find the relationship between angles $\theta$ and $\phi$ using the > equations of equilibrium and solve for $\theta$. > > Express your equation for $\theta$ in terms of $\phi$. > > _Hint: To derive the relationship between angles $\theta$ and $\phi$, you > first must write the equations of equilibrium for the pulley. Once you have > the equations of equilibrium, you then can isolate the angles and solve the > two equations_. I know that $T_D\cos\theta=T_C\cos\phi$. I also know that $T_D\sin\theta=T_C+T_C\sin\phi$. I tried solving these equations for $\theta$ in terms of $\phi$, I get keep getting stuck. ![Diagram](http://i.stack.imgur.com/G78kL.jpg)


title: Simulate the magnetic field of magnet

text: I'd like to numerically simulate the magnetic field due to a cylindrical rare earth magnet of known dimensions at a bunch of points $\vec{r}=(x,y,z)$ from its origin. My goal is to be as accurate as possible up to some global normalization which ultimately doesn't matter for my application. My approach is to simply assume the magnet is made of a continuum of dipoles and do the relevant integral: $$ \frac{\mu_0 m}{4\pi}\int\int\int \frac{3\left(\hat{m}\cdot\frac{\vec{r}-\vec{r}'}{||\vec{r}-\vec{r}'||}\right)\frac{\vec{r}-\vec{r}'}{||\vec{r}-\vec{r}'||}-\hat{m}}{||\vec{r}-\vec{r}'||^3}d\vec{r}' $$ where the dipole moment norm $m=||\vec{m}||$ is the aforementioned global normalization. Performing this integral is easy and it works etc., my question is about the physics: am I leaving anything out? Will a commercial solver include any physics that I haven't? In general, what will be my biggest source of error (except that I don't know $m$)? Thanks!


title: Why do wave packets spread out over time?

text: Why do wave functions spread out over time? Where in the math does quantum mechanics state this? As far as I've seen, the waves are not required to spread, and what does this mean if they do?


title: Two masses connected by a string in horizontal frictionless table

text: Suppose that two masses with different mass are connected by a string in horizontal frictionless table. Then when there is equal acceleration for two masses, string force would extend in some direction. My question here, why don't two boxes create canceling effect for string's stretching? (Often, in we just calculate one box's force opposite to the direction of acceleration and equals to kx, which solves the problem. But why?)


title: insulator based gauss law questions

text: My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply. Here's a question I'm working on that isn't part of my book. ![question](http://i.imgur.com/y2cDZdl.png) where the radii are $a,b,c,d$ from smallest to largest and gray regions are insulating spherical shells with charge distributions. > Given $a,b,c,d,q$ Find:-   >  1)$E(r)$ for all the different positions   >  2)Graph $E(r)$   >  3)Find volume charge densities   * I've never done "partial" shaped insulators, my thought process is that since $\Phi = \frac{q_i}{\epsilon_0}$ and $q_i$ is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make: $\rho = \frac{q}{V}$ $\rho \cdot V_i = q_i$ $\int^r_a \rho 4 \pi r^2 dr = q_i$ is this the right process?   * Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure. Thanks for any help.


title: Explaining Lenz's Law without conservation of energy

text: I was often told by my professor, using the following example, to demonstrate the relationship of conservation of energy and Lenz's Law. If you push a conductor into a constant magnetic field. By Lenz's Law, voltage will be induced to oppose the "cause" which then resists the conductor from moving quicker which would be a violation of conservation of energy. In other words, if you push the rod very slightly, and the induced force turns out to push it even further, you generate infinite energy which then contradicts the conservation of energy law. However, I wasn't happy enough by this answer, even though the fact is that you won't get infinite energy. I was thinking, whether it is something to do with the things happening on the atomic scale. Considering a more trivial example, a magnet moving towards a current loop, so why would it produce a opposite pole to resist the change? Is it something to do with the cutting flux of the magenetic field? Why must a field be created to cancel the effect? Why can't nothing happen? Or is it just a matter of fact in nature? I am finding this hard to understand how this really works. Is it a virtual particle? Please explain the above phenomena without relating it to energy conservation law. ![MOVING conductor in a magnetic field](https://encrypted- tbn2.gstatic.com/images?q=tbn%3aANd9GcQDqLDM2ItVWprRaOhuwQLfirdc2Rwgh0r15ONevI9yT0ZiEMQB-g)


title: Dimension & non - locality problem in string theory

text: I have some questions with string theory:   1. Why is it that there is exactly 4 large spacetime dimensions while the rest remain small?   2. It is a nonlocal QFT. How could that fit in GR?


title: Does the Nakajima-Zwanzig equation preserve the trace of the projected density matrix?

text: Looking at the Nakajima-Zwanzig equation, wich gives the time evolution of a projection $\cal {P} \rho$ of a full density matrix $\rho$, I am wondering if the trace of $\cal P \rho$ is preserved under time evolution. The terms like $LX \stackrel{def}= \dfrac{i}{\hbar} [X,H]$ have a null trace, but it seems there is no reason why terms like $\mathcal {P} L X$ necessarily have a null trace, so it seems that the trace of the projected density matrix is not necessarily conserved. Is it correct ?


title: Angular acceleration of stone disk

text: I have a conceputal question regarding the following problem: A round massive stone disk with diameter $0.600 m$ has a mass of $50.0 kg$. The stone rotates at an angular velocity of $115.2 rad/s$, around an axis located at the center of the disk. An axe pressed against the disk applies a tangential frictional force, $F_f$ at $50.0 N$. Assume that we turn off the rotating power of the disk, so that the frictional force is the only force acting on the disk. What is the magnitude of the angular acceleration, $\alpha$, of the disk? OK, so I have calculated the torque ($-15 Nm$), and the moment of inertia ($I = 2.25 kg \cdot m^2$). By using the formula: $$\tau = I \alpha$$ It is easy to show that $\alpha = -6.67 rad/s^2$, which is also the correct answer. However, say I want to try to solve this in another way, without using the torque and moment of inertia. Since the frictional force is the only force acting on the disk, I would assume that we would have: $$F_f = ma_T$$ $$-50 = ma_T$$ $$-50 = 50 \cdot a_T$$ $$a_T = - 1 m/s^2$$ And since we have: $$a_T = r \alpha$$ This gives: $$\alpha = \frac{-1}{0.3} = -3.33 rad/s^2$$ Which is not the same answer. So why doesn't this second approach work? If anyone can explain this to me, I would really appreciate it!


title: Is the Portal feasible in real life?

text: Firstly, I assume prior knowledge/experience with the game Portal. Should it be possible that two openings (circles/unidentified-constructions) would work as interchangeable gates? With one opening analyzing the molecular structure of the object passing through and the other reconstructing it accordingly? Maybe as a replica? The object doesn't need to be alive or biological at all.


title: What equations govern the formation of droplets on a surface?

text: When some smooth surface (like that of a steel or glass plate) is brought in contact with steam (over e.g. boiling milk) then water is usually seen to condense on that surface not uniformly but as droplets. What are the equations which govern the formation and growth of these droplets ? In particular what role does the geometry of the surface plays in it? Also it is possible to prepare experimental conditions where no droplets are formed but water condenses uniformly ?


title: What does QFT "get right" that QM "gets wrong"?

text: Or, why is QFT "better" than QM? There may be many answers. For one example of an answer to a parallel question, GR is better than Newtonian gravity (NG) because it gets the perihelion advance of Mercury right. You could also say that GR predicts a better black hole than NG, but that's a harder sale. For QFT versus QM, I've heard of the Lamb shift, but what else makes QFT superior?


title: Retarded (Advanced) GreenFunction

text: I need to show that Green Function: $\displaystyle G(\vec{r},t;\vec{r}^{\prime},t^{\prime}) = \frac{\delta(t-t^{\prime}\pm |\vec{r}-\vec{r}^{\prime}|\,/c)}{|\vec{r}-\vec{r}^{\prime}|}$ Obeys $\displaystyle \nabla^2 G -\frac{1}{c^2}\frac{\partial^2 G}{\partial t^2} = -4\pi \delta(\vec{r}-\vec{r}^{\prime})\delta(t-t^{\prime})$ I tried to use the identity for Laplacian : $\displaystyle \nabla^2 (\psi\phi) = \phi\nabla^2\psi + \psi\nabla^2\phi + 2\vec{\nabla}\phi\cdot\vec{\nabla}\psi $ As follows: ![My work](http://i.stack.imgur.com/9DJKa.jpg) But I couldn't get nice results. Any suggestions?


title: Can someone explain the solution (provided) of this conical pendulum work problem

text: In the image, it looks like the tangential direction is always 45 degrees away from the string, not 90 degrees. Is it not the circular path that the solution is talking about? ![enter image description here](http://i.stack.imgur.com/dyjFb.png)


title: Does the Fermi sea have plane waves, or wave packets?

text: Consider a zero-temperature, one-dimensional crystal with allowed electron momenta $k_n = \frac{2\pi n}{L}$. **Question:** Which is the more correct way to think about the Fermi sea?   1. Sharp plane waves -- $$ \prod_{\epsilon_k<\epsilon_f} c_{k\uparrow}^\dagger c_{k\downarrow}^\dagger \lvert 0\rangle$$ or   2. Wave packets that are very narrow in momentum space -- $$ \prod_{\epsilon_{k_1}<\epsilon_f, \epsilon_{k_2}<\epsilon_f} \alpha_{k_1\uparrow}^\dagger(x_{k_1}) \alpha_{k_2\downarrow}^\dagger(x_{k_2}) \lvert 0\rangle,$$ where $$\alpha_{k\uparrow}^\dagger(x_k) = \sum_q \exp\biggl[-\frac{1}{2}\biggl(\frac{q-k}{\delta}\biggr)^2 + i q x_k\biggr]\ c_{q\uparrow}^\dagger,$$ with a small width $\delta$ and randomly distributed positions $x_{k_1},x_{k_2}$. Also, if (2) is more correct, what determines the width $\delta$? **Discussion:** I expected sharp plane waves. But wave packets seem necessary to make sense of the semiclassical equation of motion: $$\frac{d}{dt}k = -e E\tag{3}$$ which, as I understand it, applies to the center $k$ of a given wave packet. For a definite example where wave packets seem necessary, consider Bloch oscillations. One solves for the positions $x_k$ as a function of time using (3).


title: Total internal reflection problem -- could the textbook be wrong?

text: This regards the following problem: A ray of light is traveling in glass and strikes a glass/liquid interface. The angle of incidence is $58.0^\circ$ and the index of refraction of the glass is $n = 1.50$. What is the largest index of refraction that the liquid can have, such that none of the light is transmitted into the liquid and all of it is reflected back into the glass? My solution: We have $n_1 \sin \theta_1 = n_2 \sin \theta_2$. We wish to maximize $n_2$ provided $90^\circ \leq \theta \leq 180^\circ$. Plugging in our givens, we have $(1.50)(\sin 58^\circ) = n_2 \sin \theta_2 \rightarrow n_2 = \frac{(1.50)(\sin 58^\circ)}{\sin \theta_2}$. Since we wsh to maximize $n_2$, we should minimize $\sin \theta_2$, which can be any value in $(0, 1]$ so there is no theoretical limit on the size of $n_2$ (according to this math) However, the textbook says the correct maximum is $1.27$, which is taking $\theta_2 = 90^\circ$. I don't think this is right at all, since if anything that is the _minimum_. Consider $1 < n_2 < 1.27$. Then $1.27 > \sin \theta_2 > 1$, which is impossible given the range of the sine function over the reals. Who is right?


title: Rate of probability loss from absorbing boundary

text: The following is the solution to the 1D diffusion equation with diffusion coefficient D, initial particle position $x_0$, and a perfectly absorbing boundary at $x=0$ (s.t. $P(x=0)=0$). $$ P(x;t)=\frac{1}{\sqrt{4 \pi D t}}e^{-\frac{(x-x_0)^2}{4 D t}} - \frac{1}{\sqrt{4 \pi D t}}e^{-\frac{(x+x_0)^2}{4 D t}} $$ If I understand correctly, for an $x_0>0$. $$ P(\text{no collision at time $t$})=\int_0^\infty P(x;t) dx $$ In other words, the total probability in allowed space at time $t$ is exactly the probability that the particle _never_ contacted the absorbing boundary at $x=0$ up to time $t$. What I want to compute is the rate of probability loss $k(t)$. From above, it seems that would be: $$ k(t) = \frac{d}{dt} \int_0^\infty P(x;t) dx $$ evaluating with mathematica reveals: $$ k(t)=-\frac{D x_0}{2 \sqrt{\pi}} \left(\frac{1}{D t}\right)^{3/2} e^{-\frac{x_0^2}{4 D t}} $$ which seems reasonable. It seems that there should be a way to compute $k(t)$ _without_ computing the spatial integration across $x$, perhaps some computation involving only the boundary. I thought since all the loss occurs at $x=0$, the time derivative of $P(x;t)$ evaluated at $x=0$ should be k(t). However, the result of that calculation is 0. _Question: is there a way to compute k(t) without computing the spatial integral over the $x$ domain?_


title: How to calculate the ground-state energy for the Ising model?

text: I'm learning about the 2D ferromagnetic Ising model in zero field and trying to verify what I know by calculating the ground-state energy for the state with all 'up' spins in a 3x3 lattice. $$H = -J\sum_{<i,j>}s_{i}s_{j}$$ where the sum is over nearest neighbors. My question is, how do you include the energy values for each spin? Do you just calculate the hamiltonian for each site and then add the sites together? In that case, I get, assuming fixed boundaries, -4J for the central spin, -2J for each of the four spins on the corners (two nearest neighbors), and -3J for each of the four spins in the middle of the edge rows and columns (three nearest neighbors). Adding it all together, I get H = -24J for the entire lattice. In Chandler's stat mech book, he says that the lowest energy of the Ising model on a square lattice is given by -2NJ, where N is the number of spins. He doesn't specify what the boundary conditions are, but I assume he means fixed boundaries. Here, that means the lowest energy should be -18J. What am I doing wrong?


title: Can atoms have nonzero dipole moments?

text: Let's make the question easier by considering two-level atoms(with spin states, i.e. spin up $|\uparrow\rangle$ and spin down $|\downarrow\rangle$). An article I recently read claims that atoms do not have dipole moments when they are in energy eigenstates (i.e. when you put it into a magnetic field in z direction). I was thinking if it's an eigenstate, since the spin cannot be pointing in z direction (remember it's actually pointing in a cone area), how could it not have a dipole moment?


title: Does a particle lose its (location) wavefunction if its location is measured exactly?

text: As the title says, does a particle lose its location wavefunction if its location is measured exactly (I know this would be impossible in reality)? Also, in reality, if one measures a particle, does the wavefunction of a particle become something different from original afterwards?


title: How does one make a particle with particular wavefunction?

text: I was always curious how scientists achieve a particle with particular wavefunction (of location and spins etc.) So how do they achieve it? Or is this impossible?


title: Counterpart of the  Klein Gordon Equation on the "Coordinate Shell"

text: The relation $$\psi=Ce^{i/\hbar(Et-\mathbf{p}\cdot\mathbf{x})}\tag{1}$$ satisfies the Klein Gordon equation on the mass shell, i.e. for $E^2=p^2+m^2$. Now let's think in the reverse direction. Relation (1) should satisfy the PDE: $$\frac{\partial^2 \psi}{\partial E^2}-\frac{\partial^2 \psi}{\partial p_x^2}-\frac{\partial^2 \psi}{\partial p_y^2}-\frac{\partial^2 \psi}{\partial p_z^2}=0\tag{2}$$ on the "coordinate shell": $$ t^2-x^2-y^2-z^2=0 $$ Could relation (2) be related to a gravitational wave? [You may assume that observation is being made from a Local Inertial Frame(your lab). Alternatively you may think of upgraded forms of the given equations in the curved spacetime context] Allied issue: Going "off the mass shell" has produced interesting results in particle physics?What about the prospects of going "off the coordinate shell"?


title: Is there a deep reason why springs combine like capacitors?

text: I was solving a practice Physics GRE and there was a question about springs connected in series and parallel. I was too lazy to derive the way the spring constants add in each case. But I knew how capacitances and resistances add when they are connected in series/parallel. So I reasoned that spring constants should behave as capcitances because both springs and capacitors store energy. This line reasoning did give me the correct answer for how spring constants add, but I was just curious if this analogy makes sense, and if it does, how far one can take it. That is, knowing just that two things store energy, what all can you say will be similar for the two things.


title: Why is causality preserved in special relativity?

text: **PART 1** :   I was reading the article Relativity of simultaneity Wikipedia. I couldn't understand this line: > "if the two events are causally connected ("event A causes event B"), the > causal order is preserved (i.e., "event A precedes event B") in all frames > of reference." Is this an assumption or a consequence of STR? Please explain. * * * Note: My question consists of 2 parts this is the 2nd part.   Below is a genral version of my previous question question:Breaking the simultaneity. **PART 2:**   Let there be three events $A$,$B$ and $C$ s.t: $C$ is the result of Simultaneous occurrence of $A$ and $B$. In other words $C$ occurs _iff_ $A$ and $B$ are simultaneous.   Now as we know in STR any two events separated in space are not simultaneous in different frames. So In some frames $C$ will occur and in some $C$ will not occur which will cause paradox.   I tried many thought experiments to make such a paradox but i failed. In all the experiments that i thought i could not break the causality even by breaking the simultaneity because everytime the fact: "all signals move slower than light" preserved the causality. So why causlity remains preserved always? Is it due to the fact that nothing can move faster than light?


title: Can I move the atom nucleus only?

text: I was wondering if it is possible to move the atom nucleus and leave behind the electrons? I can imagine that the electrons will follow the nucleus. But what if the speed of the nucleus is almost the same as the speed of the electrons or faster. where will the electrons go? If it is not possible, do we have a theory I can read to explain what could happen?    _(Edit: as of the comments, "core" actually refers to "nucleus" -changed)_


title: Why is the moment of inertia for a hollow sphere higher than a uniform sphere?

text: I have completely no idea and I am inquiring about this as it is an interesting question that popped in my head while doing physics homework.


title: Most suitable metric for the Solar system?

text: 1. If I wanted to solve the Einstein equations for the solar system, which choice of $g_{\mu\nu}$ and $T_{\mu\nu}$ is more suitable?    2. I thought about using a Schwarzschild metric near each planet, but how to connect them?


title: Shrinking and Expanding objects in a CFT

text: In a conformal field theory, is it possible to construct a machine that shrinks or expands objects?