title: Why does milli- mean 1/1000

text: I suppose this is also an English question, but I'll ask it here first. Why does the milli- prefix mean 1/1000 when it sounds so much like million? According to the internet, this dates back to the 18-19th centuries. Did it make more sense back then? Are we stubbornly holding on to meanings from borrowed prefix's languages (such as milli meaning 1000 in Latin)? Not that I'm qualified in any way to make this kind of statement, but if I were able to rename our unit prefixes, I would shift everything from milli- to femto- down 3 orders of magnitude and eliminate atto-. The resulting pairs would be:               thousand-    kilo    (placeholder)     million-     mega    milli     billion-     giga    micro     trillion-    terra   nano     quadrillion- peta    pico     quintillion- exa     femto     sextillion-  zetta   zepto     ...      Which to me, sounds better. But I suppose I answered my own question by saying that since they are the units everyone uses, social inertia prevents us from changing. Would this be correct?


title: Question about buoyancy

text: I took an empty clear sphere with radius r, put some weight inside this sphere, and put in into the water. I calculate the buoyancy force as: Volume of the sphere = Volume of the water displaced (Vdisplaced) = (4/3) _pi_ (r^3); Weight of the displaced water = Buoyancy force (B) = Vdisplaced * density of water; Wtotal= Wsphere + Wweight; Then, the sphere will float when Buoyancy (B) > Wtotal, otherwise it will sink. I assume that I am right so far?? So the air inside the sphere will affect sphere's ability to float. My confusion is that I assume that I have already considered this effect during the aforementioned calculations (since density of the sphere itself is low). Is that right? Please note that the sphere is not flexible.


title: Glycerol: refractive index & absorption spectra in 0.2-0.4um range

text: Could anyone suggest where can I find absorption spectra & refractive index of Glycerol? I am specifically interested in UV range, 200-400nm, everything I was able to find out was for standard conditions only... Is there any software which can get these parameters through simulation?


title: Carrier Electrons Generation and Recombination Time

text: When a Electron gets promoted to the conduction band from valence band (In generation) lets say for example in Silicon at room temperature. Is there any way to determine (on average) how long it will last before falling back down in the hole it just left. What about with a Voltage Applied? Thanks


title: Hamiltonian (temperature?) and frame of reference

text: So we can define a particle by defining its kinetic and potential energy, knowing that we can get a wavefunction describing a particle. But the kinetic energy involves motion, and motion can be described in many different frames of reference as different quantities, so is the Hamiltionian not uniquely defined? I mean, is the quantum state than dependant on in which frame of reference you look at the particle? Or it is just taken as a velocity in the Earths frame of reference as we cannot extract the energy contained in the velocity due to rotational motion around the Sun and the center of Galaxy? And also what is the same case with temperature? I found some things about it but I don't fully understand I think. relevant: Unruh effect I searched over the physics stackexchange and read about the energy in different frames of reference and the temperature and so on, and well I still don't feel that I understand it, but the main question is: **isn't the wavefunction absolute description of the state of the particle?**


title: Put yourself in the shoes of Wolfgang Pauli (1930): How could Pauli have narrowed the culprit down to one particle, instead of many?

text: A while ago, during my introductory physics course, my professor purposefully neglected to tell us about the existence of the anti-electron neutrino in beta decay; he made it an assignment(on our honor) to propose a theory to explain where the missing energy ran off to. Since I was not very experienced at the time, I did not come to the conclusion that the culprit had to be neutral (to conserve charge), but I was aware of basic particle collisions and how scientists smashed particles together in order to observe smaller, more basic ones. Consequently, I came to the conclusion that when the electron broke away from the nucleus, particle fragments (where the electron broke off) were released as well (so, a bit like detritus which would have accounted for the deviation in the missing energy, as a different number of particles could have broken off each time). Now, clearly, I had an advantage over Pauli (since I was aware of particle diversity, and the separable nature of baryons), yet I am still not certain exactly how he was able to narrow his choices down to a single particle (especially since he was decades away from being able to detect such an elusive creature). How would you have come to such a conclusion (if possible, perhaps another response besides Occam's Razor)?


title: Photon Quantum Field proportional to Electromagnetic Field?

text: Does it make sense to say that the quantum field of a photon is exactly proportional to the photon's electromagnetic field? \begin{align} \bar{\Psi} = \dfrac{\bar{E}+i\bar{B}}{\sqrt{\int (E^2+B^2)dV}} \end{align}


title: SuperHiggs Mechanism on different Backgrounds & Compactifications

text: I've been studying Bagger & Giannakis paper on the SuperHiggs Mechanism found here. The paper shows how SUSY is broken by a $B_{\mu\nu}$ gauge field background restricted to $T^3$ in $M^7\times T^3$ Compactification of the heterotic string. _My question is, have these results been generalised to different Backgrounds and/or Compactifications (Perhaps even Calabi Yau 3-folds)?_ So far my search has shown up no results, any pointers in the right direction are greatly appreciated, Thanks!


title: Keeping air in a well

text: Let's say I've got an Earth-like planet with no atmosphere: it's just a barren ball of rock. I want to live there, but I don't like domes, so instead I'm just going to dig a big hole and let gravity keep the air in. How deep a hole do I need? According to a chart I found, the density of the atmosphere drops to pretty much zero by about 50km, at the top of the stratosphere. But 'pretty much zero' is not zero; the mesosphere beyond that extends up to about 80km and while vanishingly thin is responsible for dealing with most meteors. If my hole is a mere 50km deep, then, some of my air is going to diffuse out of the hole and onto the planet's surface. But the surface of my planet is largely flat; there's nowhere for the air to _go_ , so it's just going to hang around and form a dynamic equilibrium. (Unlike, say, if I built a 50km wall and tried to keep the air inside. Air would leak over the top of the wall, fall down into the vacuum on the other side, and be lost forever. Which is why the Ringworld had walls 1000km high.) So I don't really know how shallow a hole I can get away with. I _can_ replace the air, but I would like it to go without maintenance for at least small geological timescales. Any advice before I start up the earth-moving equipment? (Yes, it's SF worldbuilding.)


title: Could someone explain to me why this is sometimes right and sometimes not?

text: I do not remember when, but a while a ago I was told that for a spring with stiffness $k$ and a mass $m$, the equation $-kx = ma$ never holds. (assume a horizontal spring) So if I was given a problem like this: > You pull a mass $m$ attached to a spring with stiffness $k$ to the right of > the equilibrium point $x = 5\text{ m}$ of the spring and you let it go, what > is the acceleration of the mass? Then is this question meaningless (or any other that is similar)? I forgot what the real question is like, but I have seem such a method was used to tackle these problems? As such an attempt to write $-kx = ma$? Could someone please jog my memory? I realize I am asking you guys to 'read my mind', but please bear with me.


title: How would normal matter behave under conditions found in the core of the sun?

text: Considering how low the power density is at the sun's core, I seem not to be able to expect what would happen to matter in case it was thrown inside the sun's core. For example, let's assume an Earth-like planet is placed at the center of the Sun's core, and with the power density of 276.5 $watts$/$m^3$ which is very low to even raise the temperature of the Earth by any noticeable degree. That was one thought. The other thought was that, the temperature in the core is already 15 million degrees K, so any matter there should get close to this temperature quickly enough. So now I'm very confused, like will the planet stay there intact for thousands or even millions of years until it has accumulated enough energy to melt or vaporize ? Or there are other types of energy absorption the planet would experience and thus have a shorter time staying as one piece in the core ? Just for trying to get a practical and numerical answer to this question, let it be : how long can the Earth as a whole survive in the core of the sun ?


title: How are qubits better than classical bit?

text: WHAT I KNOW: classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states. Now when we make a "measurement" (to determine the state of qubit), it changes the state of qubit, collapsing it from its superposition of 0 and 1 to the specific state consistent with the measurement result. MY QUESTION: If, from measurement of a qubit we obtain only a single bit of information (0 or 1 beacuse the qubit collapses to either of the states) then how is a qubit better than a classical bit..... since ultimately we are only able to get either 0 or 1 from either classical or quantum bit. [I hope that i have made the question clear enough to convey what i think]. To those who answer this please try to explain with an example if you can.


title: Eigenfunctions in a harmonic oscillator

text: This assignment is about the one dimensional harmonic oscillator (HO). The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at $t = 0$, is given by: $\psi \left( x,\,\,t=0 \right)=A\left( {{\phi }_{0}}\left( x \right)+2i{{\phi }_{2}}\left( x \right) \right)$ Now I have to calculate A, so that $\psi$ is normalized. My question is, what is ${{\phi }_{0}}\left( x \right)$ and ${{\phi }_{2}}\left( x \right)$ given by ? Otherwise I guess is just doing the usual: $\int_{-\infty }^{\infty }{{{\left| \Psi \left( x,\,\,t \right) \right|}^{2}}}dx=1$ To figure out A.


title: Angular momentum after elastic collision

text: If two balls collide (elastically) and there is no friction between them, will their angular momentum change after the collision?


title: Mathematical proof of non-negative change of entropy $\Delta S\geq0$

text: I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that $$\Delta S\geq0$$ via Clausius' theorem. My question is, how can I prove this in a mathematical way?


title: Conservation of total angular momentum in $\Phi$-meson decay

text: I am looking into the decay of a $\Phi$-meson decaying into $K^+$, $K^-$. My problem is, the $\Phi$-meson has a total angular momentum of 1 and the two Kaons have a total angular momentum of 0. On the first glance this seems to be a violation of the angular momentum conservation law. I tried to explain it to myself using the quark picture of the system. So the $\Phi (s \bar{s})$ goes under the production of a $u\bar{u}$ pair into $K^+(u \bar{s})$ and $K^- (\bar{u}s)$. Using Clebsch Gordon coefficients i noted down the possible combinations and that works out so far. My question is, how can the 'effective' total angular momentum be explained as it seems to me, that the conservation law is not conserved, which can not be. Do i miss something or have i got something wrong?


title: Do color-neutral gluons exist?

text: If I'm correct a quark can change color by emitting a gluon. For example a blue up quark $u_b$ can change into a red up quark by emitting a gluon: $$u_b \longrightarrow u_r + g_{b\overline{r}}$$ (Here, the subscript indicates color and $\overline{r}$ means anti-red). This is needed to keep the color balance (left hand side: $b$, right hand side $r+b+\overline{r}=b$). My question is then, do color-neutral gluons exist? Eg a gluon that is blue- anti-blue? If it would, it could be created by any quark then: $$u_b \longrightarrow u_b + g_{b\overline{b}}$$ I'm learning about the Standard Model in school, but the text isn't always that clear.


title: Is the Higgs bare mass larger than the physical mass?

text: The Higgs boson propagator can be written $$\frac{1}{p^2-m^2+\Sigma(p^2)}$$. If we take $p^2=m_P^2$ the physical mass, we get $m_P^2=m^2-\Sigma(m_P^2)$. Now, if $\Sigma\sim \Lambda^2$, we get $m^2\sim\Lambda^2+m_P^2$. It had assumed that the mass correction from fermion loops was positive, but from this it appears that the Higgs mass is renormalized to be smaller than the bare mass. Is this physical ?


title: Entangled event horizons

text: Assuming it is possible in principle to entangle the degrees of freedom of the event horizons of two black holes, and that this is something that can be done, either after the black hole is formed, or only by careful preparation before collapse. > **Question:** Could exist a physically realisable entanglement configuration > of the horizons that behaves as a traversable wormhole, in the sense that > infalling information on one mouth becomes non-thermal Hawking radiation on > the other mouth, that preserves some or all the original information? A while ago I made a relevant question regarding creating black holes with entangled light. That method suggested there could provide two such entangled black holes


title: How to make appropriate statements concerning simultaneity or sequence of pitches

text: This answer to a recent question related to Einstein's thought-experimental definition of (how to determine) simultaneity contained the following statement: > Suppose two people, $C$ and $D$, stand equal distances from you and are > known to pitch balls at exactly the same speed. With everyone standing at > rest, $C$ and $D$ each toss you a ball. You get the ball from $C$ *before* > the one from $D$. This is not a logical inconsistency. It simply means $C$ > threw a ball *before* $D$ **in your reference frame** [emphasis added]. I believe that I understand the described setup and the conclusion (" _It simply means $C$ threw a ball _before_ $D$_") as such. But I question whether it is necessary to add the qualification " _in your reference frame_ ". Carefully applying Einstein's definition of (how to determine) simultaneity, as referenced above, which for the given setup involves a suitable observer " _at the midpoint between_ $C$ and $D$", is there even any reference frame at all (necessarily other than " _your reference frame_ ") "in which" $C$ threw a ball *simultaneous to* $D$ throwing a ball ? Or is there even any reference frame at all (again necessarily other than " _your reference frame_ ") "in which" $C$ threw a ball *after* $D$ ? (If there are no such reference frames, then the qualification " _in your reference frame_ " is apparently not necessary; and, indeed, it would seem inappropriate and misleading to add such a qualification as if it were necessary.)


title: Time required to fill a pipe line

text: This is quite embarrassing to ask, but I haven't done a fluid flow calculation in a very long time and when you don't use it, you lose it! I have a natural gas pipeline that I want to purge of air with natural gas. It's a 3" and 4" line totalling about 6,600 feet. I'll be injecting natural gas into the line through a 2" hose with a pressure of 15 psi and the outlet will be another 2" hose at the other end. My question is: How long will it take to push all of the air out of the pipe and fill it with natural gas (purge the line of air)? I've spent the last few hours Googling fluid flow questions and answers and just can't figure it out. Thanks in advance!


title: Drift Speed and Current in Two Different Inertial Frames

text: We have a long, cylindrical wire carrying a constant current I in an inertial frame. At a distance of R from the center of the wire, the magnitude of magnetic field is $μI/2πR$. What is the magnitude of magnetic field in another inertial frame moving at a certain speed opposite to the direction of electric current? Since the observed drift speed of the electrons is now greater, does this mean that the current as observed from this frame is greater? If so, what about the magnetic field due to this current? Does this change too? In general how do currents vary between different frames of reference?


title: Water Level and Pipe Widths

text: I ran into a bit of physics yesterday, and couldn't understand the physics at work. I've been scouring the Internet, but haven't found the answer yet. I'm guessing there's a basic principle I'm misinterpreting or ignorant of. Basically, the sewer backed up into my house. Among other points of entry, water flowed up the shower drain, and up the toilet bowl. The shower filled to a bit under the lip of its basin. The toilet filled to a bit under the lip of the bowl, but neither overflowed. So basically I had a reservoir (the sewer), with one pipe (shower) extending to floor height + 4 inches, and another pipe (toilet) extending to floor height + 24 inches. Where I'm getting confused is that in my physics textbooks I recall seeing a diagram of a U-shaped vessel with differently sized "legs." I think that the water level in each leg of the U had to be the same, because otherwise there'd be a pressure differential at the base of the U preventing the system from stabilizing. Edit: Here's an example of what I'm talking about. What would allow for this difference in water levels?


title: Moment of inertia of disc with a hole

text: Suppose we have a disc with a hole, when computing moment of inertia of this about the disc's centre. Why do we subtract the moment of inertia of the removed part from the moment of inertia of complete disc?


title: Why force $F$ is $ma$ but not $md$ or $mv$? How can I observe and understand "force" in real life?

text: As a layman, i can calculate approx "displacement" just by observing the moving object. And accurately by using a simple "scale". Similarly, again, I can calculate angle from origin by using displacement in $x$ and $y$ dimensions. Similarly I can use a stopwatch and scale to understand velocity. But when I read about force, first of all it confuses with the english word "force", we use in real life. To some extent I am sure, it has nothing to do with that. So exactly what is it in the real sense. How can a layman, see force as, just like he can see displacement or angle? Or force is just a quantity defined by physicists to simplify the combinations of $ma$, they might be facing every time. And thus came up with term "force" ( which is similar in spelling to english word in oxford dictionary). And lastly, why not force has just been called as something proportional to mass and it's displacement or velocity. Why something at the level of change of velocity has been used to define it.


title: Regarding the theory of the origin of water on earth through meteorites, why wouldn't the water evaporate on impact?

text: Water on earth has been theorized to have come through comets trapped inside crystals. But why wouldn't that water evaporate on impact, and wouldn't the atmosphere at that time allow the vapours to escape Earth? Also, what is the current scientific opinion of the validity of this theory ?


title: Geometric optics- Sign conventions

text: Why do we need to use the sign convention again in the mirror equation while solving numericals when we know we have already used a convention while deriving the mirror equation? The question is not about the importance of sign conventions but why do we need to use the sign conventions twice? Doesn't the equation already include a sign convention? 1/u + 1/v = 1/ f Or say, in the magification formula: height of image/ height of object = - (v/u) Why do I need to bother about the signs ( -u or - v or +f) while using the above equations?


title: Frequency of Light Near a Massive Object

text: We know that near a massive object, light's wavelength and frequency changes, but its speed remains same. I'd like to know how it is possible for frequency to change, unless we change the light source?


title: Eigenvalues of the Spin Operator on a two-spin-system

text: I am not sure if I understand spin operators correctly. Given a two spin system in state $|++\rangle$ and an operator $S = S^{(1)} + S^{(2)}$ Then I have $$ S_z |++\rangle = (S^{(1)}_z + S^{(2)}_z) (|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes |\tfrac{1}{2}, \tfrac{1}{2}\rangle) = (S_z|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes S_z|\tfrac{1}{2}, \tfrac{1}{2}\rangle) = (\tfrac{\hbar}{2} |\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes \tfrac{\hbar}{2} |\tfrac{1}{2}, \tfrac{1}{2}\rangle) = \tfrac{\hbar}{2} (|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes |\tfrac{1}{2},\tfrac{1}{2}\rangle) = \tfrac{\hbar}{2} |++\rangle $$ But everywhere I read, I see $$ S_z |++\rangle = \hbar |++\rangle $$ What did I do wrong?


title: How thermally conductive is a black body?

text: Does a black body (imagine like a square of solid black-body-matter) thermally conduct well at room temperature?


title: $\tau$ pair production question

text: There's a question on my homework about the process $e^{-} e^{+} \rightarrow \tau^{+} \tau^{-}$. Specifically, it is claimed that the minimum energy required of the colliding positron and electron beams is slightly less than twice the $\tau$ mass, and I am asked to explain this deviation and compute it. In the context of this course, we have only discussed the relativistic kinematics of such processes (which would predict a minimum energy of twice the $\tau$ mass), so I am not sure what might be responsible. I'm grasping at straws here, but might it have something to do with the Coulomb interaction between the opposite charges? Thanks in advance.


title: Is the potential in Schrödinger equation an operator?

text: In the Schrödinger equation in the position representation $$ i\hbar\frac{\partial}{\partial t}\Psi(x,t) ~=~[\frac{-\hbar^2}{2m}\nabla^2+V(x,t)]\Psi(x,t), $$ is the potential $V(x,t)$ an operator acting on $\Psi$ or merely a scalar?


title: What is solid- solid transformation?

text: I found this solid-solid transformation in wikipedia. http://en.wikipedia.org/wiki/Phase_transition#Types_of_phase_transition Please tell me what it is? It's present in types of phase transition in wiki.


title: Is there an open oriented superstring?

text: Type I superstring theory is unoriented, and it seems that it needs to be so in order to exist. Now, we always have open-closed duality, that connects at least the ultraviolet sector of a theory with the infrared sector of another, so in principle we should have some oriented open strings coming from it, by duality with a closed oriented theory. And we have all the D-brane stuff, that surely produces another kinds of open string theories with the restriction of terminating there in the branes. ¿Is some of these D-brane examples an oriented theory? ¿Is there some canonical, well known, example of a consistent oriented theory with open strings?


title: Using 2D position, velocity, and mass to determine the parametric position equations for an orbiting body

text: I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do this, I need the parametric equations for the body's position for any given time (i.e. I need an $x(t)$ and $y(t)$ function). I have access to each body's position, velocity, and mass. I have no other accessible variables. P.S. Here is a link to what I have so far. The equations currently used to plot the orbit are $x(t)=x+v_xt$ and $y(t)=y+v_yt$.


title: Photoelectric effect: Experimental Physics

text: Suppose you are doing an experiment to determine the work function of a metal. You get $KE_1$, $\nu_1$ and $KE_2$, $\nu_2$. We know that $KE = h\nu - W$ but when you solve the simultaneous equations, we have a $h$ slightly different from the textbook value. Question: In such a situation should you   1. Use the textbook $h$ then average {$W_1,W_2$}; or   2. Simply solve the simultaneous equations for $W$ I believe that the values obtained will be different. Thank you. Added: Assume you don't get to do more repeats etc.


title: BCS Theory of Superconductivity

text: I'm currently taking an introduction to Solid State Physics class, and is now on the subject of superconductivity (SC). Currently I'm reading about the BCS theory, and how this works on a microscopic scale. I then get presented with this picture (Electron-Phonon Interaction): ![Electron-Phonon interaction](http://i.stack.imgur.com/ZJiFm.png) Now, as far as I have understood, the electrons, when below $T_{C}$, attract the ions, but are too fast compared to the ions, which means that the ions contract after the electron is gone. This creates a higher potential in the area where they are "squeezed" together which the next electron is much more attracted to that usually. This again means that all electrons pretty much follow the same path, and somehow bond together in Cooper Pairs (Is this the way they get entangled?). Now, my main question is: Does this attraction of ions, after an electron has moved past them, not happen to a normal metal ? I mean, the electrons move in a normal metal, and also past ions. So don't they attract the ions as well, and make this attraction that another electron then can follow as well ?


title: Opposite field's acting on a soft ferromagnetic material

text: To external fields(H, - H) not equal to each other are acting on that material. **Based on the hysteresis loop** what would be the result? The hysteresis area of that materials is very narrow(i.e easy to magnetize & demagnetize) H = 1000 A/m and, - H = 500 A/m. I know they are both vectors so it would be H - H = H(total). However, the material's coercively is 0.1 A/m. The thing is I can't imagine this condition properly, because both fields are opposing each other, and that ferromagnetic material is placed in-between them both. What would be the result? The material responds based on it's hysteresis... H points on the hysteresis loop. Why is it incorrect to state magnetization = 0? I'm relating this to an object that has to forces acting on it, they are both on opposite directions. F1 = 10N F2= 5N [x]= is the object. 10N ->[x]<\- 5N = 5N ->[x] Although it makes sense... The hysteresis loop changes everything. Magnetization depends on how the material reacts. The material could become magnetized and fully saturated at 100A/m, now we have both of those conditions... So M should = zero?! To picture what I mean, please take a look at this: http://uk.tdk- lambda.com/content/glossary/128522219667677500_Hysteresis%20Loop%20image.png The two points on the loop on the H axis are 100 A/m(that is the force needed to magnetize the material), however, the field applied H = 1000 A/m and - H = 500 A/m Hope it helps!


title: Self-inductance of a toroidal inductor

text: I am trying to determine the self-inductance of a toroidal coil of mean radius $R$ with $N$ loops of radius $a$ with a current $I$ flowing within them. I have calculated the magnetic field by noting that it must be in the circumferential direction (i.e. in the $\hat{\boldsymbol{\theta}}$ direction) and then using Ampéres Law to get: $$\oint_{\partial \Sigma} \mathbf{B}\cdot \mathrm{d}\boldsymbol{\ell}=\mu_{0}I_{\text{enc}} \implies \mathbf{B}=\frac{\mu_{0}NI}{2\pi r}\hat{\boldsymbol{\theta}}$$ I know that we can get the self-inductance $L$ by using the relation: $$\Phi=LI$$ And we know that: $$\Phi=N\iint_{\Sigma}\mathbf{B}\cdot\mathrm{d}\mathbf{A}$$ Where $\Sigma$ is the area of a single loop. However, I am not sure how evaluate the surface integral, I'm not sure if perhaps I should be using the mean radius $R$ to give us: $$\Phi=\frac{\mu_{0}N^{2}}{2\pi R}\pi a^{2}I=\frac{\mu_{0}a^{2}N^{2}}{2R}I$$ Or if I need to evalute the integral in a more complete way?


title: Meaning of Smooth Dynamical System?

text: What does smooth dynamical system mean? It is the title of a paper I am supposed to read in non linear systems.


title: Gravity through a portal

text: Ok, this is definitely a silly question and is partly inspired by the last 20 minutes or so of the film _The Avengers_ , so look to that if you can't picture the situation. In the film a portal is opened up above new york, to somewhere in deep space. I.e. from an area where the gravitational field is effectively uniform and field lines would be parallel, to an area with negligible net gravitational acceleration. My question is, assuming this portal has literally linked the two bits of space, it makes sense that the gravity of the earth would be transmitted through the portal in some way, but in what form would the field take on the other side of the portal? Would it behave like a point source, or similarly to a diffraction slits? Would a mass slightly off to one side from the portal experience a force? Let's ignore all the practical factors like the air rushing out into the vacuum and the question of what happens on the "other side" of the portal (the bit you'd be looking at if you flew up from new york to above the portal) although there's plenty of scope for interesting things happening there as well.


title: Basic Spin or Double Cover Experiment

text: We know that Spin is described with $SU(2)$ and that $SU(2)$ is a double cover of the rotation group $SO(3)$. This suggests a simple thought experiment, to be described below. The question then is in three parts:   1. Is this thought experiment theoretically sound?    2. Can it be conducted experimentally?    3. If so what has been the result? The experiment is to take a slab of material in which there are spin objects e.g. electrons all (or most) with spin $\uparrow$. Then rotate that object $360$ degrees (around an axis perpendicular to the spin direction), so that macroscopically we are back to where we started. Measure the electron spins. Do they point $\downarrow$?


title: Phase transition classification of a made-up system

text: I am having some troubles trying to classify a modified photon gas into which phase transition it belongs (if it really is a phase transition). First of all, it is a photon gas that interacts with an external electric field, so the q-potential (from the grand canonical ensemble) depends on the external field and the temperature alone. The potential is continuous but not analytic only when the external field is varied (if the external field is maintained fixed it might be on one side or the other of the critical point, independently of the temperature). Because the density of energy is the derivative with respect to $\beta$, it has the same qualitative properties of the q-potential. Now, I've found two definitions for phase transitions, Ehrenfest's one and the "modern" one. Following Ehrenfest's classification I found that it's a first order transition since the discontinuity appears in the first derivative of the potential with respect to a thermodynamic variable, the electric field. But, following the "modern" definition, I found that it is a second order phase transition, or, in the modern classification, a continuous phase transition, because the entropy doesn't have a discontinuity and thus the system doesn't require a latent heat to perform the transition. My questions are, have I well understood the definitions? Is the system really having a phase transition? And, if it does, which one is it having or it is of a third kind I didn't mention? Thanks


title: Is there a maximum possible acceleration?

text: I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...


title: Electricity Flow and Ground Wire

text: Pre-face: My step-father and I were turning the heat down on the water heater. He demonstrated that touching the ground wire doesn't shock you. My understanding is that the ground wire doesn't have current unless the case of a short-circuit, or over-abundance of energy. The wire also has very little resistance. My question, if the water heater had a short-circuit or had an access flow of energy. Would he have been shocked? Please explain instead of yes or no.


title: What is the difference between a QCD "glue ball" and a Higgs Boson?

text: Although they have never been observed, theoretically gluons can exist outside of the nucleus of an atom in the form of a "glue ball". Since the predominant mechanism of Higgs creation at the LHC was observed to be a gluon-gluon interaction (with various virtual particles playing out in the conversion), what are the chances that a "glue ball" as predicted by QCD is the same animal from the particle zoo as a Higgs boson?


title: Feynman diagram for pair production in matter

text: I'm aware that electron pair-production from a single photon requires the presence of matter — say some large nucleus — able to absorb momentum, as in the process \begin{align} N \gamma \rightarrow N e^- e^+ \end{align} where $N$ represents the nucleus. My question is, how would one represent this process with a Feynman diagram? I'm having trouble constructing one with valid vertices that makes sense. Would the neutron interact with the photon? With the electron-positron pair? Both? Any help would be appreciated.


title: How much electricity can be generated from ambient sources?

text: I know that recent advances in technology are doing amazing things with very low amounts of electricity, with RFID being one of the most familiar examples, but I'm not very familiar with the principles involved. It makes me wonder: is it possible (with current technology, not "is it theoretically possible?") to use ambient sources (including body heat) to generate enough power to light up an LED, all in a device small enough for a person to hold in their hand? If so, how small could the whole assembly be made? I've actually got a very specific application in mind, but if it turns out we don't have the capability for it, that'll save a lot of time right there.


title: Moment of inertia of a planet

text: Is there a good way to directly measure a moment of inertia of the Earth, or say, other planet?


title: Is fire plasma?

text: Is Fire a Plasma? If not, what is it then? If yes why, don't we teach kids this basic example? ![enter image description here](http://i.stack.imgur.com/MLPSn.jpg) **UPDATE:** I probably meant a regular commonplace fire of the usual temperature. That should simplify the answer.


title: Do magnets redshift light?

text: Do magnets redshift light? Suppose we have an extremely powerful magnet (say the size of the Sun) and we have a smaller paramagnetic material above it (say. Titanium Brick which is indestructible) . Due to magnetic attraction it will fall toward the big magnet. Now suppose that when it hits the surface of the bigger magnet, the smaller paramagnetic material (Titanium Brick) is somehow converted into photons (light) equivalent to its mass using $E=mc^2$, plus its kinetic energy, $KE_1$. These photons are shot upwards via an perfect mirror perpendicular to the paramagnetic material above. When they reach the magnet's original position they are again converted into mass in the form of the titanium brick. If this is repeated many times it seems we will gain free energy, since the iron brick gains kinetic energy when it falls, but light is not effected by magnetic fields. (Or am I wrong?) But this will breach the energy conservation laws in specific "Energy cannot be created nor destroyed". Therefore I must conclude light is (or should be) redshifted (loses energy) as it travels through magnetic field. The problem arises when you take into consideration that light is not charged so it should not be effected by any magnetic fields but my intuition tells me light should still be affected so is my conclusion valid or not? Is light red shifted in presence of an magnetic field? If light is not red shifted then what is lost to ensure the system is not gaining energy but in this experiment it does not make sense since we are using photons which are not effected by magnetic fields and then recreating the para magnetic material (like Iron brick we used) so we should not loose energy as we are simply recreating the same object again.


title: Quantum Field Theory phenomenology

text: Suppose you know everything about Quantum Field Theory, but nothing about the very specific interactions and particles which exist in our real word. Which physical or mathematical principles could be used to reduce the infinite number of possibilities of QFT, to finish with some class of theories, in which the Standard Model, for instance, would belong. [If the question is too "extreme", one may soften it by considering having some partial information, to be detailed, about our real world]


title: Why do organisms accumulate potential energy?

text: I can understand that animals need some battaries to run. But, we learn that plants serve like batteries for animals because they accumulate the sun energy in the first place! You can eat them or burn to extract the accumulated energy. This means that they consist of structures that they want to blow-up and disintegrate to fall apart at the lower energy level. But why? This is strange to me since the most fundamental law of nature says that battaries spontaneously leak and discharge themselves. This means that the hydrocarbon structures that all life organisms are made of on the Earth are not stable. The photosinthesis, $\mathrm{H_2 O + CO_2 + \text{photo} \mapsto O_2 + CH_2O}$, is costly. It not only needs (photo) energy but uses it to produces the hydrocarbons, the $\mathrm{CH_2O}$-like spontaneously degrading structures! Why do you want to consist of something unstable that has tendency to blow up as soon as possible (why not immediatly, BTW?) if your purpose is survival, as any life organism on the Earth? I watched the Gibbs Free Energy but could not understand anything. Is it because of the min. energy law we have everything at the min energy already on the Earth and if you want to produce some structures (fortunately, there is a Sun), you have no other choice but to make them unstable?


title: A photon travels in space for 10 billion years. What are the odds it will arrive here without interacting with a atom on the way?

text: Space isn't a perfect vacuum and I wonder how an image of a galaxy can travel billions of years without becoming diffused by photon collisions with space matter?


title: Example where angular momentum and angular velocity are not parallel

text: I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.


title: Simple Quantum Mechanics Question about The Commutator of Translation Operators

text: Say there is $\hat{J} = \exp[-i \hat{p} l/ \hbar]$ and $\hat{U}= \exp[-i\hat{H}t/ \hbar]$, where $\hat{H}$ is time-independent. Can we say anything about $[\hat{J},\hat{U}]$? Is it zero? How do we show this? For example if $\hat{H} = \hat{p}^2 /2m + m\omega^2 \hat{x}^2/2$.


title: What is the gapless excitation for traditional Bose-Einstein condensates?

text: I want to know the properties and the behavior of the gapless excitation for the traditional BECs. Could you give me some idea or references about this?


title: How come a rigid body has 6 degrees of freedoms (DOFs) ? Isn't velocity a DOF?

text: For rigid body we need to know position of three points and their velocities to determine everything. So that would make 12 DOF. Why do text books say it has six DOFs?


title: Does the concept of a wormhole violate the law of mass-energy conservation?

text: If my understanding of wormholes is correct, anything that moves into a wormhole can be transported from one region of space-time to another. Consider a situation where an object of mass $m$ in space at $(x_1,y_1,z_1)$ and time $t_1$ travels through a wormhole and appears at $(x_2,y_2,z_2)$ in a distant future time $t_2$. In between time $t_1$ and $t_2$, it seems this object of mass $m$ doesn't exist. Hence during this span of time, the total mass-energy of the universe should be less than before. Doesn't this violate law of conservation of mass-energy?


title: Gravity on a upward moving object

text: I know I should have listened to my teacher in physics class but I didn't. I need help on a thing I am trying to do for a game. I want to be able to calculate Gravity pushing down on a object over a certain amount of time. (I want the object to slow down to a stop and then go back down due to gravity). I've been looking on the internet and I guess I'm not using the right search terms. So I am hoping that this fine community can help me. *The object(Player) is only moving upward. The Player is not moving forward or anything. Just Up Given the initial velocity, how do I compute the motion (position, velocity) of the object as a function of time?


title: String theory and the SM spectrum

text: Long ago, I realized this: (super)string theory can NOT give a well- defined/unique prediction of why the electron (muon, tau) or the neutrino (any flavor) masses have the masses we measure. String theory can NOT give a concrete prediction of any SM particle mass (even resonances like the Higgs and other particles). The question is: Is this lack of predictive ability of the mass of the SM "elementary particles" a hint that string theory in its current status is not complete or wrong? Or perhaps even better: **Even when string theory provides a framework in which you can accomodate every Standard Model field, and hence, a priori you can have the SM spectrum, we have not a string theory explanation of the values of the masses and charges. Should a explicit derivation of particle properties like (rest) masses and (bare) charges (like the electron charge value) be "predicted" and "derived" in a more fundamental version of the theory?**


title: Heat generated on thin disc plate in magnetic field

text: There are the eddy currents in thin circular copper plate thickness h and radius a, in a harmonic magnetic field which is perpendicular to plate and the effect of auto-induction is negligible. Now we must get average heat generated on it. As I said, I have final equation, but how do you get to this eqution. Does anyone know solution from first step to this? $$ \overline P=\frac{1}{16}\pi\gamma ha^4B_0^2\omega $$


title: Question about (complex) motion of Moon

text: In an ideal situation, we can use a simple formula to determine the velocity at which a body revolves around a massive body at a particular distance. I was wondering if there is an intuitive way to understand the motion of a body influenced by two other massive bodies (say the moon being influenced by the earth and the Sun). Is there any analogy to the motion of a wheel that can be considered as a combination as translational and rotational motion (and both these motions can be mathematically treated separately)? Or do we need a simulator to visualize the actual path?


title: Seiberg-Witten theory and Superconductivity

text: There seems to have some (deep) relation between Seiberg-Witten theory and superconductivity. e.g. this Witten paper. > Q: Could someone introduce the relations between the twos both **physically > in terms of intuition**? and **mathematically in terms of formalism**? How > exactly is the relation?


title: Finding cooling time using an impulse of heat energy

text: > A chip has a thermal resistance of 0.007 K/J s and thermal capacitance of > 1.6 J/K. You give it an impulse of heat equal to 100 J. How long does it > take for the chip to cool to within 10% of the ambient temperature? I understand that I have to implement Newton's Law of Cooling, but I can't seem to grasp how I can find the ambient temperature nor the initial temperature. Any and all help is greatly appreciated.


title: What does Orion's Belt look like from the Equator?

text: I've been struggling with this question all morning, yet I get the feeling the answer is frightfully simple. If Orion appears upside down in the Southern Hemisphere and the right way up in the Northern Hemisphere, what does it look like in equatorial countries such as Kenya, Colombia, and Ecuador, bearing in mind that Orion itself is in the equatorial region of the celestial sphere? I initially thought it could just be a matter of perspective: If you're on the equator and facing North you'll see it the right way up,but see it upside down if you're facing South. But then surely that approach would apply even if you were in the Northern or Southern Hemisphere. I reckon the times Orion is visible in various parts of the world will also have to be factored in. For example, it is visible at night late spring to summer in the Southern Hemisphere. Could anyone offer me some advice? I fear I may be over-thinking this. Thanks in advance.


title: Was Aristarchos' method to compute Earth-Sun distance ever rediscovered in medieval or modern times?

text: Ancient Greek astronomer Aristarchos who lived around 300 BC found a method to compute the Eart-Sun distance by applying geometry. In this video about the cosmic distance ladder, at 26:30, Terence Tao explains that Aristarchos was basically limited by nonexisting clock technology. So he was not able to accurately measure the time difference between the time of (1/2 (new moon - fullmoon)) and time at which sun-moon distance was exactly at 90 degrees to the intersection of earthorbit - moonorbit. See screenshots. ![Aristarchos 1](http://i.stack.imgur.com/YnS0l.jpg) ![Aristachos 2](http://i.stack.imgur.com/bGR9e.jpg) Why was his method never refined in more modern times? Someone could have independently discovered the computation by a similar way of reasoning, but with better clocks. Or _did_ some European Astronomer else do this after mechanical clocks were invented, and it was just not accurate enough so they went for the transit-of- venus-method?


title: Two planets in same orbit - not planets?

text: Let us pretend for a moment that there are two identical planets that are exactly opposite their star from each other and are the same distance from said star. (This would make them, at all times, double the distance from their star apart from each other.) Would they, under the definition of a planet, be considered planets? One could argue they have not cleared their neighborhood by virtue of one not having cleared the other. But, it would seem strange to assume a planet would be capable of clearing something that always has its sun in the way.


title: Understanding Dynamic light scattering

text: I'd like to understand the physics of dynamic light scattering experiment. In particular I want to understand the basic relation between relaxation time $\tau_q$ and the diffusion coefficient $D$: $\tau_q=(q^2 D)^{-1}.$ I suppose that more or less the following steps are necessary: 1) Calculate the scattered wave from Maxwell equations. 2) Find a relation between the scattered intensity autocorrelation function and the brownian motion of the particles. I found this book by Berne and Pecora, but at least for point 1 I got lost because there seem to a strange version (or an approximation) of maxwell equations that I don't understand (it is citing Landau but looking at this book was not such an help). Is there any book were I can find what I need or at least point 1 written with some detail? thank you


title: Incorrect IR temperature reading on stainless steel?

text: Using a Fluke 62 Mini Infrared Thermometer today on a stainless steel pipe with coolant I noticed that it gives incorrect temperature readings. There is a temperature sensor inside the coolant saying about 90° Celsius. I spray painted a spot on the pipe and the IR thermometer instantly gave more correct readings on the painted spot. So why? Why is it the coolant fluid is about 90° Celsius (both the painted spot and the temperature sensor suggest that), while the unpainted clear stainless steel says about 50° Celcius? I.e. apx 55%


title: Projects for a physics club

text: It's a physics club for undergraduates (first three years of university); I'm looking for projects idea that aren't too obvious like a small rocket or an electromagnet (school projects) but also not too advanced. Since most members know Newtonian mechanics, electrostatics & magnetostatics and some simple notions of thermodynamics, waves, special relativity & geometric optics, I came up with the project " _The Solar System_ " with the following objectives:     * Study the motion of the earth in the gravitational field of the fixed sun (analytical solution) and compare the results to the available data.   * Study the earth as a 2-body system (analytical solution)   * Study the sun-earth-moon system numerically (3-body problem)   * Study the sun-earth-moon-other planets as a 10-body problem   * Treat the bodies as point particles and then as rotating solid bodies   * Calculate the value of the year Any refinements to this projects are welcomed. Any other project?


title: Why do people use C++ in Computational Physics?

text: Once day, I talked to my Prof. about Computational Physics and he showed me his work. I'm quite surprised that why Prof. use C++ for computation because C++ quite complicated. I heard he talked about memory talk about pointer. Why didn't he use Python or Java that more easier? no need to manage memory no need to busy with pointer.


title: Magnifying factors of multiple lenses (closely packed)

text: Well the following question I really struggle to find an answer > A thin lens creates an image of an object with magnification -3. A second > identical lens is positioned very close to the first lens such that the > distance between the two lenses can be neglected. What is the magnification > with this two lens system assuming that the object distance has not changed? At first the solution seemed very simple, name the distances between some virtual objects $d_0$, $d_1$ & $d_2$. Then the total magnifying factor can be found using: $$M_t = -\frac{d_2}{d_0}$$ $$M = -3 = -\frac{d_1}{d_0}$$ $$M = -3 = -\frac{d_2}{-d_1}$$ (last equation has an extra minus sign as the image is a virtual location, the image $d_1$ is behind the lens, the distance of this virtual image to the lens is $d_1$ given that the lenses are "positioned very close". Now the problem is: I can't solve this, 4 unknowns and only 3 equations. Also going by hand and stating simply "well the magnification factor is the combination of both lenses so $M_t = M * M = 9$ results in a "wrong answer".


title: Confusion in fourier's law

text: My book starts section 2.2 like this: ![enter image description here](http://i.stack.imgur.com/obS89.png) Equation 1.1 is this: $$q_x=-k\frac {\partial T}{\partial x}$$ As you can see in the picture I posted, my book says that one can go from equation 1.1 to equation 2.1 by integration. I don't see how this is done by integration at all. Thank you


title: How to determine an exponential acceleration curve?

text: I've always been not so bad in mathematics, but I'm terribly bad at physics. For me, abstract concept are totally understandable, but when it come to reality, I'm lost ! So, for my job, I need to understand something. I have an object, travelling during $t_o$ on a distance $d_o$. It has an inital speed $v_1$, and a final speed $v_2$. I need to find an exponential curve which fits the condition, and I'm lost in my equation, I don't know where to begin. I try to start from the equation of the acceleration. I wan't it to be exponential, so $$ a = e^{kt} $$ The speed curve is then the integration of the acceleration $$ v = \frac{e^{kt}}{k}$$ I can substitute condition for finding k, $$ v_1 = \frac{e^{k\cdot0}}{k} \implies k = \frac{1}{v_1}$$ $$ v_2 = \frac{e^{k\cdot t_0}}k \implies v_2 = v_1\cdot e^{{t_0}\cdot{v_1^{-1}}}$$ Which makes no sense. Where did I go wrong ? My final idea is to have something like $$ t = f(d) $$ so I can find the time with the distance, and vice verse.


title: Physical Significance for Duality Formula for Entropy

text: I am studying quantum statistical mechanics from the mathematician's perspective. I don't quite understand what the duality formula for entropy is _really_ saying (or why there is a "duality"). If $A$ is an $n\times n$ Hermitian (self-adjoint, diagonalizable) matrix, then $$S(A)=\sup\bigl[{\operatorname{Tr}(AH) - \ln\bigl(\operatorname{Tr}[E^H]\bigr) : H \in H_n}\bigr]$$ where $H_n$ is the set of Hermitean matrices. What does this even mean?


title: Help with Hologram problem

text: Can someone help me out with a simple yet interesting 3D hologram related problem and solution, which can help me understand the subject and then teach the subject to a group of students.


title: What are some ways that humans could have influence over what sequence a star was in?

text: How would a society go about either preventing our sun in its primary sequence from going into a Red Giant a billion years from now? Or perhaps, accelerating the process of going from main sequence of our start to a red giant prematurely. What catalysts would have to happen, implemented by humans, so no natural phenomenon could play a part in it, that would have an impact, even slight, on the future processes of the sun's lifecycle. Any thoughts or help would be great!!!!


title: Why do books have dog ears?

text: I googled the question and found no explanation. It seems that dog ears are inevitable (for paperbacks, notably) even if you've always been careful. From my experience, they are about equally likely to appear on the top corners as on the bottom corners (for both the beginning pages and the ending ones). Dog ears for the middle pages of the book are less likely but they can also appear in frequently used old books. Can someone explain why? ![dog ears on the bottom corners for the beginning and ending pages](http://i.stack.imgur.com/rw85F.jpg) ![dog ears for the beginning pages of a book](http://i.stack.imgur.com/bbpa6.jpg) I apologize if this is not the right kind of question to post here. I can find no other sites on SE for it.


title: QFTs which are pure constraint

text: I am interested in (typically topological) field theories arising from Lagrangians of the form. $f(\Phi) \lambda$, where $\lambda$ is a Lagrange multiplier field not appearing in $f(\Phi)$. Perturbatively, the partition function just counts the solutions to $f(\Phi)=0$. What about nonperturbatively? Are there exponentially suppressed kinks that affect the partition function? Has anyone considered these?


title: Inelastic Collision and incident angle

text: This problem is puzzling me. Scenario 1: A certain sphere is having an innelastic collision with a plane of a very large mass. Let the angle between the sphere's velocity and the surface be 90 degrees. The escape angle will be the same as the incident angle, therefore the sphere velocity will be 90 degrees from it's origin. Scenario 2: The same as above, but now the ball is static, and the surface is moving towards the sphere with the same speed. I was expecting exactly the same result, since on my mind (and obviously wrong), the speeds were relative. The sphere in scenario 2 leaves the collision plane on a trajectory normal to the surface. Note that I mention speed, because I have a gut feeling that the problem I'm having is with summing up the vectors. I'm having problems visualizing and coming up with an intuitive explanation for why.


title: Very basic question about QFT at finite density

text: This must be the first question everyone asks when starting to study field theory at finite density and zero temperature. To introduce a finite density one adds a Lagrange multiplier which fixes the number of particles in a non-relativistic field theory or the number of particles minus the number of antiparticles in a relativistic field theories. To be concrete, in a non-relativistic field theory one has the Lagrangian density: $$\mathcal L=i\psi ^*\partial _t \psi -{1\over 2m}\nabla\psi ^*\nabla\psi - V[\psi ^*\psi]$$ and then the same theory at finite density is described by: $$\mathcal L=i\psi ^*\partial _t \psi -{1\over 2m}\nabla\psi ^*\nabla\psi - V[\psi ^*\psi]+\mu \psi ^*\psi \,\,\,\,\,\,\,\, [1]$$ where $\mu$ is the chemical potential and the number of particles is $N=\int \psi ^*\psi$. What disturbs me is that one may redefine the field: $$\chi\equiv e^{-i\mu t}\psi$$ with $t$ the time. And after replacing in [1]: $$\mathcal L=i\chi ^*\partial _t \chi -{1\over 2m}\nabla\chi ^*\nabla\chi - V[\chi ^*\chi]$$ The "finite density term" disappears. Moreover, the path integral measure is invariant under this trivial field redefinition so that the finite density QFT seems equivalent to the zero density one. (Those who are familiarized with the non-relativistic limit of relativistic equation —such as Klein-Gordon or Dirac— will recognize this term and field redefinition.) Something similar happens in the relativistic case. What am I overlooking? (Note that the theory is at zero temperature so I am in real time formalism and I don't have to impose periodic boundary conditions (I think). I am interested in time evolution, scattering, etc.) **Reply to Ron's answer:** (I here will overlook Thomas' comments, I will answer him tomorrow.) Ron makes an interesting point, but I think his answer is not correct. The Hamiltonian density of the theory in the original fields is:$$\mathcal H={1\over 2m}\nabla\psi ^*\nabla\psi + V[\psi ^*\psi]-\mu \psi ^*\psi $$ What he correctly pointed out is that the Hamiltonian in the new fields is not just the previous Hamiltonian written in the new fields. This is right and in classical mechanics it is well-know that one has to add a piece to the Hamiltonian when one makes an explicit time dependent transformation. He pointed out the case of quantum mechanics, and the field theoretic version is: $$i\partial _t \, \chi =i\partial _t \, (e^{-i\mu t}\psi )=i(-i) \mu \, e^{-i\mu t}\psi + e^{-i\mu t}[\psi , H]=[e^{-i\mu t}\psi ,\, \mu N + H] $$ And therefore the Hamiltonian for the field $\chi$ is: $$H'=\mu N + H=\int {1\over 2m}\nabla\chi ^*\nabla\chi + V[\chi ^*\chi]$$ This is of course the Hamiltonian corresponding to the Lagrangian written in terms of $\chi$. In this way, one sees how the "standard" theory (without the $\mu$ term) is recovered in the Hamiltonian formalism as it was in path integral formalism. And this makes a lot of sense because the theory with $\mu = -m$ has to be equivalent to the theory with $\mu=0$ because we are just subtracting the rest energy. Of course, this is true as long as one does not impose periodic boundary conditions.


title: Euler Lagrange equation in different frames

text: Suppose I have an inertial frame with coordinate $\\{q\\}$. Now I define another reference frame with coordinate $\\{q'(q,\dot q,t)\\}$. I obtain the equation of motion in $\\{q'\\}$ in two different ways:   1. First obtain the equation of motion in $\\{q\\}$ by the Euler Lagrange equation $$\frac{d}{dt}\left(\frac{\partial L}{\partial \dot q}\right)-\frac{\partial L}{\partial q}=0$$ and then rewrite the equation in terms of $\\{q'\\}$.   2. First transform $L(q,t)$ to $L'(q',t)=L(q(q',t),t)$ and then obtain the equation of motion $$\frac{d}{dt}\left(\frac{\partial L'}{\partial \dot q'}\right)-\frac{\partial L'}{\partial q'}=0$$ Are the two answers just the same?


title: Law of Gauss. Electrostatics

text: I have seen on the internet that many times people assert that inside a cylindric condenser the electrostatic field is null due to the fact that the Gauss flux inside is null. But I wanted to make clear that this is not the reason. The reason lies on the symmetry of the condenser. Am I right? If the electrostatic field was null inside the smaller radius conductor, it would mean that if we put a test particle there, it would not resist any force. However if I am right, this would not happen. The only thing that could happen so that the particle did not move, would be that the charge in the condenser could be reorganized in presence of that particle. Do I have the concepts right?


title: Properties of 3D waves

text: I have a few questions about 3D waves:   1. Are all 3D waves types of electromagnetic radiation?   2. Are all 2D waves mechanical?


title: Why does quantum mechanics invalidate one of locality and realism?

text: I am approaching this from an intuitive perspective and I don't speak the language. However, I have been doing a lot of reading about Bell's Theorum and how invalidates either locality or counterfactual definiteness. From my point of view, locality is the concept that there is no way that two particles can interact with each other "instantaneously" at a distance (i.e. faster than light.). Realism/counterfactual definitiveness is the concept that all particles have some true value for all variables at some instant regardless of whether or not that value was observed. Let's assume for the sake of this question that locality is true, which I believe is the current popular model in QM. Assuming locality, why do Bell's Inequalities show that conterfactual definiveness must be false? **Edit to respond to below post:** This is crazy. Let me see if I am following you. I'll use your framework. I'm not really sure what spin is but I'm seeing it as an observable phenomenon that exists as a function of a specific direction in a given particle at an instant of time, and the spin itself at any angle changes (randomly?) over time. A and B are, we are assuming, perfectly correlated so so the spin at angle θ in A is definitely the same as the spin at angle θ in B. In any given electron (let's just take A) we can define some angle θ as the angle between two 'directions' on that electron that have an exactly 99% correlated spin. There's no way we can measure those two directions on the same particle at the same time, but since A and B are perfectly correlated, we can measure A at 0 degrees and B at θ degrees and experimentally we would see that they are the same spin This is crazy. Let me see if I am following you. A and B are, we are assuming, perfectly correlated so so the spin at angle θ in A is definitely the same as the spin at angle θ in B. In any given electron (let's just take A) we can define some angle θ as the angle between two 'directions' on that electron that have an exactly 99% correlated spin. There's no way we can measure those two directions on the same particle at the same time, but since A and B are perfectly correlated, we can measure A at 0 degrees and B at θ degrees and they will be the same spin 99% of the time. Similarly, if we measure the spin at θ in A and at 2θ in B, we will see that these two values are the same spin 99% of the time. Assumingly, this will work for any two angles that are exactly θ apart -- with enough measurements they will be correlated exactly 99% of the time. However, if we measure the spin at 0 in A and at 2θ in B, they are only correlated 96% of the time. If V0 is at most 1% off from V1, and V1 is at most 1% off from V2, V0 should be anywhere from 0-2% off from V2. But, we find, according to QM and experimentation, it is not! It is less heavily correlated than that. This is where I lose you. Why does saying no to realism resolve this issue?


title: Radiation interactions: how is the transition from the "electric" regimen to "particle-like" regimen?

text: When we study the interaction of the electromagnetic radiation with free electrons we can find two different approaches in the literature: for low frequency (RF, light...) a classical view is used and it is said that the electrons oscillates due to the electric field of the wave, but for high frequency radiation (X-rays, gamma), the type of interaction seems totally different (Compton effect and the like) and radiation is usually modeled as "particles". For an radiation with "intermediate" frequency such as UV or very low energy X-rays, would interactions be "electric-like" or "compton-like"?. How is the transition between both regimens?


title: Interaction of coherent X-rays with matter

text: If we could irradiate a metal or a plasma with a coherent beam of hard X-rays, would the main effect be an ordered oscillation of the electrons like with a classical EM wave, or "compton-style" collisions?


Like any set of massive objects separated by distance, the Earth and Sun have a center of mass. How far in meters from the Sun's center is the Earth-Sun center of mass? Just curious? Also what percent of the Sun's radius is this distance?


title: How to measure the energy consumption class of a home appliance?

text: Some of you may be familiar with the EU energy consumption classes for domestic appliances (or equivalents in other areas). Let's say we have a domestic appliance which was made before the energy directives were made active. How can one measure (approximately) the energy consumption using whatever is available in one's kitchen or home and check which class the appliance could be put under? **Clarification:** Of course one can use a power meter an extract some results. The question is more precisely about what can one do using things (and methods) available in one's kitchen. It would be best to describe a mehod to implement this task and furthermore the method should be able to classify (approximately not laboratory precision required) the appliance in terms of the EU energy classes. Answers that mention the power company power supply meter are in the spirit of what is asked.


title: Quantum tunelling problem - got a weird imaginary ratio in the end

text: **1\. The problem statement, all variables and given/known data** > Beam of electrons with energy $10eV$ hits the potential step ($8eV$ high and > $0.5nm$ wide). How much of the current is transmitted? **2\. Relevant equations** I know that energy mentioned in the statement is kinetic energy so keep in mind when reading that $E\equiv E_k$. In our case the kinetic energy is larger than the potential energy $\boxed{E>E_p}$ and this is why stationary states for the regions 1, 2, 3 (picture) are as folows: \begin{align} \psi(x)_1 &=Ae^{iLx}+B^{-iLx} && L=\sqrt{\tfrac{2mE}{\hbar^2}}=1.619\times 10^{10}\tfrac{1}{m}\\\ \psi(x)_2 &=Ce^{iKx} +De^{-iKx} && K=\sqrt{\tfrac{2m(E-E_p)}{\hbar^2}}=0.724\times 10^{10}\tfrac{1}{m}\\\ \psi(x)_3 &=Ee^{iLx} \end{align} ![enter image description here](http://i.stack.imgur.com/RbNgm.png) **3\. The attempt at a solution** I first used the boundary conditions for the border 1-2 and got a system of equations: \begin{align} A+B &= C+D\\\ iLA-iLB&=iKC-iKD\\\ &\downarrow\\\ A+B &= C+D\\\ A-B &= \tfrac{K}{L}(C-D)\\\ &\left\downarrow \substack{\text{I used the assumption that}\\\\\text{$E \gg E_p$ and got the simplified}\\\ \text{relation between L and K:}\\\ \tfrac{L}{K}=\sqrt{E/E_p}\gg 1 \Longrightarrow L\gg 1\\\ \text{and hence}\\\ \tfrac{K}{L}=\sqrt{E_p/E}\ll 1 \Longrightarrow K\ll 1} \right.\\\ A + B &= C+ D\\\ A-D &= 0\\\ &\downarrow~\Sigma\\\ 2A &=C+D\\\ &\downarrow\\\ C&=2A-D \end{align} Now i used the boundary conditions for the border 2-3 and got a system of equations in which i inserted the above result: \begin{align} Ce^{iKd} + De^{-iKd} &= Ee^{iLd}\\\ iKCe^{iKd} -iK De^{-iKd} &= iLEe^{iLd}\\\ &\downarrow\\\ Ce^{iKd} + De^{-iKd} &= Ee^{iLd}\\\ Ce^{iKd} -De^{-iKd} &= \tfrac{L}{K}Ee^{iLd}\longleftarrow\substack{\text{Things get weird}\\\\\text{when i insert }C=2A-D}\\\ &\downarrow\\\ 2Ae^{iKd} -De^{iKd} + De^{-iKd} &= Ee^{iLd}\\\ 2Ae^{iKd}-De^{iKd} -De^{-iKd} &= \tfrac{L}{K}Ee^{iLd}\\\ &\downarrow \substack{ \text{$L$ is very big while $K$ is very small}}\\\ 2A &= Ee^{iLd}\\\ 2A -2D &= \tfrac{L}{K}Ee^{iLd} \end{align} Now this result is what i don't understand. First equation gives me a ratio $E/A=2\exp[-iLd]$ which i think i need to calculate the transmissivity, but it is a complex exponential. Is this possible? How do i continue? Is this the way to solve this kind of case or did i go completely wrong? This is my first finite potential well problem and i have been searching the web for a loong time to even find 2 videos (video 1 and video 2) for a **similar problem** but for the case when $E<E_p$. The professor in the video allso uses similar approximation - but in his case $E \ll E_p$. On this hyperlink there is allso a scan of the problem solved on the paper just in case anyone likes it this way. It is in Slovenian language but i added some headings to help you reading.


title: Why do we say that irreducible representation of Poincare group represents the one-particle state?

text: Only because   1. Rep is unitary, so saves positive-definite norm (for possibility density),   2. Casimir operators of the group have eigenvalues $m^{2}$ and $m^2s(s + 1)$, so characterizes mass and spin, and   3. It is the representation of the global group of relativistic symmetry,  yes?


title: What would a person experience in a free-falling elevator in a shaft long enough to reach terminal velocity?

text: Assume we had an elevator shaft long enough for a free-falling elevator to reach terminal velocity. As I understand it, when the elevator begins to fall a person inside would experiences weightlessness because they would be accelerating downward at the same rate as the elevator. The rate of downward acceleration for the elevator should reach a constant when air resistance equals gravity (right?). However, the person in the elevator would not be exposed to air resistance and should continue to accelerate downward. So would they gradually sink back to the floor and experience gravity as though the elevator were at rest... at least until the inevitable termination of the experiment?


title: Radiant barrier effect on inside of a hot water tank

text: I am trying to determine if a radiant barrier on the inside of a hot water tank would increase its insulating value. Normally radiant barriers are used in house construction to reduce heat loss by reflecting radiant heat back into the house. The reflective surface is placed against an air gap on the exterior wall facing inwards and the thermal radiation is reflected back across the air gap into the drywall and hence into the home. I am trying to determine if a radiant barrier placed directly against a liquid would have the effect of reducing heat loss from the liquid. Lets say we have a tank designed to store hot water and keep it hot by reducing heat loss to the ambient surroundings. For example, the tank is metal and surrounded by a insulating layer of foam, fiber glass etc. with a high R value (A measure of resistance to heat transfer). Lets say there are two versions of this tank. The first tank has a grey or dark interior, similar to what would be found in a glass lined steel water tank commonly used a domestic water heater. The second tank is identical except that its interior is coated with a reflective silver surface facing towards the mass of hot water. Would the reflective surface increase the effective R value of the tank's walls and reduce heat loss from the tank? The possible effect is that thermal radiation emitted from the hot water molecules would reflect back from the silver surface and be reabsorbed by the hot water mass as it passes back into the body of the water. This might seem similar to a thermos type vacuum flask, the main difference being that in a thermos flask there is a vacuum behind the radiant barrier so I don't know if their is difference in the radiant barrier effect between having a vacuum behind the radiant barrier and having solid conducting material behind it as we do in the water tank example. if their is any R value enhancement by virtue of the slivered lining of the water tank, how could we quantify it in terms of R value? Thanks.


title: What happens to a photon when it enters a black hole?

text: The photon has a mass of 0, but it has energy because of its motion. When it is sucked into the black hole and becomes a singularity, it loses its energy because it is no longer moving. It is not possible for something to be sucked out of a black hole, so it has no potential energy that the kinetic energy could have been transformed into. If I haven't missed a point, then energy has just been destroyed. Everyone knows that it isn't possible for energy to be destroyed because of the first law of thermodynamics a.k.a. the conservation law of energy. Therefore I must have missed a point, because I am not ready to criticize famous scientists that have indefinitely more knowledge then I do. Please tell me what I did wrong :)


title: Time Dilation Effects from simply being on a spinning planet orbiting a star in a rotating galaxy in an expanding universe.

text: I am a layman, so take this with a grain of salt. I saw a TV show the other day which showed a Russian Cosmonaut who had spent more time in space than any other human. The relativistic effects of the low gravity and extreme speeds at which he had spent a decent part of his life had pushed him a small, but surprisingly non-trivial fraction of a second into the "future" as compared to the rest of us observers here on earth. I want to say it was something like a 50th of a second. What, if any, are the relativistic effects all of us experience in an average lifespan simply by being on the earth as it travels through space in orbit and as the galaxy rotates and the universe expands. By effects I mean as compared to a hypothetical observer who is able to remain completely motionless in space? Is it even measurable? I know gravity is not being taken into account, so is this question even answerable? Thanks for your patience with my question.


title: How to block neutrons

text: What is a good way to block neutrons and what is the mechanism that allows this? It's my understanding that polyethylene is somewhat effective. Why?


title: Lattice QCD and attempt to prove that the universe is a simulation

text: Assume that we have access to a computer with unlimited computing power. As with the Lattice QCD can try to prove that we live in a simulated universe? Apparently, one may use the issue of cosmic rays. Here is full article Quote: > If we were living in a simulator, we'd expect to find evidence of that > lattice if we looked close enough to the edges of the observable universe - > and that's what Silas Beane from the University of Bonn and colleagues have > calculated, in a paper published in arXiv. As cosmic particles fly through > the universe, they lose energy and change direction and spread out across a > spectrum of energy values. There's a known limit is how much energy Those > particles have, though, and Beane and his colleagues have calculated That > this seemingly arbitrary cliff in the spectrum is consistent with the kind > of boundary that you ''d find if there was an underlying lattice governing > the limits of a simulator. It should also, if present, scatter the particles > in a Certain Way as they come up against it, and the should be able it > investigate Whether that's the case. Do you have any idea?


title: Feynman Lectures: Trigonometry Error in Rotational Dynamics?

text: I'm reading through Vol. 1 Chaper 18, and Feynman says that in the system: ![enter image description here](http://i.stack.imgur.com/G3AZG.png) (See here for a higher resolution copy - can't embed SVGs), the length of $PQ$ is equal to $r\Delta\theta$: > If $OP$ is called $r$, then the length $PQ$ is $r\Delta\theta$, because of > the way angles are defined. I'm probably being stupid, but surely this should be $r*\tan(\Delta\theta)$? Also, the diagram itself appears to depict an impossible figure. If the lengths of $OP$ and $OQ$ are equal, then the angle $OPQ$ cannot be 90 degrees. Like I said I'm probably being stupid, so hopefully someone can show me where I'm going wrong.


title: Total multiplicity and entropy of Einstein solids

text: This is really a question to get a little more insight about a homework exercise. **_1._** In my text book, the sum of multiplicities for all possible macrostates is given to be: $$\sum \Omega_\mathrm{total}=\binom{N_A+N_B+q_\mathrm{total}-1}{q_\mathrm{total}}$$ For two Einstein solids $A$ and $B$ of $N_A$ oscillators in solid $A$, $N_B$ oscillators in solid $B$ and $q_\mathrm{total}$ units of energy in the system. I tried deriving this myself (which the text book doesn't require) but no dice there. How can I derive this myself? * * * **_2._** The problem here is that the followup question pretty much defines the long term entropy of this system to be: $$S=k\ln\left(\sum\Omega_\mathrm{total}\right)$$ Now there's confusion. I simply have no idea what I'm doing. Why is the sum of all the multiplicities together the long term entropy? How should I reason that this is the correct answer? Some explanation would be very, _very_ welcome.


title: Ideal gas in a vessel: kinetic energy of particles hitting the vessel's wall

text: Reading Landau's Statistical Physics Part (3rd Edition), I am trying to calculate the answer to Chapter 39, Problem 3. You are supposed to calculate the total kinetic energy of the particles in an ideal gas hitting the wall of a vessel containing said gas. The number of collisions per unit area (of the vessel) per unit time is easily calculated from the Maxwellian distribution of the number of particles with a given velocity $\vec{v}$ (we define a coordinate system with the z-axis perpendicular to a surface element of the vessel's wall; more on that in the above mentioned book): $$ \mathrm{d}\nu_v = \mathrm{d}N_v \cdot v_z = \frac{N}{V}\left(\frac{m}{2\pi T}\right)^{3/2} \exp\left[-m(v_x^2 + v_y^2 + v_z^2)/2T \right] \cdot v_z \mathrm{d}v_x \mathrm{d}v_y \mathrm{d}v_z $$ Integration of the velocity components in $x$ and $y$ direction from $-\infty$ to $\infty$, and of the $z$ component from $0$ to $\infty$ (because for $v_z<0$ a particle would move away from the vessel wall) gives for the total number of collisions with the wall per unit area per unit time: $$ \nu = \frac{N}{V} \sqrt{\frac{T}{2\pi m}} $$ Now it gets interesting: I want to calculate the total kinetic energy of all particles hitting the wall, per unit area per unit time. I thought, this would just be: $$ E_{\text{tot}} = \overline{E} \cdot \nu = \frac{1}{2} m \overline{v^2} \cdot \nu $$ The solution in Landau is given as: $$ E = \nu \cdot 2T $$ That would mean that for the mean-square velocity of my particles I would need a result like: $$ \overline{v^2} = 4\frac{T}{m} $$ Now, I consider that for the distribution of $v_x$ and $v_z$ nothing has changed and I can still use a Maxwellian distribution. That would just give me a contribution of $\frac{T}{m}$ each. That leaves me with $2\frac{T}{m}$, which I have to obtain for the $v_z$, but this is where my trouble starts: How do I calculate the correct velocity distribution of $v_z^2$?


title: Higgs boson and quasiparticles

text: Do we know exactly the difference between particles and quasiparticles? Is Higgs boson a particle or a quasiparticle? I ask this because if I understood well, Higgs boson created by a spontaneaous breaking symmetry and correspond to a Goldstone mode. Maybe I am wrong in my explication.


title: Reversing Noether's theorem

text: Noether's theorem states: any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is this statement invertible? I mean, if a conservation law exists, this implies there is a differentiable symmetry in the action?


title: Mobility in semiconductors

text: Good afternoon everybody. I am reading on a book about semiconductor mobility. I have fully understood the definition, but I also noticed that often one talks about high or low mobility. My question is: what are the **advantages** of having a **high** mobility? I mean, in the technological applications or experimental uses of the semiconductor/etherojunction. Do you know any main **methods** to improve mobility (in Si and/or Ge semiconductors for example)? Any **bibliography** about them?


title: Kerr-Newman black holes and infinite charge

text: Recall the first law of BH thermodynamics $ dM=\frac{\kappa}{8\pi} dA + \Omega dJ + \Phi dQ $ Now, let's consider the Reissner-Nordstrom solution $J=0$ such that $m>Q$ but only slightly greater. Suppose I have a small bit of charge $dQ$ which I bring in from infinity to the BH horizion. 1) Question: Is the extremal BH solution $m=Q$ possible? I would think that if we consider the work to be done to bring $dQ$ from $\infty$ to BH horizon, this would blow up $\Phi$ and cause M to go to $\infty$ as well. Therefore, I would guess the extremal solution cannot be achieved in this scenario. 2) Now, this extremal solution DOES seem possible in the Kerr solution, but how would this affect $J$ and $\Omega$ ?


title: What's so special about wave solutions of EM?

text: Maxwell's equations allow for wave solutions via oscillations between electric and magnetic field content. Couldn't we generate electric waves also if that solution didn't exists? Imagine there was no magnetic field, only the electric field. If at one point in space we generated an electric field nicely varying in a sinus pattern of constant frequency, wouldn't this propagate with light speed, just like a plane EM-wave of that frequency, even though there was no magnetic field?


title: neutron transport approximations for nuclear rocket modelling

text: I'm pretty ignorant regarding neutron and nuclear transport modelling, but i'm interested in trying to pursue it for a particular pet project. It regards modelling of nuclear reactions like those required for NERVA-like rockets or this one. I would appreciate any references or some explanations of the required approximations for the models required to compute neutron transport that i would have to take in consideration for this exercise.


title: Explanation for breaking up of a stream of water into droplets

text: Water falling from a tap eventually breaks into droplets at a particular distance from the tap. The distance(from the tap) at which it breaks into droplets is observed to be an increasing function of the volume flux of the water flowing out of the tap. What is the valid explanation for this phenomenon? My own line of reasoning is as follows : let $D$ be the critical distance measured from the tap, i.e. the distance at which the water breaks into droplets. At a distance $d<D$ the flow can be assumed to be streamlined to a good approximation; in which case the cross-sectional area of the stream goes on steadily decreasing down the flow. Due to this, the surface energy per unit volume associated with the surface of the water should go on increasing with the distance from the tap until it reaches a point where it becomes greater than/equal to the surface energy of the same volume of water as a water drop. At this distance, by minimisation of potential energy the water should break into droplets to minimise the surface energy. Let's say this happens when the cross section of the flow reaches a threshold value $A$. Now if the volume flux is low; it would mean that the cross sectional area at the tap is itself low. Due to that, the threshold area $A$ would be attained at a lesser distance from the tap. This probably explains the observation that the distance(from the tap) at which it breaks into droplets is observed to be an increasing function of the volume flux of the water flowing out of the tap. Am I right? Please correct/add to my explanation.


title: Is temperature quantized?

text: I'm learning quantum mechanics on my own. I've known that energy is quantized and I've started wondering about temperature. From thermodynamics we have: $$U=\frac{3}{2}NkT $$ (for ideal gas, of course)   Both U and N aren't continous, so i think T shouldn't be, too. Is that formula correct also for quantum mechanics?   I'm really sorry because of my language, I'm still working on it.


title: Quantum Boltzmann Equation

text: What is the Quantum Boltzmann equation and what does it describe? I think it describes the propagation of electrons and photons but I am not sure.


title: Explanation on the resulting forces of two positive point charges

text: Why will the resulting force lines of two positive point charges be like this: ![enter image description here](http://i.stack.imgur.com/3jnkx.jpg) I would expect this: ![enter image description here](http://i.stack.imgur.com/KIltz.jpg)


title: Double internal energy, how much will the entropy change?

text: Approaching the following question > Imagine we have a collection of $N = 100$ simple harmonic oscillators. The > total internal energy is $U = q \epsilon$ where $q$ is the number of energy > quanta. Assume $q >> N >> 1$. If we double the internal energy, by how much > will the entropy of the collection change? The question was originally found here under _Question 5_. The answer is $\sigma_{final} - \sigma_{initial} = 69.3$ How is this determined? I know $S = k_b ln \Omega$, where $S$ is entropy, $\Omega$ is the number of micro-states, $\sigma = \frac{ 1}{ \Omega}$, $k_b$ is the Boltzmann constant. I know $<energy> = 1/2 k T$ per quadradic term. I know $\frac{ 1}{ T} \equiv \frac{ \partial S}{\partial U}$ But how does doubling energy effect entropy? Specifically, what equation am I looking for to determine this?


title: Nuclear based wireless power?

text: I would like to ask if there is any Nuclear process which can be used to produce a wireless power ? Is there any nuclear process can be radiate to the environment with no harm to human beings? * * * # How can I use the photo electric effect with some high Intensity radiation ?


title: Local $U(1)$ gauge invariance of QED

text: The Lagrangian density for QED is $$ \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+\bar{\psi}(i\gamma^{\mu}D_{\mu}-m)\psi $$ with $$F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu} $$ $$ \bar{\psi}=\gamma^{0}\psi^{\dagger}$$ $$D_{\mu}=\partial_{\mu}+ieA_{\mu}$$ $U(1)$ local gauge transformations are $$\psi\rightarrow\psi^{'}=e^{-i\alpha(x)}\psi$$ $$A_{\mu}^{'}=A_{\mu}+\frac{1}{e}\partial_{\mu}\alpha(x)$$ I'm trying to see that $\mathcal{L}$ it is invariant under those $U(1)$ transformations, but I finish my calculation with $$\mathcal{L}^{'}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+e^{-i\alpha(x)}\bar{\psi}[i\gamma^{\mu}D_{\mu}-m-\gamma^{\mu}\partial_{\mu}\alpha(x)]e^{i\alpha(x)}\psi $$ Any hint will be appreciated thanks


title: What is electron momentum density in solids and molecules?

text: Can someone kindly help me to know how can i get electron momentum density for one orbital like home? what is the theory of electron momentum density? how can I derive electron momentum density from real electron density? how can i use Fourier transform?


title: why is it important to find stability of supergravity solutions?

text: I want to know about the importance of the stability, generally,why is stability important in super-gravity? and why do we like these solutions?


title: Relationship between nuclear spin and nuclear magnetic moment?

text: We know that nuclear magnetic moment can be expressed in terms of the expected value for nuclear spin as: $$\langle\mu\rangle =[g_lj+(g_s-g_l)\langle s_z\rangle]\frac{\mu_N}{\hbar}$$ (Cf. Krane), where $\vec{j}$ is the _total_ angular momentum, $\vec{l}+\vec{s}$. How does the expected $\langle s_z\rangle$ value relate to the $\vec{j}$-component of spin, $\langle s_j\rangle$? Krane mentions that only that value is needed, given that it remains constant.


title: When jumping into water, how deep should the water be to survive?

text: How deep can I go if jumping from 50m?


title: Scaling of Static Electric Field

text: The electric field of a point charge goes like $\displaystyle\frac{1}{r^2}$ The electric field of an infinite line goes like $\displaystyle\frac{1}{s}$ The electric field of an infinite plane is constant Is there an intuitive way or some insight to understand such results and realize that they are expected?(One of my friends said that the electric field due to an infinite plane does not change at all because it looks infinite no matter how close or far from we are it. Is this argument correct? I am not convinced because we can say the same about the infinite line, it looks infinite no matter how close or far we are from it, yet it changes parametrically with the distance)


title: Does one require calculus to work with uncertainities?

text: I'm very young so know no calculus whatsoever. I want to be able to calculate uncertainties for a Physics course I'm doing online, but I believe you need to have knowledge of differentials to do this in some cases. Do you need knowledge of calculus to be able to calculate with differentials?


title: Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?

text: I have earlier posted the same question here on `math stackexchange` but without any answer. As the question concerns tensors, I guess that I have come to the right place i.e. to physicists. Say I have the following equation of motion in the `Cartesian` coordinate system for a typical mass spring damper system: $$M \; \ddot{x} + C \; \dot{x} + K \; x = 0$$ where the dot $^\dot{}$ represents differentiation with respect to time. Now I would like to convert this equation to `Polar` coordinates. So I introduce $$x=r \; \cos{\theta}$$ to obtain $$\dot{x}=\dot{r} \; \cos{\theta} - r \; \dot{\theta} \sin{\theta}$$ and $$\ddot{x}=\ddot{r} \; \cos{\theta}-2 \; \dot{r} \; \dot{\theta} \; \sin{\theta}-r \; \dot{\theta}^2 \; \cos{\theta}- r \; \ddot{\theta} \; \sin{\theta}$$ I can insert $x, \; \dot{x} \; \text{and} \; \ddot{x}$ in my original equation in the `Cartesian` coordinate system to yield $$M \; (\ddot{r} \; \cos{\theta}-2 \; \dot{r} \; \dot{\theta} \; \sin{\theta}-r \; \dot{\theta}^2 \; \cos{\theta}- r \; \ddot{\theta} \; \sin{\theta}) + C \; (\dot{r} \; \cos{\theta} - r \; \dot{\theta} \sin{\theta}) + K \; (r \; \cos{\theta}) = 0$$ **Note: I am just showing the equation and derivatives in the x-direction. But the full system has both $x$ and $y$ components.** I wonder if the above way of thinking is right. I am **very** new to tensors and I after reading about **covariant derivatives** , I am now thinking that one should include consider the basis vectors of the `Polar`coordinate system (a `non-Cartesian`coordinate system) also since unlike the basis vectors of the `Cartesian` coordinate system which _do not_ change direction in the 2D space, `Polar` coordinate basis vectors _change_ direction depending on the angle $\theta$. I am thinking about `covariant derivatives` as the conversion process includes differentiation with respect to the bases. For example if $x=r \; \cos{\theta}$, then $$\dot{x}=\frac{dx}{dt}=\frac{\partial{x}}{\partial{r}} \cdot \frac{dr}{dt} + \frac{\partial{x}}{\partial{\theta}} \cdot \frac{d\theta}{dt}$$ So we have terms like $\frac{\partial{x}}{\partial{r}}$ and $\frac{\partial{x}}{\partial{\theta}}$ that concern basis vectors both in the `Cartesian` and in the `Polar` coordinate systems. Hope that someone can shed some light on this.


title: A very elementary question regarding force of friction

text: When I first studied friction I faced f = $\mu$ N where f is force of friction, $\mu$ is coefficient of friction for the surface considered and N is the normal force for the body on surface. Now f is a force so it must be a vector which means it has a direction. N is normal force so it has direction too. But both f and N are mutually perpendicular to each other! And $\mu$ is a constant, so how can we write f and N in one equation? They do not have the same direction! I think this is not clear to me because I have never read about the origin of this equation. From where do we get it?


title: Electronic filter

text: Can you explain, please, **step-by-step** how an electronic filter does work? For example, high pass filter. I know It's a trivial things, but I can't get it completely. Don't bring me formula and etc. Just explanation in three words.


title: Simple step in time evolution of position operator in simple harmonic motion

text: When considering the 'Heisenberg' picture of the harmonic oscillator, I've come across the step: $$\begin{align} \left\langle n\left|(\hat{q_H}\hat{H}-\hat{H}\hat{q_H})\right|k\right\rangle &= (E_k- E_n)q_{nk} \end{align}$$ where $\hat{q_H}$ is a position operator. I realise that this must be a pretty simple step for someone who is familiar with Dirac notation, but I'm not sure how the author has _unlocked_ the $\hat{H}$ from the $\hat{H}\hat{q_H}$? Any comments greatly appreciated as always.


title: Water Electrolysis Calculations

text: From Wikipedia (http://en.wikipedia.org/wiki/Water_electrolysis#Efficiency): > The electrolysis of water requires a minimum of 237.13 kJ of electrical > energy input to dissociate each mole. Each mole of water gives you 2 grams of Hydrogen and 16 grams of Oxygen (http://www.lenntech.com/calculators/molecular/molecular-weight- calculator.htm). The energy density of the Hydrogen is 141.86 MJ/kg (http://en.wikipedia.org/wiki/Energy_density#Energy_densities_ignoring_external_components). Calculation for 1 kg of water (55.55 moles): > Energy for electrolysis: 237.13 kJ * 55.55 = 13.173 MJ > > Energy released by Hydrogen combustion: 0.002 * 55.55 * 141.86 MJ = 15.76 MJ These calculations are not taking in account efficiency and energy loses, they are purely theoretical. In various Wikipedia articles there are claims regarding to electrolysis similar to following: > The energy required to generate the oxyhydrogen always exceeds the energy > released by combusting it. > > Electrolysis-based designs have repeatedly failed efficiency tests and > **contradict widely accepted laws of thermodynamics (i.e. conservation of > energy)** **First Question:** In theory (in practice we always have less efficiency and must take those in account), is there anything wrong with my calculation? **Second Question:** Can someone clarify to me the claims about laws of thermodynamics and conservation of energy - I do not see ANY CONNECTION between energy needed to electrolyze water and energy released by hydrogen combustion?


title: Non-Conservative Behaviour of Static Electric Field

text: Static electric fields are supposed to be conservative in nature and therefore give $0J$ work if traversed over a loop. However in the following problem I got non zero work by a static electric field. How can I explain this work ? ![enter image description here](https://lh4.googleusercontent.com/-S3oWGGy_30Y/UuLvVIXZnFI/AAAAAAAAAhE/kRutOGK9Q88/s1668-Ut/2014+-+2)   **Note :** This is done in field of line charge, diagram shows a cuboid type structure but that is just for differentiating between traversed path and line charge. I am writing some of the important parts/equations here, but I have written the whole derivation here. $$W_{AB} = \frac{q\lambda}{4\pi\epsilon_0} [ln|\frac{(\sqrt{(L)^2+(r_1)^2}+L)(r_1)}{(\sqrt{(\frac{L}{2})^2+(r_1)^2}+\frac{L}{2})^2}|]$$ $$W_{BC} = \frac{q\lambda}{4\pi\epsilon_0}[ln|\frac{(\sqrt{(\frac{L}{2})^2+(r_1)^2}+(\frac{L}{2}))(r_2)}{(\sqrt{(\frac{L}{2})^2+(r_2)^2}+(\frac{L}{2}))(r_1)}|]$$ $$W_{CD} = \frac{q\lambda}{4\pi\epsilon_0} [ln|\frac{(\sqrt{(\frac{L}{2})^2+(r_2)^2}+\frac{L}{2})^2}{(\sqrt{(L)^2+(r_2)^2}+L)(r_2)}|]$$ $$W_{DA} = \frac{q\lambda}{4\pi\epsilon_0}[ln|\frac{(\sqrt{(L)^2+(r_2)^2}+(L))(r_1)}{(\sqrt{(L)^2+(r_1)^2}+(L))(r_2)}|]$$ $$W=W_{AB}+W_{BC}+W_{CD}+W_{DA}$$ $$W = \frac{q\lambda}{4\pi\epsilon_0} [ln|\frac{(\sqrt{(\frac{L}{2r_2})^2+1}+\frac{L}{2r_2})}{(\sqrt{(\frac{L}{2r_1})^2+1}+\frac{L}{2r_1})}|]$$ If field were to behave conservatively $W=0$ must have been satisfied, but unless $r_1 = r_2$, $W \neq 0$. Thus field is not behaving conservatively. PS : This is not a homework question ! I am trying to explain the behaviour.


title: Projectile Motion Question involving a ball and a ramp inclined at an angle

text: The question is to finde the initial horizontal velocity of the ball at end of the ramp, where it is released. I know how to do this using gravitational potential energy and kinetic energy ($v=\sqrt{2gh}$), assuming all potential energy is converted into kinetic energy but the question is asking me to find the error in the experiment. It gives me the values on $y$ as the ramp is lifted up (it is lifted up about 10 cm each time) and the corresponding values of $x^2$. I drew a graph of $x^2$ vs $y$ and found the gradient. How can I use this to find the experimental initial horizontal velocity? This sketch shows what the experiment looks like: ![Experiment](http://i.stack.imgur.com/RfGvy.png)


title: Colors of light

text: White light is always said to contain all the different wavelengths of light. Why, then, can we 'make' new colors simply by adding wavelengths? Is it just a matter of our perception, that, when two colors are added together, they appear to be the wavelength of another color. Or are the waves actually forming into another, differently 'waving' wave, with a different wavelength?


title: is walking on ground identical to walking on treadmill

text: For the same speed and inclination, is the physics acting on the body equivalent? Lets assume the person keeps pace with something that moves perfectly uniformly.


title: Prove that negative absolute temperatures are actually hotter than positive absolute temperatures

text: Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in the sense that if a negative- temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system).


title: Proof of existence of lowest temperature $0 K$

text: Im mathematics there is a concept of infinity meaning that whenever you pick a number and say that it is the smallest/Largest there is a way to further reduce/increase that number by subtracting/adding any other number. But in physics/chemistry i see that the absolute temperature does not have a negative reading and the lowest temperature is $0 K$. What is the proof that temperatures below zero cannot exist?


title: Negative temperature

text: How can we prove that if a negative-temperature system is in contact with a positive-temperature system, then the heat flow from the first to the second (and finally, the temperature of the second increases) ? I haven't found a proof on the Internet...