title: Can a glass window protect from heat radiation?

text: I have been reading in this and found a statement saying : " Glass will not transmit heat radiation.". So now I am confused. If glass won't transmit heat radiation, then why do we feel hot when we sit in front of a glass window in a sunny day ? Also, why do we find the car seats facing the windshield so hot in a sunny day ? One other thing, let's say a nuclear detonation happened somewhere nearby and I was standing behind a glass window, will this window protect me from thermal or heat radiation effects of the bomb ?


title: Are composite bosons always bosonic (e.g. the pion-cloud surrounding the nuclei)?

text: The $\pi$-meson is a boson, but consists of quark-antiquark (fermions). It seems to me that at some energy level (equivalently distance) the inner structure (fermionic nature of the quarks) of the particle in question should become important and the bosonic nature less so. Question:   Can we have a bunch of pions occupying the same quantum state at all temperatures, or is this model bound to fail due to the fermionic nature of its constituents? I'm thinking for example of the pion-cloud (in some models) surrounding the nuclei. EDIT: I found this question which is very related to the present one. Although I should add that my question (regarding the pion-cloud) is more specific and less general.


title: Are images of three-dimensional objects also three-dimensional?

text: Suppose that I produce an image of a dog using a converging lens. I can draw ray diagrams for the nose of the dog as well as the back leg. These are definitely longitudinal points, not transverse. However, one typically captures a two-dimensional image of the dog using some screen. But isn’t this dog really a three-dimensional image? If so, how would one capture such an image?


Meteorilogical stations in my country report relative humidity. I am not sure why as this is actually misleading, as relative humidity will change with temperature. Unless I miss my guess, what is important for human feeling is a dew point. How can I calculate dew point from relative humidity and temperature? PS: I have found quite a nice tool: http://www.dpcalc.org/


title: Definition of Fluctuations and Perturbations

text: The terms _fluctuations_ and _perturbations_ are frequently used in physics with different meanings. But they are confusing. Both terms seems to be same. Is there any one who can explain lucidly these terms and show difference between these two terms?


title: Relation between wavenumber and propagation constant

text: What is the exact difference between wavenumber and propagation constant in an electromagnetic wave propagating in a medium such as a transmission line, cause i am a bit confused. Does it have to do with loss in the medium?


title: Query regarding interference

text: In Young's Double Slit experiment, why is it that two waves vibrating perpendicular to each other doesn't show interference? I know that for interference to happen, the waves must be coherent ( i.e., they maintain a constant phase w.r.t each other) and if the waves meet at same point in the screen it results in constructive interference and destructive if there is a phase change of lambda/2 and so on. Any help regarding the query would be nice.


title: How to obtain the distance traversed by a free falling body equation?

text: I know that the distance that a free falling body has traverse through time is given by $d=0.5*g*t^2$. I would like to know how to get to this equation to study a bit more how it was obtained. I have been searching around with any luck. Could anybody give any tip?


title: Glass that only allows light of specific amplitude to pass through it

text: Is there a type of glass, mirror or lens that allows only lights of amplitude equal to or greater than a fixed value to pass/reflect through them?


title: Are all central forces conservative? Wikipedia must be wrong

text: It might be just a simple definition problem but I learned in class that a central force does not necessarily need to be conservative and the German Wikipedia says so too. However, the English Wikipedia states different on their articles for example: > A central force is a conservative field, that is, it can always be expressed > as the negative gradient of a potential They use the argument that each central force can be expressed as a gradient of a (radial symmetric) potential. And since forces that are gradient fields are per definition conservative forces, central forces must be conservative. As far as I understand, a central force can have a (radial symmetric) potential but this is not necessarily always the case.


title: Quantum mechanics and Couder experiments

text: Couder experiments ( https://www.youtube.com/watch?feature=player_embedded&v=W9yWv5dqSKk and https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf), published in 2006, state that by dropping silicon droplets into a vertically vibrated bath, we can observe the whole paths of these droplets and see how interference works out. 1) Wouldn't this violate the uncertainty principle that states that $\sigma_x$ or $\sigma_p$ can never be zero? The only way I could imagine is that $\sigma_p$ becomes infinite. Can any experiment produce the case where $\sigma_p$ is infintie quantum-theoretically? (and is this paper's conclusion - that $\sigma_p$ is infinite during the experiments?) 2) This experiment is macroscopic; but some people are saying that this in fact reveals much about quantum world, and I am curious how macroscopic observation be directly applicable to microscopic world. 3) We all know that photons behave differently; we cannot see photons until they hit the screen and we can only know their interference patterns. We have to try to measure them before they hit the screen, but then interference is destroyed both in reality and in theory. Does this experiment imply that there might be a way to see the whole path and the interference pattern of photons together? 4) The path taken by each droplet seems still probability issues - while we can see them, there is no way we can predict exactly where the droplet goes. Does this experiment in any way reopen the question like Einstein's dream of determinism?


title: Infrared remote flashes blue light in camera

text: I know that if you held an infrared remote in front of a digital camera, it'll flash a blue/purplish light when you press the buttons. Why?


title: Velocity Time Dilation

text: In Wikipedia article about time dilation, it says: "Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners...the moving clocks were expected to age more slowly because of the speed of their travel." Is it really true? My belief was that only acceleration/deceleration takes effect when comparing two clocks in the same frame after certain kinds of motions. According to my belief, I thought the time difference of two clocks in the aforementioned test is the same regardless of the length of the flight, if we ignore the difference of gravitational potential caused by different heights.


Is there any true inertial reference frame in the universe? Newton's first law states that an object at rest remains at rest, and an object performing uniform motion performs uniform motion, until and unless acted upon by an external force, if viewed from an inertial frame. It is the definition of an inertial frame of reference. And Newton's second law states that the net external force acting on a particle equals its mass times its acceleration. Thus we need to have an inertial frame in order for Newton's 1st and 2nd laws to be applicable. Scientists claim that Earth is an inertial frame, either the ECEF frame or the ECI frame. Why is that? Earth's different parts have different accelerations when it performs rotational motion about its axis. Now you may say that Earth's axis is inertial, but the Earth is also revolving around the Sun. Thus Earth's frame should be non-inertial. Even supposing that earth's frame is inertial, then it means that rest of the universe is non-inertial, because only a frame that moves with constant velocity with respect to an inertial frame is also an inertial frame and according to various scientific experiments there is no other matter in this universe which satisfies that criterion. Now you may say that earth is an approximate inertial frame, but still, my question is: is there any perfect inertial frame in the universe where Newton's laws are exactly applicable?


title: confused about ball rolling and rotational energy

text: I was solving a practice test problem and it was just a conservation of energy problem where a spherical ball is falls from a height h to the ground such that $$mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$$ what I can't quite picture in my head is how there is an energy contribution from the rotation at a fixed point in time. obviously there is a instantaneous rate of change of the center of mass $$v_{cm} = \frac {d \vec {x_{cm}} }{dt}$$ for any fixed point in time in my head I can see this as contributing to energy but the angular velocity can't be similarly treated like it is all at a point $$ \vec{\omega} = \frac{d\ \vec{\theta} } {dt}$$ here i understand this vector of angular rotation exists but I am confused as to why it adds to the energy of the system I just somehow can't wrap my head about energy of rotation when there is already some energy due to the center of mass' translation... i'm not sure exactly why sorry if this is vague but I figured i'd ask if someone has some way to think about this. maybe in terms of DOF's?


title: determine temperature at which pita bread will expand in a toaster

text: suppose you have a pita pocket of radius 5cm or .05m. We will model the pita pocket as consisting of disk with a layer of air of volume V which is contained by the surface of the bread. We will assume that no cracks or perforations exist in the pita pocket. supposing the thickness of the pocket is d = .5cm = .0025m. we can calculate the volume from the radius and thickness of the disk $V_{pita}$ = $\pi r^2d$ suppose that the pita contains a volume of air inside $V_{air} = \frac {V_{pita}}{5}$ and that the rest of the volume of the pita is a solid. Model the forces and pressure that cause the pita to expand. at what temperature will the air pressure inside be able to break the bonds holding the top sides of the bread together and allow it to expand under your models assumptions? rough order of magnitude estimates are fine--- but all answers should agree with experimental values of pita expansion as a function of Temperature


title: How to quantize the free electro-magnetic field in 2d?

text: I am wondering how one can quantize the free electro-magnetic field in the two dimensional space-time. The standard method of fixing the Coulomb gauge in 4d does not seem to generalize immediately to 2d. If one tries to generalize it directly then, as in 4d, after a gauge transformation one may assume that the scalar potential vanishes. Thus $A_\mu=(0,A_1)$. Then the Maxwell equations imply easily that $$\frac{\partial A_1}{\partial x^0}\equiv C=const$$ where $x^0$ is the time coordinate. Hence $A_1(x)=C x^0+h(x^1)$. Now one can apply a gauge transformation such that $h$ will vanish: $A_\mu(x)=(0,Cx^0)$. **Thus there is no degrees of freedom to quantize!!** **Another problem is that the expression $\frac{1}{q^2+i0}$ which appears in the free photon propagator in 4d, is not well defined in 2d** for purely mathematical reasons if I understand correctly (there is no such generalized function: the problem in at $q=0$). Is there a treatment of this in literature? Actually the above question was motivated by my attempt to read J. Schwinger's paper "Gauge invariance and mass, II", Phys. Review, 128, number 5 (1962). There he studies QED in 2d (so called Schwinger's model). Is there a more modern and/or detailed exposition of this paper?


title: differential equation with periodic conditions

text: given the differential operator Eigenvalue problem $ -D^{2}y(x)=E_{n}y(x) $ with boundary periodic conditions $ y(x)=y(x+1)$ my question is if there is a similar probelm for the Dilation operator $ T= xD $ with 'D' the derivative respect to 'x' i mean solve $ T^{2}y(x)=E_{n}y(x)$ with dilation periodic condition my question is how can i impose PERIODIC conditions but not for the traslation group (Yx+1) but for the Dilation group, i believe that some periodic conditions involving dilations would be $ y(x)=y(2x)$ but i am not sure how can i impose PERIODIC conditions if the LIe group is just the Dilations in 1-D ?? thanks.


title: Online QFT video lectures

text: I'm aware of Sidney Coleman's 1975/76 sequence of 54 lectures on Quantum Field Theory. Are there any other high-quality QFT lecture series available online?


title: Lagrangian of 2D square lattice of point masses connected by springs

text: Zee's QFT book mentions the Lagrangian of a square 2D horizontal lattice of point masses, connected by springs, and considering only vertical displacements $q_{i}$, as $ L = \frac{1}{2} \sum\limits_{a}(m \dot{q}_{a}^{2}) - \frac{1}{2} \sum\limits_{ab}(k_{ab}q_{a}q_{b}) - \frac{1}{2} \sum\limits_{abc}(g_{abc}q_{a}q_{b}q_{c}) - ...$ I have done elementary exercises in Lagrangian Mechanics, using $\frac{1}{2}k(l-l_{0})^{2}$ as the potential energy of the springs, but, after naively trying to derive (with which I mean "to build") that Lagrangian by myself, I suspect I must be missing some kind of additional cross- contributions to the potential energy (and I have no idea where did that triple products $q_{a}q_{b}q_{c}$ emerged from...). I know this is the _abc_ of solid state physics, that gives rise to the phonons and other interesting stuff, but I am almost completely ignorant in that area. Can anybody at least put me in the right track on how to derive (i.e. to build, departing from some given assumptions) that Lagrangian? NOTE: In other words, say you want to _build_ that Lagrangian, considering only vertical movements of the masses. The kinetic energy term is obvious, but for the potential energy, is it enough to naively sum $\frac{1}{2}k(l-l_{0})^{2}$ of all the springs? (of course written as a function of the $q_{i}$). Or, perhaps, is there any additional contribution to the potential energy that comes from the fact that the springs are somehow having some influence on each other? * * * EDIT with some remarks: Remark 1: A somewhat similar approach to what I am looking for, can be found for a linear chain of atoms, here (Ben Simons, Notes on Quantum Condensed Matter Field Theory, chapter 1) Remark 2: Thanks very much for correcting my misuse of the english word "derive". Ok, a Lagrangian is not derived. When I say "to derive a Lagrangian" I want to mean "to build a Lagrangian departing from some assumptions" like is the usual approach. For example, I can build the Lagrangian from a double pendulum from the assumptions that the masses of the rods can be neglected and there is no friction, and so I simply add the kinetic energy of the two masses and subtract their gravitational potential energy.


title: Quantum Conservation versus classical conservation

text: If energy is conserved in all quantum mechanical interactions, how are there classical interactions in which energy is _not_ conserved, given that classical interactions are a macroscopic approximation to the quantum mechanical interactions?


title: Could micro black holes obey the Eddington limit?

text: A stellar-mass black hole has recently been discovered in the Andromeda galaxy. One interesting part of the release is that this black hole shines close to its Eddington limit. > Quasars are supermassive black holes shining at or near the Eddington > luminosity, and microquasars are likely stellar-mass black holes whose > accretion is similarly close to the theoretical maximum. Wikipedia derives the equation for the Eddington limit (although I'm not sure about the applicability of its assumptions to small black holes) to be proportional to $M$. The Hawking radiation from a black hole goes as $1/M^2$. This implies that a cross-over point where both formulas calculate the same power. I can calculate this to be about $4 \times 10^{10} kg$. What would be an accurate picture of a micro black hole, given sufficient matter around to feed it? I think that the Eddington limit is a balance between the gravitational pull and the radiation pressure, but in the case where Hawking radiation is present, would the picture be significantly different?


title: What does "equinox of date used" mean?

text: The documentation for an API I often use for quick astronomical modeling and figure drawing says > Positions are given in FK5 heliocentric coordinates in the equinox of the > date used. What does "equinox of the date used" mean. Does it simply mean that the epoch for a value at time $t$ is $t$, rather than some other time (e.g. J2000)?


title: Semiconductor problem: how much Boron is required to establish a certain amount of charge carrier density

text: The problem description is as follows: > Boron is used to dope 1 kg of germanium (Ge). How much boron (B) is required > to establish a charge carrier density of 3.091 x 10^17 / cm^3. One mole of > germanium has a volume of 13.57 cm^3 and weighs 72.61 gram. Give answer in > grams of boron. I'd like some advice on how this problem should be solved. I've tried finding the conductivity first, but it seems that this practice exam did not have a graph for the Hole Mobility (I suppose a Hole Mobility vs. Impurity Concentration graph), so I assumed there must be another way of solving this.


title: Difference between voltage and potential energy in a capacitor

text: I'm confused about the difference between voltage and potential energy in a capacitor. Suppose you have a capacitor with a voltage V and capacitance C, and you release a particle with charge $+Q$ from the positive end of the capacitor. Is the potential energy of the particle that gets converted to kinetic energy $(1/2)CV^2$ or $QV$? What is the difference between these two quantities?


title: How to obtain Maxwell's Lagrangian from complex scalar fields?

text: I've looked in several books and they all show how to obtain electrical interactions by forcing local gauge invariance of any complex scalar field Lagrangian (like Klein-Gordon or Dirac). I manage to separate the new Lagrangian into the original one (the free Lagrangian) and the interaction part of it. But how I get Maxwell's Lagrangian from this? As the fields that are inserted to keep the Lagrangian gauge invariant should have it's dynamics described by Maxwell's. So, how to does the term $F^{\mu\nu}F_{\mu\nu}$ enter the new Lagrangian naturally? Thanks


title: Why 3 dipole terms in a multipole expansion?

text: As can be seen on this page http://en.wikipedia.org/wiki/Multipole_expansion when we take a multipole expansion _without_ assuming azimuthal symmetry we end up with $2l+1$ coefficients for the $l^{th}$ moment in the expansion. So the dipole moment has 3 terms, the quadrupole has 5 and so on. This is different to the case of azimuthal symmetry as each we need only one co- efficient for each term. Interpreting 3 coefficients for the dipole moment isn't too bad. I'm guessing it represents the dipole moments along the 3 Cartesian axes? And how do we interpret having to have $2l+1$ coefficients for each term?


title: Luminosity distance from angular diameter distance

text: Consider that I know the cosmological angular diameter distance at a given redshift : $$D_{A}\left(z\right)=\frac{x_{object}}{\theta_{observer}}$$ Is there a general formula to compute the luminosity distance $D_{L}$ from $D_{A}$ without assuming an homogeneous cosmology ?


title: First and second order phase transitions

text: Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article (at the time of writing) starts by explaining that Ehrenfest's original definition was that a first-order transition exhibits a discontinuity in the first derivative of the free energy with respect to some thermodynamic parameter, whereas a second-order transition has a discontinuity in the second derivative. However, it then says > Though useful, Ehrenfest's classification has been found to be an inaccurate > method of classifying phase transitions, for it does not take into account > the case where a derivative of free energy diverges (which is only possible > in the thermodynamic limit). After this it lists various characteristics of second-order transitions (in terms of correlation lengths etc.), but it doesn't say how or whether Ehrenfest's definition can be modified to properly characterise them. Other online resources seem to be similar, tending to list examples rather than starting with a definition. Below is my guess about what the modern classification must look like in terms of derivatives of the free energy. Firstly I'd like to know if it's correct. If it is, I have a few questions about it. Finally, I'd like to know where I can read more about this, i.e. I'm looking for a text that focuses on the underlying theory, rather than specific examples. The Boltzmann distribution is given by $p_i = \frac{1}{Z}e^{- \beta E_i}$, where $p_i$ is the probability of the system being in state $i$, $E_i$ is the energy associated the $i^\text{th}$ state, $\beta=1/k_B T$ is the inverse temperature, and the normalising factor $Z$ is known as the partition function. Some important parameters of this probability distribution are the expected energy, $\sum_i p_i E_i$, which I'll denote $E$, and the "dimensionless free energy" or "free entropy", $\log Z$, where $Z$ is the partition function. These may be considered functions of $\beta$. It can be shown that $E = -\frac{d \log Z}{d \beta}$. The second derivative $\frac{d^2 \log Z}{d \beta^2}$ is equal to the variance of $E_i$, and may be thought of as a kind of dimensionless heat capacity. (The actual heat capacity is $\beta^2 \frac{d^2 \log Z}{d \beta^2}$.) We also have that the entropy $S=H(\\{p_i\\}) = \log Z + \beta E$, although I won't make use of this below. A first-order phase transition has a discontinuity in the first derivative of $\log Z$ with respect to $\beta$: ![enter image description here](http://i.stack.imgur.com/n5nNt.png) Since the energy is related to the slope of this curve ($E = -d \log Z / d\beta$), this leads directly to the classic plot of energy against (inverse) temperature, showing a discontinuity where the vertical line segment is the latent heat: ![enter image description here](http://i.stack.imgur.com/gvTuX.png) If we tried to plot the second derivative $\frac{d^2 \log Z}{d\beta^2}$, we would find that it's infinite at the transition temperature but finite everywhere else. With the interpretation of the second derivative in terms of heat capacity, this is again familiar from classical thermodynamics. So far so uncontroversial. The part I'm less sure about is how these plots change in a second-order transition. My _guess_ is that the energy versus $\beta$ plot now looks like this, where the blue dot represents a single point at which the slope of the curve is infinite: ![enter image description here](http://i.stack.imgur.com/j3btZ.png) The negative slope of this curve must then look like this, which makes sense of the comment on Wikipedia about a [higher] derivative of the free energy "diverging". ![enter image description here](http://i.stack.imgur.com/xEbg0.png) If this is what second order transitions are like then it would make quite a bit of sense out of the things I've read. In particular it makes it intuitively clear why there would be critical opalescence (apparently a second-order phenomenon) around the critical point of a liquid-gas transition, but not at other points along the phase boundary. This is because second-order transitions seem to be "doubly critical", in that they seem to be in some sense the limit of a first-order transition as the latent heat goes to zero. However, I've never seen it explained that way, and I have also never seen the third of the above plots presented anywhere, so I would like to know if this is correct. If it is correct then my next question is _why_ are critical phenomena (diverging correlation lengths etc.) associated only with this type of transition? I realise this is a pretty big question, but none of the resources I've found address it at all, so I'd be very grateful for any insight anyone has. I'm also not quite sure how other concepts such as symmetry breaking and the order parameter fit into this picture. I do understand those terms, but I just don't have a clear idea of how they relate to the story outlined above. I'd also like to know if these are the only types of phase transition that can exist. Are there second-order transitions of the type that Ehrenfest conceived, where the second derivative of $\log Z$ is discontinuous rather than divergent, for example? What about discontinuities and divergences in other thermodynamic quantities and their derivatives? Finally, as I said, I'd really appreciate pointers toward a good resource on this stuff, where the focus is on the behaviour of thermodynamic variables and statistical quantities near phase transitions in general, rather than on working through specific examples.


title: Thermal Dynamics Conduction Comparison

text: I didn't have to take much physics for my advanced college degree, so I apologize if my question is painful. From reading and experience it seems that water is a better thermal conductor than air. I wish to verify this as well as know how water compares against: alloys, pure metals, and oil. If my question is too general, please school me on what additional knowledge I should know to ask a better question. :) **Edit:** So doing some searching, I found http://www.coolmagnetman.com/magcondb.htm which gives a good break down of resistance of different metals. This lead me to some googling, which lead me to wikipedia's http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity The wiki looks to mention the water's resistance depends on the amount of salt, which makes sense, as I believe salt is an electrolyte. The wiki also has a reference of "drinking water" which is compared to the other types. It clearly looks to be that metal conducts better. From https://van.physics.illinois.edu/qa/listing.php?id=1854 it looks like pure metals conduct better than alloys. I'm still not sure how oils fit in the comparisons though.


title: Find the Unit Vector of a Three Dimensional Vector

text: How can I find the unit vector of a three dimensional vector? For example, I have a problem that I am working on that tells me that I have a vector $\hat{r}$ that is a unit vector, and I am told to prove this fact: > $\hat{r} = \frac{2}{3}\hat{i} - \frac{1}{3}\hat{j} - \frac{2}{3}\hat{k}$ I know that with a two-dimension unit vector that you can split it up into components, treat it as a right-triangle, and find the hypotenuse. Following that idea, I tried something like this, where I found the magnitude of the vectors $\hat{i}$ and $\hat{j}$, then using that vector, found the magnitude between ${\hat{v}}_{ij}$ and $\hat{k}$: > $\left|\hat{r}\right| = \sqrt{\sqrt{{\left(\frac{2}{3}\right)}^{2} + > {\left(\frac{-1}{3}\right)}^{2}} + {\left(\frac{-2}{3}\right)}^{2}}$ However, this does not prove that I was working with a unit vector, as the answer did not evaluate to one. How can I find the unit vector of a three- dimensional vector? Thank you for your time.


title: Kinetic energy and potential energy variation over distance in SHM

text: When you compute the average potential energy of a horizontal spring mass system from the mean position to the positive amplitude A, the value comes out to be $\frac{1}{6}kA^2$. For the average kinetic energy over the same range and direction, it is $\frac{1}{3}kA^2$, which is double the average potential energy. What the physical explanation of the different average values of PE and KE? P.S. No mathematical explanations please, i.e. area under the graph, etc, only explanations in terms physics of the event are appreciated. The question does not involve time averages of PE and KE. Snapshots of derivations can be uploaded if requested.


title: How to perform a scale (invariance) transformation?

text: According to this wikipedia article in the $\phi^4$ section, the equation $$\frac{1}{c^2}\frac{∂^2}{∂t^2}\phi(x,t)-\sum_i\frac{∂^2}{∂x_i^2}\phi(x,t)+g\ \phi(x,t)^3=0,$$ in 4 dimensions is invariant under $$x\rightarrow \lambda\ x,$$ $$t\rightarrow \lambda\ t,$$ $$\phi\rightarrow \lambda^{-1}\ \phi.$$ I have a problem seeing this, which might be because I don't really know what to do with the derivatives. If I just replace $\phi(x,t)$ by $\lambda^{-1}\ \phi(\lambda x,\lambda t)$, then I get $$\frac{1}{c^2}\lambda^2\lambda^{-1}\frac{∂^2}{∂(\lambda\ t)^2}\phi(\lambda x,\lambda t)-\lambda^2\lambda^{-1}\sum_i\frac{∂^2}{∂(\lambda\ x_i)^2}\phi(\lambda x,\lambda t)+\lambda^{-3} g\ \phi(\lambda x,\lambda t)^3=0,$$ which doesn't work out. If I compare with the last section then this seems to be what one should do. Because In that case $$x\rightarrow \lambda\ x,$$ $$t\rightarrow \lambda\ t,$$ $$\rho\rightarrow \lambda\ \rho,$$ $$u\rightarrow u,$$ and therefore the naviar stokes equation with $$...+\rho\ u\ \nabla u+\mu\ \nabla^2 u+...$$ is such, that its invariant if the derivative produces an additional $\lambda$, the way I did above. Sidenote: is _scale invariance_ $\phi(x)=\phi^{-\Delta}(\lambda x)$ of fields something that should more acurately be called self similarity? Also, I don't understand the last sentence in the $\phi^4$ paragraph, which says that the dimensionlessness of the coupling $g$ is "the main point". Why is it a problem to also scale the coupling? However, I never understood why dimensionless couplings are prefered anyway. If the coupling is somehow unique, then why does it make sense to search for a process dependend coupling in renormalization theory?


title: How do I account for the direction of friction acting on a spring?

text: I would like to set up the equations of motion for a simple spring oscillator. Let's have a spring lying horizontally; we attach a small mass $m$ to the (massless) spring. The force of the spring on the mass is $$F_\text{spring} = - k x$$ where $k$ is the spring constant, and $x$ is the displacement from the position of rest. Since I am considering the system in motion, I only need to account for the kinetic friction. I know that the magnitude for the kinetic friction is: $$F_\text{fric} = F_g \mu$$ where $\mu$ is the coefficient of kinetic friction, $F_g$ equals the Normal Force on the surface and is also equal to the gravitational force. But the direction of the force is always antilinear to the direction of motion. How do I set this up correctly in my approach for the equations of motion? My approach is $$m a = -k x - \operatorname{sign}(x) F_\text{fric}$$ where $a$ is the acceleration of the mass point, and $\operatorname{sign}$ is the sign function. Is this correct?


title: What un-ionizes an electron after the photo-electric effect?

text: In an x-ray tube, the atoms in the anode are ionized by incident electrons "knocking" their K-shell electrons out of orbit. Following this, an outer- shell electron decays to fill the vacancy. Now: > An atom remains ionized for a very short time (about $10^{-14}$ second) and > thus an atom can be repeatedly ionized by the incident electrons which > arrive about every $10^{-12}$ second. (NDT) What causes the un-ionization, if there's another $10^{-12}$ second until the next incident electron arrives?


title: About constructing potential energy functions

text: There are many classical systems with different potential functions. My problem is that I do not understand how one can construct a certain potential function for a certain system. Are there any references I can look up in order to understand how the potential functions must look for a system that I am interested in building?


title: Regulating the sum in Casimir Force

text: I am trying to evaluate the Casimir force using a Gaussian regulator (I know there are other much easier ways to do this, but I want to try this!) We then are reduced to evaluating the sum $$ \sum\limits_{n=1}^\infty n e^{-\alpha n^2} $$ Moreover, I am interested in the series expansion of the above sum around $\alpha = 0$. Any ideas how I would go about obtaining this sum? PS - I don't want to use the Euler-Mclaurin formula.That was used to show that a general regulator would always give one the same answer, so this would just be a special case of the that proof and not a very novel way. Any other ideas?


title: Measurements from inside conductors

text: We have known for some time now that when electric field is applied across any conducting shell, then electric field inside it would be zero. It also has some fantastic applications such as electrostatic shielding. However, is it possible to know for sure that the field inside a conductor becomes zero? For example, if we place a transmitter inside a conducting shell to resolve whether the field inside shell is non-zero or otherwise, won't it disturb the field setup while transmitting the message? In other words, is it possible to be sure about this effect for a uniform conducting shell, and similar closed-body structures?


title: What is spin stiffness?

text: I read the defination of spin stiffness here ![enter image description here](http://i.stack.imgur.com/Odf86.png) But I can't understand how to twist an angle. Any help will be appreciated!


title: Long range repulsion in anomalous solids

text: As far as I know things like rocks, walls, rubber balls, polished tables etc. exert a short range repulsive force on other everyday objects that is responsible for hardness, softness, collisions, friction etc. Take a pair of electrically neutral solid materials. I am not interested in pairs of magnetic materials or astral bodies. Related to this I have a question: Are there any such pairs with significantly longer range repulsions? So significant, in fact, that we can observe them repelling each other at large macroscopic scales. Could such materials have applications like anti-gravity?


title: Translate a two dimensional classical Dirac theory to a (1+1)-dim quantum theory

text: Suppose I have a two dimensional _classical_ Dirac Hamiltonian with $\Psi=(\psi_1,\psi_2)^T$: $$ H=\int \mathrm{d}x \mathrm{d}y \Psi^\dagger(\sigma^x i\partial_x+\sigma^y i\partial_y+m\sigma^z)\Psi. $$ The partition function is given by $$ Z=\int[\mathrm d\psi^\dagger][\mathrm d\psi]e^{-H}. $$ How can I relate it to a (1+1)-dim _quantum_ system? A simple replacement $x\rightarrow t$ seems to be wrong. Because in the standard (1+1)-dim Dirac action, the time derivative term must be $\Psi^\dagger\partial_\tau\Psi$, i.e. with identity matrix in front of the time derivative, to ensure the conjugate momenta of $\Psi$ is just $i\Psi^\dagger$.


title: Is String Theory formulated in flat or curved spacetime?

text: String Theory is formulated in 10 or 11 (or 26?) dimensions where it is assumed that all of the space dimensions except for 3 (large) space dimensions and 1 time dimension are a compact manifold with very small dimensions. The question is what is assumed about the curvature of the large 3 space and 1 time dimensions? If these dimensions are assumed to be flat, then how is String Theory ever able to reproduce the equations of General Relativity which require curved space time in the presence of mass-energy (of course, the actual source term for General Relativity is the stress energy tensor). On the other hand if String Theory is formulated on a general curved space- time with an unknown metric (usually signified by $g_{\mu\nu}$) how do the equations of General Relativity that puts constraints on $g_{\mu\nu}$ arise from string theory? It is well known that General Relativity requires a spin-2 massless particle as the "force mediation" particle (similar to the photon as the spin-1 massless force mediation particle of electromagnetism). It is also well know that String Theory can accommodate the purported spin-2 massless particle as the oscillation of a closed string. But how does this graviton particle relate to the curvature of the large dimensions of space-time? I am aware that " How does String Theory predict Gravity? " is somewhat similar to this question, but I do not think it actually contains an answers to this question so please don't mark it as a duplicate question. I would especially appreciate an answer that could be understood by a non-theoretical ("String Theory") physicist - hopefully the answer would be at a level higher than a popular non-mathematical explanation. In other words, assume the reader of the answer understands General Relativity and particle physics, but not String Theory. _Update from Comment to Clarify: If you start with flat space then $g_{\mu\nu}$ isn't the metric tensor since you assumed flat space. If you start with arbitrarily curved space why would and how could you prove that the components of the graviton give you the metric tensor? I am interested in the strongly curved space case since that is where GR differs the most from Newtonian gravity. In flat space you could sort of consider weak Newtonian gravity to be the result of the exchange of massless spin-2 particles. But strong gravity needs actual space curvature to be equivalent to GR._


http://io9.com/5744143/particles-can-be-quantum-entangled-through-time-as- well-as-space http://arxiv.org/abs/1101.2565   1. How to make timelike entanglement in the laboratory?   2. How to test whether mixed state exist in time series or control system in math?


title: What happens to internal energy in high-density materials?

text: Normal-density materials have internal energy, which is the sum of the average energies associated to each of the degrees of freedom. Degrees of freedom can be described as vibrational, translational, and rotational. If you compress this material in such a way that matter cannot escape, you can detect energy escaping in the form of heat. Now imagine an extremely high-density material such as a neutron star or black hole. I suspect it's not possible to describe the internal energy of (or anything about) an individual atom inside a black hole, since it's impossible to inspect beyond the event horizon, and since I assume that atoms don't exist in an distinguishable form there. But presumably the atoms _had_ energy when they became part of the thing. How is that energy accounted for?


title: Strange behavior and motion of bubbles in a glass of beer

text: _Very unintuitive observation:_ I pour myself a Guinness and the bubbles in my glass seem to move down toward the bottom of the glass instead of rising directly to the top of the glass as foam. How can this be explained? Why is it that I observe this behavior drinking Guinness and not other carbonated drinks? What system properties (ie, temperature, nature of the solute and solvent) would affect this behavior?


title: Pendulum question

text: > A small ball of mass $m$ is connected to one side of a string with length > $L$ (see illustration). The other side of the string is fixed in the point > $O$. The ball is being released from its horizontal straight position. When > the string reaches vertical position, it wraps around a rod in the point $C$ > (this system is called "Euler's pendulum"). Prove that the maximal angle > $\alpha$, when the trajectory of the ball is still circular, satisfies the > equality: $\cos \alpha = \frac{2}{3}$. ![Illustration](http://i.stack.imgur.com/2HcJU.png) In the previous part of the question, they asked to find the velocity at any given angle $\alpha$, and I solved it right using the law of conservation of energy: $V_{\alpha}=\sqrt{gL(1-\cos\alpha)}$ Now, they ask to find the maximal angle at which the ball will still be in circular motion. The ball is in circular motion as long as the tension of the string is not zero. Therefore, we should see when the tension force becomes zero. So I did the following: In the radial axis we have the tension force and the weight component (it might be negative - depends on the angle). So the net force in that direction equals to the centripetal force: $T_{\alpha}+mg\cos\alpha=m \frac{V_{\alpha}^2}{L}$ If we substitute the velocity, we get: $T_{\alpha}=m \left(\frac{V_{\alpha}^2}{L}-g\cos\alpha \right)=m \left[\frac{gL(1-\cos \alpha)}{L}-g\cos\alpha \right]=mg(1-2\cos\alpha)$ When the tension force becomes zero: $0=1-2\cos\alpha\\\ \cos\alpha=\frac{1}{2} $ And that's not the right angle. So my question is - why? Where's my mistake? I was thinking that maybe I've got some problem with the centripetal force equation, but I can't figure out what's the problem. Or maybe the book is wrong? Thanks in advance.


title: Do WIMPs have to interact non-gravitationally with each other or other particles?

text: I know many collaborations are attempting to detect the interaction of WIMPs with nucleons or with themselves, with the recent result from Ice Cube (http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.131302) showing no evidence for WIMP self-interaction. I am wondering if WIMPs might actually have zero non-gravitational interaction with SM particles and zero self- interaction. Is such a thing possible or likely? If so, what sorts of theories predict such WIMP candidates, and could they be detected indirectly by other means (e.g., cosmological ratio of WIMP mass-energy to ordinary matter mass- energy, or something like that)?


title: Bend or concentrate magnetic field?

text: What are the ways to modify the form of magnetic field from the permanent magnet? For example I have a permanent neodymium magnet. Its magnetic field is distributed at large volume around the magnet, with decreasing strength at larger distances from the magnet. I'd like to make it concentrated in very small distances around this magnet, and to have no field or largely less strong field beyond some given distance from the magnet. Is it possible at all, and if yes, how?


title: Particle production channels [s,t] in HEP?

text: In high energy physics there are different channels of particle production: t-channel, s-channel. What do they mean? And are there any other channels besides "t" and "s"?


title: Is a purely vertical or almost vertical orbital launch possible?

text: Is it possible, for the sake of argument, to launch a payload into an orbit around the earth by putting almost all the energy going at a 90 degree angle? What velocity would it take, and what horizontal orbital burns would you need?


title: Is a plasma necessarily made of monoatomic ions?

text: Is it possible to have a plasma made of polyatomic ions instead of monoatomic ions? I want to know all the details why such a thing may be attainable or not and, if possible, what methods we can use to create such a substance.


title: Static electric charge

text: When some materials are chafed one to another, they obtain opposite electric charges. Does it mean that if these materials will then be connected to the ground, the direct currents of opposite direction will occur? And if we put some dc device like a lamp in the open of wire connecting statically charged material with the ground, should it light until the static charge is gone?


title: Amplitude decrease during geometrical spreading of a seismic pulse

text: I'm looking at amplitude decrease of a seismic pulse as a result of geometrical spreading. Starting with the energy contained in a unit area, $I = E / (4 \pi r^2)$, where $E$ is the original energy from source, we know that energy falls off as $1/r^2$, thus amplitude falls off as $1/r$. From Wikipedia: > "The energy or intensity decreases (divided by $4$) as the distance $r$ is > doubled" This makes sense to me, as when $r$ is doubled we have the energy divided by $(2r)^2 = 4r^2$ (which is $4 \times r^2$). From this same principle, I would expect that the amplitude is divided by 2 when the distance is doubled as we have $1/2r$ instead of $1/r$. However from a Louisiana State University website: > Geomteric spreading makes the amplitude of a signal falls off in proportion > to the distance traveled by the ray. So that if the path of flight is > doubled the amplitude will decrease by a factor of ${\sqrt 2}$. I can't see how they got their factor of $√2$ instead of $2$. Is there a mistake or am I missing something?


title: How to measure resistance of DI water

text: It is known that good DI water have resistance ~20 MΩ·cm But how can I measure that? Using good vanilla ohmmeter (with 2000 MΩ range) showed crazy results (too low, not much dependent from distance between probes). I need that to compare DI water from 2 sources.


title: What does the $y$-axis represent in the atomic spectra and what is its significance?

text: ![enter image description here](http://i.stack.imgur.com/TgQNG.jpg) The picture is an emission spectrum of Helium. The spectrum has sharp lines (peaks) at certain wave lengths characterizing it as helium. Agreed that it characterizes Helium as atomic spectral line characterize gases and they are based on allowed energy states of electrons in an atom. Well and good, but what i don't know is the $y-axis$. what does it represent? It is shown as intensity (counts) but I want to know what it is and how does it vary from element to element. Does this count also characterize the elements, or is it same for all elements? Appreciate if you could throw some light on it. Question : I mean if i keep the position of lines(pulses) same but change their relative amplitudes, what happens? does it represent a different gas? Picture taken from the internet.


title: Does it take a lot of energy to heat metals up?

text: Why does it take a lot of energy to heat metals? And to do it quicker it requires much more energy? What about the use of lasers would that be an efficient process that is quicker and requires less?


title: Can the compactified dimensions of M-Theory/String Theory become uncurled?

text: ![enter image description here](http://i.stack.imgur.com/H2nRB.jpg) Is it possible for the curled dimensions described in superstring theories to become uncurled and open up. I have read that the big bang could have been the uncurling over 3 dimensions through collisions of branes: http://universe- review.ca/I15-39-collision.jpg. Is their any theoretical mechanism that causes this uncurling of dimensions?


title: Help me to visualize this wave equation in time, to which direction it moves?

text: The wave is $\bar{E} = E_{0} sin(\frac{2\pi z}{\lambda} + wt) \bar{i} + E_{0} cos(\frac{2 \pi z}{\lambda}+wt) \bar{j}$ Let's simplify with $z = 1$. Now the xy-axis is defined by parametrization $(sin(\frac{2\pi }{\lambda}+wt), cos(\frac{2\pi }{\lambda} + wt)$ where $t$ is time and $\lambda$ is wavelength. This parametrization satisfy the equation $1^2=x^{2}+y^{2}$, a circle. Now, let's variate the value of $z$. We know now that it cannot move into x or y coordinates or do we? Not really, the latter simplification is naive -- $x-y$ parametrization depends on the dimension $z$ -- but can we see something from it? If so, how to proceed now? The solution is that the wave moves along the $z$ -axis to the negative direction as $t$ increases, a thing I cannot see. The way I am trying to solve this kind of problems is:   1. Parametrize the equation   2. suppose other things constant and change one dimension, observe   3. check other variable ...now however I find it hard to parametrize the $z$ so a bit lost. So how can I visualize the wave with pen-and-paper?


title: Spaghettification while still in orbit

text: THIS POST does a pretty good job of giving an idea as to what the differences in forces becomes as you approach a black hole. For a small enough black hole, you would reach the dangerous tidal force distance before you reached the event horizon, which means you could have a stable orbit around the black hole near that dangerous distance. So to prevent from getting torn apart, you could lay down like a plank, facing the black hole while orbiting in the danger region, the differences in force on different parts of your body would be uncomfortable but survivable. But if you suddenly extended an arm towards the black hole, that arm would have a dramatically different force acting on it. Assuming you are far enough so it doesn't quite rip your arm off, would this sudden change in forces acting on your body change your orbit? My initial thought was that since you haven't changed your momentum or center of mass at all, your orbit would remain the same. Then I realized that since the gravitational force is proportional to 1/r^2, that means that even though your COM is the same, the total force acting on your body has increased by stretching your mass out perpendicular to the gravitational body, which means your orbit would change right? How would it change your Apoapsis and Periapsis, if you started in a perfect circular orbit? As a follow up question IF you can change your orbit this way: Could you build a machine(and thus higher tolerances than any human) that could orbit a black hole, and just by moving its mass around at the right times in orbit, change its orbit dramatically?


title: interpretation of $\{H,L^2\}$

text: In Hamiltonian mechanics, we show $\\{H,L_z\\}=0$, which can be interpreted as the conservation of angular momentum around $Oz$. Following the same idea, how can we interprete $\\{H,L^2\\}$? Is the interpretation the same (or _only_ similar) as in quantum mechanics for $[H,L_z]$ and $[H,L^2]$?


title: Image Reconstruction:Phase vs. Magnitude

text: Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. $$ f(x,y)= ∑_(u=0)^(U-1)∑(v=0)^(V-1)\ |F(u,v)| exp^(1j*2Π*xu)/M) * e^(1j*2Π*(vy)/N) / $$ Figure 1.(d) shows the Test image reconstructed from PHASE spectrum only. We can say that intensity values of HIGH frequency (edges,lines) pixels are comparatively more than LOW frequency pixels. Why this magical contradiction of intensity change (or exchange) is present between Test image reconstructed from MAGNITUDE spectrum only and Test image reconstructed from PHASE spectrum only, which when combined together form the original Test image? $$ f(x,y)= ∑_(u=0)^(U-1)∑(v=0)^(V-1)\ exp(j*angle(u,v)) *exp^(1j*2Π*xu)/M) * e^(1j*2Π*(vy)/N) $$ ![enter image description here](http://i.stack.imgur.com/nIRwF.png) ![enter image description here](http://i.stack.imgur.com/J5Xlb.png)


title: Why diaphragm in diffraction experiment using electrons is quantum object?

text: In the book _Quantum Mechanics - Volume 1_ written by Albert Messiah, page no. 142-143, author says: > _...But the diaphragm is a quantum object, just like the electron. Its > momentum is not defined to better than dp...._ I did not understand why diaphragm is a quantum object ? Also, it is not clear to me what author says below, > _....One must postulate that the measuring apparatus is a quantized object > which also obeys uncertainty relations....."_ On the other hand, N. Bohr says that measuring apparatus is always a classical object (i.e. instrument which follows rules of classical mechanics). Any CLEAR explanation?


title: What is the minimum pressure of a medium for which a sound wave can exist?

text: At what pressure will be particles in a medium be unable to form a sound wave when disturbed? How can this pressure be described mathematically? My guess is that this would correspond to the point at which the restoring force due to pressure is unable to create a transverse wave and the disturbed particles travel infinitely far away before the hypothetical wave reaches it's amplitude. But I have no idea how you would even begin to start finding a quantitative value for this point.


title: Anyons: Effect of braiding on fusion multiplicities

text: In the theory of non-abelian anyons, essential information is stored in the fusion multiplicities or Verlinde coefficients $N_{ab}^c$. Having the Pants Decomposition in mind, it is possible to use these coefficients to calculate the dimension of the topological/fusion Hilbert space for $p$ anyons 3, which is $${\rm \ dim} H= \sum_{\\{a_i\\}}N_{b_1 b_2}^{a_1} N_{a_1 b_3}^{a_2}...N_{a_{p-3} b_{p-1}}^{b_p}$$. My question is: What is the effect of braiding of , for example, anyon 1 with anyon 2 on the dimension? What is the effect of a twist? Knowing that $N_{ab}^c=Z(S^2\times S^1; R_a, R_b, R_c)$ (Witten `89) braiding of anyons $a,b$ should give rise to a phase, when considering subsections 4.4 and 4.6 of 4 or chapter 18 of 5. Can this affect the overall dimension $dim H$?


title: A question related to tractrix

text: I'm a novice to physics, so maybe it's rather stupid. According to wiki, the tractrix could be considered a trajectory: Suppose $AB$ is a stick on a smooth plane $\pi$, and the initial position of $AB$ is $A_0B_0$. $\mathbf v$ is a vector on $\pi$ such that $\mathbf v\perp \overrightarrow{A_0B_0}$ (It's not necessary, but it simplifies the problem). Now let's drag $B$ side of the stick $AB$ such that the speed is constantly $\mathbf v_B=\mathbf v$, then the locus of $A$ is a tractrix. I tried to solve out the equation of that locus and then prove that it's a tractrix, but failed because I don't know the exact properties of a stick. Somebody told me that $\mathbf v_A\parallel\overrightarrow{AB}$ any time the stick is moving, but I can't prove that. Can anybody help me formulate all the properties of sticks (just as properties of $\mathbb N$ in Peano's axiom system), well, there're something trivial, for example, $\left\lvert\overrightarrow{AB}\right\rvert$ is constant, and prove that $\mathbf v_A\parallel\overrightarrow{AB}$? Thanks!


title: Water-cooled fast neutron reactors

text: Can anyone explain why fast neutron reactor designs use sodium/lead/salt cooling, instead of water (heavy/light)? Is that because neutron absorption by water would not allow to break even in fuel cycle? Will heavy water help here? Or water slows neutrons so efficienly so that even if we reduce amount of water inside the reactor (by increasing flow speed) - it still will significantly lower neutron energy, while sodium does not slowdown neutrons at all?


title: How could pinion in automatic quartz watch be rotated at 100K RPM?

text: Wikipedia article on automatic quartz watch describes the watch mechanism as follows: a rotating pendulum is attached to a pinion and when the wearer moves his hand the pinion is rotated at **_up to 100 thousand revolutions per minute_** and that pinion rotates an electric generator. AFAIK the fastest hard disk drives currently reach only 15K RPM and they have serious problems with heat dissipation - a fan is required for cooling the drive. How can a miniature pinion inside a watch be rotated at such speed without the whole assembly being worn out by friction in no time?


title: acceleration of the universe

text: Moments after the Big Bang, the universe was expanding at an incredible rate, (I've heard) faster than the speed of light. Due to dark energy, scientists predict the rate of expansion will pick up again. Space itself will be expanding faster than light speed. Someday, we will not be able to see other galaxies because they'll be moving away so fast that the light they produce will never reach us. Nowadays, though, we can see other galaxies, which means the expansion of the universe slowed down. What caused the expansion of the universe to accelerate more slowly? If dark energy is causing the acceleration to increase, wouldn't the universe continue to expand faster after the big bang? Is there a **minimum rate** of acceleration? If so, what is it, and what determines it?


title: What is the momentum of these emitted photons?

text: `5 x 10^7 kg of radioactive material emits energy in the form of photons of red light (700 nm). (Note: photons have no mass.) What is the momentum of each photon?` We just started a new chapter, and in the process of learning it, I came across this question in the back of our book, which I am really having trouble understanding right now. Can anyone suggest how I can go about solving this (note, I would like to actually work out the problem myself; however, I need a sufficiant place to start.) Obviously, the Newtonian equations like `p =m/v` will not apply here, so I'm somewhat stuck at the moment... Any help is much appreciated, thank you.


title: Finding the appropriate source term for 2D Pressure Driven Flow in a Square Channel

text: I'm trying to solve the equation: $$ \frac{\partial^2 v_z(x,y)}{\partial x^2} + \frac{\partial^2 v_z(x,y)}{\partial y^2} = \frac{\Delta P}{\mu \Delta X} $$ This flow is supposed to be flowing in a square channel (laminar,steady,fully developed). I know I need to solve it numerically and if there was no source term I could just take the average of all four points around each node and get my answer. The problem is that I need to find the appropriate source term and I honestly don't know how to start. I also know I need to make the equation dimensionless. I know the source term can't be found analytically and I honestly am lost there. Can someone explain what the source term is and how I can start my quest to find it?


title: Many world interpretation on test

text: Is there any experiment conducted to prove Many world interpretation of Quantum mechanics? If it can't be proved why we should take MWI seriously? Recently I read some papers of Max Tegmark who is an advocate of MWI and avoids the lack of experimental prove. I think this is the same question as mine. What about the two arxiv papers this and this?


title: How to implement wedge product and form in quantum mechanics?

text: For example use p-form for p identical fermion system? * * * The Maxwell equations can be rewritten as a single function using forms plus an intrinsic equation showing the Faraday tensor is a two form. This happens because forms are antisymmetric and we can construct an antisymmetric Faraday tensor which contains all the information we need to describe a pure electromagnetic system. In quantum mechanics, we use tensor product space to describe some many- particle or many-freedom systems. Sometimes it is cute to use forms to describe an antisymmetric quantity such as the wave function of fermions. So do we use wedge product and forms massively in some quantum mechanics topics?


title: What arguments are in favour of an atomic structure to space-time?

text: The atomic theory as first theorised by Democritus has been successfully applied to matter and to energy (quanta). Space-time is still generally seen as a continuum. What arguments are there (if any) in support of there being a particulate structure of space-time?


title: Are there any non-interpretational arguments in favour of Everett's Many-Worlds?

text: As far as I understand Everett's Many-Worlds Interpretation, he makes the case for a realist theory of QM at the enormous cost of many-worlds. Are there any arguments in favour of Everett's interpretation that makes the case for his theory one a purely instrumental or operational view - in that certain calculation look easier or more 'elegant'?


title: What would happen if you put your hand in front of the 7 TeV beam at LHC?

text: Some speculation here:   http://www.youtube.com/watch?v=_NMqPT6oKJ8 Is there a possibility it would pass 'undetected' through your hand, or is it certain death? Can you conclude it to be vital, or only loose your hand? Would it simply make a small cylindrical hole through your hand, or is there some sort of explosion-effect? Assume your hand has a cross section of 50cm², and a thickness of 2cm, how much of the beam's energy would be transferred to your hand?


title: Why does $H_2$ form on such a long time scale?

text: If we were trying to figure out the time scale for a gas-phase reaction between two hydrogen atoms in a molecular cloud (which has density $~10^4/$cm$^3$), apparently the reaction would happen on a time scale proportional to the inverse of the density multiplied by $10^{15}$ years. Aside from the cloud not being dense and the probability that a collision will surpass the activation energy is small, is the time elongated because you need to induce a dipole moment between two hydrogen atoms to actually bind them together?


title: Division algebras $(\mathbb{R,C,H,O})$ and discrete symmetry

text: I once saw a statement about the relation between division algebra(which means you can define a division in this algebra, there is a theorem saying we only have 4 kinds of division algebra, real R, complex C, quaternion H and octonion O) and discrete symmetries, saying that the number of discrete symmetries(I mean time reversal, charge conjugate and parity) is limited because we only have 3 kinds of associative division algebra(octonion O is not associative, I guess the associativity is related to physical operation, since all physical operation is associative, I mean ABC=A(BC)). This statement seems to be very interesting and deep, however, I don't know much about this. Just want to attract you physicists attention and give some comments or explanation about this. Thank you very much! For more about division algebra: http://en.wikipedia.org/wiki/Division_algebra#Associative_division_algebras http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(normed_division_algebras)#Hurwitz.27s_theorem


title: Is physics rigorous in the mathematical sense?

text: I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics: Is there a set of axioms to which it adheres? In Mathematics, we have given sets of axioms, and we build up equations from these sets. How does one come up with seemingly simple equations that describe physical processes in nature? I mean, it's not like you can see an apple falling and intuitively come up with an equation for motion... Is there something to build up hypotheses from, and how are they proven, if the only way of verifying the truth is to do it experimentally? Is Physics rigorous?


title: Resistances in a circular loop

text: ![enter image description here](http://i.stack.imgur.com/B7pBq.png) I have no idea what formula I'm supposed to use.I just want to know the concept that would allow me to get the answer. I know basic concepts of electricity like charge, currents, etc., but as far resistances go I know only about series and parallel. I tried looking for resistances in a circular loop but I didn't understand what was being explained. Also I didn't find any concept that helped me understand what was to be done, probably because I didn't understand them.I used some help from a different question and got the resistances but my answer wasnt correct.


title: Electrons of conductors Free?

text: Are electrons of any conductor really free ? I mean are they always already moving or do they move only when electrostatic field of some sort is applied across them. I suppose if they were always moving each and every conductor must have some varying magnetic field around it at all times which though negligible musy be detected. Is that really so ? Or are the so called free electrons not really free ? Also is there some other experiment which i do not know about by which we have already proven that they are always moving ? does it take into account the earths and other electric fields which may be causing that movement ? Addendum : the question is not duplicate of Are free electrons in a metal really free as that post talks about ease of electrons to interact with external fields, my question is about the nature of motion of electrons in absense of external field interference as in are electrons in free motion even when they are not under the influence of any electromagnetic field.


title: can resistance be found without knowing length?

text: ![enter image description here](http://i.stack.imgur.com/X9MiJ.png)is it possible to find to resistance without knowing the length? i am tryigng to solve a problem that requires me to find the resistance.I cant seem do so without knowing the length of the circuit which is not given.Is there something that shows resistance without knowing the length or am i just looking at problem all wrong?other details include: resistivity of the upper resistance=4ohm metre,resistivity of the lower resistance=2ohm metre,battery emf V=10pi ohm, radius of the circle=1m,angle between A and B is 60.is there a special relation between resistances in parallel?


title: Has this boundary condition been used in fluid flow?

text: I would like to know whether anyone has seen a boundary condition used in a fluid flow problem, of the following type. Suppose viscous incompressible fluid is to the left of a plane $x_1=a$, so the outer normal to the fluid region is $n=(1,0,0)$. The condition specifies that the $x_1$ momentum flux is a nonnegative multiple of the velocity: $$ m\begin{bmatrix} u_1\cr u_2\cr u_3\end{bmatrix} = \begin{bmatrix}\rho u_1^2+p-2\mu u_{1,1} \cr \rho u_2u_1-\mu(u_{1,2}+u_{2,1}) \cr \rho u_3u_1-\mu(u_{1,3}+u_{3,1}) \end{bmatrix} $$ where $m$ could be a number $\ge0$ or even a nonnegative 3 by 3 matrix. (This is connected with my question at http://www.mathoverflow.net/q/163772/) Thanks for any references.


title: momentum conservation and gluons

text: The process is the following: $$e^-e^+ \rightarrow photon \rightarrow quark + antiquark$$ Regarding the momentum conservation law, how come we have a photon of spin 1 and at the end some meson with spin 0? Are gluons "behind this"? If this is correct, at which point are they radiated? From quarks? Or? Is this photon a virtual photon or not? I'm a bit confused here.


title: Misner String Singularity

text: 1. In correspondence to AdS black hole solutions, what does it mean by Misner string singularities? And when there are no Misner string singularities, what does this mean in terms of curvature singularities and event horizons and the black hole in general?   2. A related question (as far as I'm aware), what do we do if our solution contains closed timeline curves (CTCs)? Should we really only consider cases when our solution doesn't contain closed timelike curves and strictly impose restrictions on our parameters that ensure this?    3. (While on this topic, an elementary question, why does $g_{\phi \phi}<0$ imply CTCs, if we're in hyperbolic 4d space?)


title: For which temperatures are the ENDF cross-sections given?

text: In ENDF there are cross-sections given for different types of nuclear interactions. For example, this file gives the cross-sections for different neutron energies. However, it is not clear, which temperature of the medium itself (not the neutron gas) is implied. Is there a way to know, for which temperature are those cross-sections given. Or maybe to know the cross-section values for different temperatures of the medium.


title: What exactly is a virtual displacement in classical mechanics?

text: I'm reading Goldstein's Classical Mechanics and he says the following: > _Avirtual (infinitesimal) displacement of a system refers to a change in the > configuration of the system as the result of any arbitrary infinitesimal > change of the coordinates $\delta \mathbf{r}_i$, *consistent with the forces > and constraints imposed on the system at the given instant $t$*. The > displacement is called virtual to distinguish it from an actual displacement > of the system ocurring in a time interval $dt$, during which the forces and > constraints may be changing._ Then he discusses virtual work and so on. Now, I can't grasp what this thing of virtual really is. By this text there's a diference between one infinitesimal change and one virtual change and I really don't get what this virtual really is. Also, this is based on infinitesimals. How can this be expressed rigourously without refering to infinitesimals? I tried looking on Spivak's Physics for Mathematicians where he considers these virtual displacements as tangent vectors to a certain manifold, but I'm not sure this is the most "standard" way to do it rigorously.


title: Rotating platform with pulleys and stacked blocks

text: This was a practice test question. > Consider the following figure. (If the frictional coefficients are unclear, > between A and B we have $k_1 = 0.3$, B and platform is $k_2 = 0.2$. If you > further doubts about the diagram ask me in the comments below and I will > clarify.) ![enter image description here](http://i.stack.imgur.com/PRMA5.jpg) > The blocks are resting on the rotating platform (bold) attached to the rod > which is rotating at constant angular velocity $\omega\ \mathrm{rad/s}$. The > masses of blocks and distances from the pulley are as given in the figure. > The distance of the pulley from the rod (axis) is negligible. Block B is on > verge of slipping. Find $\omega$. What I did : Let mass of $A = m_1$. Distance of $A$ from axis = $r_1$. Mass of $B = m_2$. Distance of $A$ from axis = $r_2$. If block $B$ is on verge of slipping $A$ is also on the verge of slipping. Questionable observation. But leads to correct answer. Anyway, we consider a rotating frame attached to the rod. So we give a centrifugal force to $A$ = $m_1 \omega^2 r_1$ and to $B$ equal to $m_2 \omega^2 r_2$. Tension in string $ = T$. We check two cases. Let $B$ slip inwards. Then $A$ slips outwards. So $A$ slips rightwards relative $B$. $A$ was on verge of slipping. Static friction on $A = k_1 m_1 g$. Static friction on $B = k_2 (m_1 + m_2) g$. Then equating forces and solving the system and putting values we get $ \omega = \sqrt{22}\ \mathrm{rad/s}$. The other case ($B$ goes outwards) leads to contradiction. Though the result is correct, I have a few questions. Why does the fact that $B$ is on the verge of slipping imply that $A$ is also on the verge of slipping. I mean, suppose we just eliminate the rotation and add an external force on $B$ instead. Let the magnitude of force reach $k_2 (m_1 + m_2) g$. Then why is it necessary that the force of static friction between $A$ and $B$ is $k_1 m_1 g$ ? Am I wrong, and is it just that the answer matched, without correct physics? A detailed explanation of a solution to this problem would be very helpful as I'm a beginner, and I intend to clarify these essential concepts.


title: Why do ferromagnetic materials channel magnetic field lines?

text: I have read that the total magnetic field of a ferromagnet, $\vec{B} = \mu_0\vec{H}+\mu_0\vec{M}$ where $\vec{H}$ is an external magnetic field and $\vec{M}$ is the magnetic field of the ferromagnet due to the alignment of its dipoles to $\vec{H}$. On the other hand, I have read that ferromagnetic materials tend to "channel" and "concentrate" field lines. See, for example, the image below. With the solenoid alone, the shape of the magnetic field would be very different than the shape with the magnet included. The magnet has "channeled" the magnetic field lines of the solenoid. What explains this "channeling" behavior of ferromagnetic materials? In other words, is this explainable using the normal methods for magnetic field calculations such as Biot-Savart and treating the ferromagnet as consisting of infinitesimal dipoles or does the dynamic process of domain alignment need to be considered in calculating the final magnetic field? ![Magnet has affected the shape of the field due to the solenoid.](http://i.stack.imgur.com/TIlBw.png) Edit: In order to explain myself better, I have included two simulations from FEMM. One is a selenoid wrapped around an iron core which has geometry chosen to emphasis the channeling behavior I mention above. The second is identical to the first, with iron replaced with air. From the equation $\vec{B} = \mu_0\vec{H}+\mu_0\vec{M}$ I would expect the two simulations to have magnetic fields that have identical directions $(\vec{B_{iron}}/|\vec{B_{iron}}| = \vec{B_{air}}/|\vec{B_{air}}|)$ but these simulations show they do not. Why is this? ![Iron Simulation](http://i.stack.imgur.com/thqhb.png) ![Air Simulation](http://i.stack.imgur.com/FHSbF.png) Note the simulations are axisymmetric which means that they are treated as if the entire configuration is rotated around the left axis to form a three- dimensional problem.


title: How does an altimeter work?

text: In our aerodynamics class we recently discussed the concept of static and dynamic pressure and discussed their application to aircraft instruments. However, I do not understand properly how the altimeter can work. First of all a small recap of Bernoulli's law. The total pressure is given by $p_t = \frac{1}{2} \rho V^2 + p_s$ and is constant along a streamline. Consequently, the static pressure is given by $p_s = p_t - \frac{1}{2} \rho V^2$.   Now imagine a low speed windtunnel. In a reservoir the speed is so low that it can be assumed to be $V=0$ m/s. Hence here the static pressure equals the total pressure, $p_t = p_s$. Now the fluid is accelerated along a streamline, and hence the static pressure should drop according to the relation given above. Now this is where my problem is. I read that the altimeter just measures the static pressure at flight level to obtain the pressure altitude. According to the explanation given above, however, this can not be, as the static pressure in the flow will be lower than the static pressure at the same altitude at zero velocity.


title: What is the difference between a moment and a couple?

text: In mechanical engineering, the torque due to a couple is given by $\tau = P\times d$, where $\tau$ is the resulting couple, $P~$ is one of the force vectors in the couple and $d$ is the arm of the couple. A couple is made up of two forces of the same magnitude. On the other hand, a moment is also given by $M = P\times d$. However, there is only one force involved! How can the resulting torque be of the same magnitude if in one case two, in the other case only one force is involved?


title: How can a gas support tensile stresses?

text: In working through a rigorous derivation of the compressible Navier-Stokes equations, I find that the momentum flux in the X-direction should be driven not only by the normal pressure gradient $\frac{\partial p}{\partial x}$ and shear stress terms $\frac{\partial(\tau_{yx})}{\partial x}$ and $\frac{\partial(\tau_{zx})}{\partial x}$, but also by the gradient of the normal stress $\frac{\partial(\tau_{xx})}{\partial x}$. It's intuitively clear to me how adjacent lamina moving at different speeds can transfer momentum across their interface, and so the shear stress terms in the momentum equation are readily intelligible. The normal stress term, on the other hand, is far less intuitive because I cannot see how a freely-deforming fluid can support tensile stresses. Positive normal stresses (i.e. compression) are not that hard to understand, but it's proving exceedingly difficult to fully envisage an element of a fluid "pulling on" an adjacent element in a way even remotely analogous to the behavior of a solid under the same conditions. I am also unclear on the difference between "pressure" and "normal stress" in the fluid. How exactly are these terms different? I am interested primarily with gases not liquids.


title: If empty space has energy, and space is expanding, is this energy equally distributed as space expands?

text: The cosmological constant (dark energy) is often described in terms of empty space having a non 0 energy value and this energy being the source of the accelerated expansion of the universe. If space is expanding, what does this imply for energy conservation? Is this energy conserved by being more thinly distributed as space expands? Does this question make any sense or am I just crazy?


title: Explanation for different boiling points of water on different altitudes

text: I understand water boils at different temperatures depending on altitude. I am seeking to get an illustrative explanation for this, including a diagram if possible.


title: Information content of the expanding Universe

text: As I understand, in physics, 'information' is closely tied to thermodynamic entropy. Does this relationship imply that if the Universe expands and ends in 'heat death' (maximum entropy?) that it reaches a state of maximum information (so at the Big Bang it had very low entropy and information content)? I sense this is incorrect given the principle of conservation of information, so what does an increase in entropy in the Universe imply for its information?


title: Why does the state space contain states with negative norm and what would be an example?

text: My lecture script of Quantum Field Theory states that " the state space contains states with negative norm ". Why does it have to be like this and what would be an example fo such a state?


title: Why is electric potential 0 in this case?

text: On a test, we had a question where there are 4 point charges at the vertices of a square. The 2 charges at the upper vertices have charges of `+q` and the 2 charges at the lower vertices have charges of `-q`. The magnitude of the charges are equal. According to the answer sheet, the electric potential is 0 along a horizontal line halfway between the 2 upper and 2 lower charges. Why is it 0? Shouldn't the test charge be attracted to either to top or the bottom depending on its charge?               +q        +q          ------------    <--- 0 electric potential          -q        -q


title: Finding $\Delta p$ for discontinuous wave function

text: So I have a triangle Wavefunction defined as: $$\psi(x)=\begin{cases}x &0<x<\frac{L}{2} \\\ L-x &\frac{L}{2}<x<L\end{cases}$$ When I try to find the uncertainty in momentum, I find that it is zero. This cannot be possible by Heisenberg. So I am wondering if I have to (or how to) account for the discontinuity in the wavefunction when using the $\hat p$ operator.


title: An isolated Earth

text: It is known the fact that there is no way to extract energy (in any form) from any system without introducing some energy. The Earth for example, gets energy from the Sun, from nuclear fusion of hydrogen. But, what if the Earth would be isolated (there is neither an energy gain, neither loss), it would be possible for our lives to continue (without using an fuel on the Earth)? The idea of this question started from the quote "Nothing is lost, nothing is created, everything is transformed". As the energy remains inside the system, may it be transformed to be reused?


title: How absorption coefficient determines which material is used to make solar cells?

text: Does the knowledge of the material absorption coefficients aids engineers in determining which material to use in their solar cell designs? If yes, how?


title: What is elliptic genera?

text: What is elliptic genera in physics? Reading many relevant papers, they just defined elliptic genus as sort of partition function. I try to find useful materials to explain it, but I couldn't find it. Can you give some intuition for this terminology in physical view?


title: How do crocodiles jump?

text: In a video (Here), I saw crocodiles jump vertically about three meters without using any solid surface. The wonderful thing is that when they start to jump, their vertical velocity is approximately zero, unlike fish who jump using initial velocity. It seems that crocodiles create an upward force that counteracts gravity, because when they are rising, their velocity seems to be constant. How is this possible? Could anyone explain this phenomenon using physics laws?


title: Can a relativistic quantum particle be completely confined into a finite hole?

text: If we write the Klein-Gordon equation in this form \begin{equation*} c^2 \hbar^2 \nabla^2 \Psi = \hbar^2 \ddot{\Psi} + 2i\hbar (U - mc^2) \dot{\Psi} + U (2mc^2 - U) \Psi \end{equation*} we have a pleasant sense of continuity from the non-relativistic to the relativistic treatment of quantum particle (we use the Schrödinger formalism, and to get the NR solutions we only have to put $c\to\infty$). The (not Lorentz invariant) equation has to be handled with care because the manipulations I used in order to obtain it, included squaring conservation of energy, so we can get spurious solutions too. But I think that for zero-spin particles it works, because I found it in page 42 of Wachter's _Relativistic Quantum Mechanics_ (written slightly differently). If we suppose that $|\Psi|^2$ is stationary (i.e. the solution has the form $\Psi (\mathbf{r},t) = \psi (\mathbf r) e^{Ct} $ with $C$ purely imaginary) the equation takes the time-independent form: \begin{equation*} -c^2 \hbar^2 \nabla^2 \Psi = [U^2 - 2(E+mc^2)U + E^2+2Emc^2] \Psi \end{equation*} (if you are interested in the proofs search _sr.pdf_ in my Home Page, I don't transcribe here because, more than a question, this should become an article) **My question:** Suppose using this equation with a finite monodimensional hole: \begin{equation*} U(x) = \left\\{ \begin{array}{ll} -V_0 & \quad \textrm{if }-a<x<a\\\ 0 & \quad \textrm{if }|x|>a \end{array} \right. \end{equation*} In the internal region $\Psi$ is sinusoidal (with the not restrictive condition $E>-V_0$), but in the external region we get \begin{equation*} \Psi'' = k^2 \Psi ;\qquad k = \frac{\sqrt{-E (E + 2 mc^2)}}{c \hbar} \end{equation*} If $-2mc^2 <E <0$, $k \in \mathbb{R}^+$, otherwise $k$ is purely imaginary, the wave function is sinusoidal and the normalization is impossible. Not surprising that for $E>0$ we don't have stationary states with that finite hole, but:   * what about the case $E<-2mc^2$? What does it mean? The only reasonable interpretation I found, is that in this case the particle is totally confined into the hole. \- Is this wrong?


title: Equation of motion for a double pendulum

text: firstly I am a Grade 12 Physics student currently doing my final experimental investigation which I decided to do on double pendulums. Before I got into this, I was under the impression that there was some equation I could use which I could plug in my starting conditions such as starting angle, weight of pendulum arms, their lengths, and gravity to pull out a function of x and y against time. Now I am writing the report, it seems it isnt that simple and there is a lot of terminology used on sites that I am unfamiliar with and I really don't know what I am looking for. My maths/physics knowledge extends to know about integral/differentials, but nothing as complex as these Lagrangians, Hamiltonians or other university- level mathematical principles. I have researched many sites, such as Wikipedia, Wolfram ScienceWorld, and other physics stack exchange questions. However, I still have only a vague idea of what I am looking for. On the stack exchange question I linked, I became familiar with the dot notation. I guess my question is, what is the equation/function which I can use to find the path of a double pendulum given starting conditions. Looking at the wikipedia page shows me many equations of motion. Do I need the hamiltonian equations? The one linked on that stack exchange? The one on that stack exchange question uses $p_{\theta1}$ and its $p_{\theta2}$ equivalent which I don't know what they are either. Sorry if my question is not clear enough. Also, my teacher told me that I do not need to know the proof for the equation of motion, only that I include the final equation in my report to show how accurate my data is (which I know is off due to the chaotic motion).


title: Time-dependent perturbation - details in derivation

text: I get confused about two things when deriving the time-dependent perturbative approach. We have the Hamiltonian   $$H = H_0 + \lambda H^{(1)}$$ and we have solved (from Schroedinger)   $$\dot{C_f(t)} = - \frac{i}{\hbar}\sum_{k}\lambda C_k(t)H^{(1)}_{f,k}e^{i\omega_{f,k}t} $$   with the usual   $H^{(1)}_{f,k} = <f|H^{(1)_{f,k}}|i> $ and $\omega_{f,k} = \frac{E_f- E_i}{\hbar}$. Ok. Next I expand $$C_k(t) = C^{(0)}_k(t) + C^{(1)}_k(t)\lambda + C^{(2)}_k(t)\lambda^2 +...$$ Substituting that I get $$\frac{d}{dt}(C^{(0)}_k(t) + C^{(1)}_k(t)\lambda + C^{(2)}_k(t)\lambda^2 +... )= - \frac{i}{\hbar}\sum_{k}\lambda (C^{(0)}_k(t) + C^{(1)}_k(t)\lambda + C^{(2)}_k(t)\lambda^2 +...)H^{(1)}_{f,k}e^{i\omega_{f,k}t} $$ From this I am unable to see   **1) Why does the zeroth order correspond to $\lambda = 0$?**   To me this would feel like we have a situation where we have a variable, and for some reason we would be allowed to choose its value for the first term of the series? [As, it stays as a coefficient in the right side of the previous equation]   2) Ok, then if I set $\dot{C}^{(0)}_k = 0$ then I get the recursion relation $$\dot{C}^{(n)}_f(t) = - \frac{i}{\hbar}\sum_{k} C^{(n-1)}_k(t)H^{(1)}_{f,k}e^{i\omega_{f,k}t} $$ **Did we substitute $\lambda = 1$ in the last** , or what happened to lambda if not? (This is not stated in the sources that I try to study, but it's the only explanation I come up with right now)


title: Reflection Probability for Different Potentials - Quantum Mechanics

text: ![Question](http://i.stack.imgur.com/4Zvo3.jpg) My question is above. Firstly, I don't actually know whether it is true or not (!). Secondly, if I were to try to prove it, then I have very little idea how to. The potential steps that I have always done are steps from a constant level to another constant level (Heavyside), whereas this is different. I would imagine the answer is yes, but I'm not sure how to show it. Can I approximate the curve by small steps (/sums of Heavyside functions), and then show that a larger Heavyside step gives a larger probability? Thanks, Sam


title: Feynman's $i \epsilon$ prescription in loop expansion

text: I have some questions about the $i\epsilon$ factor in Feynman diagrams. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity? And third, Dyson series assume that incoming and outgoing particles are free, this can be implemented by assuming that the interaction Hamiltonian switches off adiabatically, $e^{-\eta\,t}H_{I}(t)$. Is this $\eta$ related with the $i\epsilon$?


title: Which Force would help find the mass?

text: A and B are connected to a rope. A constant upward force 86.0N is applied to box A. Starting from rest, box B descends 12.1m in 4.70s . The tension in the rope connecting the two boxes is 32.0N. What is the mass of B? What is the mass of A? ![enter image description here](http://i.stack.imgur.com/g90hu.jpg) * * * ## My work and what I am struggling with: I am trying to find the acceleration experienced by B, with that I will find the mass. I find the acceleration using: $$2\Delta_y/t^2=a$$ $$a=1.0955m/s^2$$ Then I have a problem for B do I use this equation: $$\sum F_y =32-M_b*g=M_ba$$ $$Or$$ $$\sum F_y =86-M_b*g=M_ba$$


title: Can we divide two vectors?

text: Can we divide two vector quantities? For eg., Pressure( a scalar) equals force (a vector) divided by area (a vector).


title: How to design a house to be cooled passively?

text: I live in Louisiana these days, in an area that is known for its numerous antebellum plantation homes (circa early 1800s). While touring one of these homes it was clear that almost everything about the house was designed around keeping cool in the summer. Some examples:   * 4 meter high ceilings to allow hot air to rise to the ceiling.   * Floor to ceiling windows to allow hot air at the top to escape and cool air to be drawn in at the bottom.    * Porches on the sunny sides of the house to prevent sunlight from entering the windows.   * Large central staircases to allow hot air to rise to the second floor, drawing cool air in on the bottom floor.   * Some have a cupola, a central observation room at the top of the house, again to allow hot air to escape at the top of the house and draw air in from the bottom. * * * My question is: Given our modern understanding of thermodynamics, how could one design a home today to be cooled passively? Could we do any better than the plantation owners of the 1800s? Lets define cooling as making the house more comfortable for humans. This means that it is not only important to reduce the temperature, but also to block sunlight and maintain airflow. Also, if possible, it would be very beneficial to extract moisture from the air.


Would an airplane flying through superfluid helium experience lift and drag? The airplane is presumed cold enough to not heat up the helium.


title: How can I determine transmission/reflection coefficients for light?

text: When light rays reflect off a boundary between two materials with different indices of refraction, a lot of the sources I've seen (recently) don't discuss the relation between the amplitude (or equivalently, intensity) of the transmitted/reflected rays and the original ray. Mostly they just discuss the phase difference induced by the reflection, for instance to calculate thin film interference effects. ![reflection/refraction diagram](http://i.stack.imgur.com/W8fL3.png) Is it possible to calculate the transmission coefficient $T$ and reflection coefficient $R$ based on other optical properties of the materials, such as the index of refraction? Or do they need to be looked up from a reference table?


title: Why the electric bulb turns on almost instantly when the switch is closed?

text: **The electron drift speed is estimated to be very low.How could there is current almost the instant a circuit is closed??**   ![enter image description here](http://i.stack.imgur.com/JOVuz.jpg) By the discussions it is known that **The information about beginning of the flow of current is transmitted through the propagation of electromagnetic waves(electric impulse)and not with the drift velocity of the electrons.**   But I want any one to explain how this process takes place.CURIE:)


title: How can I calculate the wave propagation speed in a copper wire?

text: First of all: I am a computer science student, so I don't have much knowledge of physics. So please keep your answers simple. I recently learned something about circuit design and its problems (differend kinds of hazards). To model the problems, we introduced a "dead time model" ("Totzeitmodel" in German, I have if it is "dead time model" in English)   We added some dead time to each element of the circuit, but we didn't add dead time to the wires of the circuit. I asked the prof. why we didn't add dead time to the wires. He responded that the signal is moving much faster and you can neglect the time that signals need to pass the wires. Now I would like to calculate the speed of the signal (is this the wave propagation speed?) for some very simple settings:   * assume we have a copper wire   * the wire is a perfect cylinder with diameter of 1mm   * the current is 2A   * the voltage is 12V Can you help me with this? Do you need something else to calculate the speed? * * * Notes: I found the wikipedia article Wave propagation speed and some questions on physics.stackexchange.com, but the questions and answers were either too complicated or didn't directly give numbers (like that one) A little side question: When I think about the electric signal, I imagine some elastic balls. When there is a signal at one end, you push the ball. It gets compressed and expands later, which compresses the next ball a bit and it expands, ... This way, the last ball gets moved and the signal arrives at the end. Do I have to get another thinking-model for simple circuits or will I be able to understand simple circuits with this model in mind?


Why turning velocity of star towards point "A" makes it's satelites, change their apoapsis to side opposite of velocity vector? Sentence above turned a bit crazy or not understandable (possible reasons: my vocabulary isn't that good; I don't know what the heck I am talking about). So I mean this: http://phet.colorado.edu/sims/my-solar-system/my-solar- system_en.html The first you get is star (yellow) and planet (purple). If you closely, you notice circle around star. It's velocity, if you move it in direction opposite to purple star. Purple planet get's crazy and flies away, as if star turns it's magnetic polar towards that planet.


title: Period of Precession

text: I'm trying to find the period of precession for a gyroscope. Now I was able to find the angular precession rate, which was 1.132 rad/s, but I have no idea how to convert this to a 'period', and google didnt find me anything useful. How do I do this?


title: Axisymmetric fluid flow

text: I'm having trouble with a boundary condition. In a fluid mechanics problem, I have flow at $z = \infty$ flowing into a solid plate at $z = 0$ and then flowing radially, and the problem is given as axisymmetric. I know that the velocity field has $v_r$ and $v_z$, and $v_\theta = 0$. How in the world would I express the symmetry boundary conditions without $\theta$?


title: Eddy Currents in Metal Implants

text: Related: Why is stainless steel a poor conductor of electricity? I recently had a metal implant, and I'm psyching myself out- should I be considered at all with eddy currents in the implant? I feel like the steel must be somewhat of a better conductor than my body, indeed in the above question it appears to be so. Couldn't eddy currents get painful?


title: Confusions regarding entropy

text: Help, I am terribly confused about entropy. On the one hand, I am taught at school that a substance such is an ice/solid has a lower entropy than its gaseous equivalent and that a process such as solidification reduces entropy, which is justified with the explanatory premise that the solid is more "ordered".   1. All this seems dogmatic to me, and it somewhat conflicts with my own intuition (probably means I am wrong). For one, if a change of entropy is measured with the equation (delta)S = q/T (btw, can anyone justify this equation / show its derivation?), take solidification - the heat content (q) falls so its exothermic, hence q is a knowable negative value (the enthalpy of fusion, if I am not wrong?) and T is the critical temperature at the given atmospheric pressure - however how about the entropy change when the temperature changes too - what if the change in the heat content results in a change in temperature - how is that measured.   2. Another idea that conflicts with my mind is why are solids/colder things said to have lower entropies at all? I understand from a statistical point of view why overall entropy increases, as things progress to chaotic, and this entails that the heat death of the universe will see maximum entropy - or another to express it: no work will be attainable from the system/universe. However, I am told that colder things have LOWER entropies? I can only intuitively understand entropy from a complete picture - where hot and cold mix to increase overall entropy - how can a part - like the cold area by itself (given it is uniformly cold so that its own potential energy, by itself, is null) even be given a entropy value? The same goes for the hot part - it only makes sense to be if we consider the entropy of the system as a whole when hot and cold are separate or mixed - but obviously, there must be something i don't get.   3. Could it be that I am confusing different kinds of entropies - btw (final point) if (in Chemistry at least) entropy is defined by change in heat content / temperature (in kelvins), then how could overall entropy ever decrease as the loss of entropy over there (via loss of heat content) would increase the entropy here (which compensates) and so on. This definition (for me) entails that entropy simply is transformed/passed on like energy. This clearly even conflicts with my own intuitive view of entropy as more of a measure of order, and hence attainable work from a system. You can see, I have many questions and if you know the answers but can't be bothered, do not hesitate to answer only a fraction of it all, I am grateful for anything. Thank you very much.


title: Current induced when dropping a magnet through a coil

text: When graphing the induced current in a coil while a magnet is dropped through it why is the total area equal to 0? The area represents the charge in the coil but why must the resultant flow of charge be 0?


title: Can life exist in intergalactic space?

text: A terrifying idea I think, to be so utterly alone. Do you recon life could exist in intergalactic space? A lot of cosmic radiation is shielded from us by the Milky Way's magnetic field, but the stars of galaxies also create a lot of radiation, so maybe it would cancel out for a planetary system floating in intergalactic space. Don't really see why not if its star is a high energy yellow dwarf. I'm talking if about if the system was magically transported to intergalactic space, but as a second part to this question, how could such a system be ejected out into the void in the first place? Super nova? Could life survive its planet being blasted out into intergalactic space? Could intelligent, advanced life, with foresight, be able to survive? What would they have to do to achieve this? Or could such a phenomenon happen gradually?


title: Lagrangian description of Brownian motion?

text: I'm interested in the existence of a Lagrangian field theory description of Bronwnian motion, does such a thing exist? Given a particle of some spin $\sigma$, which has a Lagrangian associated with it $\mathcal{L}_{\sigma}$ (which, using the Euler-Lagrange equations, produces Klein-Gordon for $\sigma$ = 0 etc) is there a way I can allow for Brownian type freedoms in this description? Hopefully such a stochastic freedom is allowed in the Lagrangian description. Any references would be warmly welcomed. Thanks!


title: Is Red-Shift experiment correct?

text: I been reading: http://www.mth.uct.ac.za/omei/gr/chap5/node2.html. The website seems credible with its contact details & location being extremely accurate and easily verified, and its mathematics seem correct so I have no doubt about it however in this thought experiment it devises a object falling then > observer has some magical method of converting all this energy into a photon > of the same energy [ this is a thought experiment after all! ] That seems slightly over-the-top expectations even for a thought experiment or is it perfectly credible and possible on contrary to my belief? I previously assumed thought-experiment had to be realistic yet this seems very un- realistic. Don't get me wrong I'm confident on this University and am sure that they have intelligent people but anyway is this though experiment for Red-Shift allowed even with its "magic" as some may call it?