title: Is there an equation for the magnetic field of a conductor attached to a magnet?

text: Let's say I have a hollow conductive rod, 10mm diameter (O.D.), and I place a magnet of known strength 50mm up the shaft. What is the microTesla (mT) or Gauss (G) of the magnetic field (or flux density, or whatever it would be) **of the shaft** 50mm away from the magnet attached to it? Here's what I'm attempting to do: I want to attach a magnet to my manual transmission's shifter lever, and then use hall effect sensors to detect it's position and display the selected gear on a display. I have the Arduino code written and the display wired. I'm having a problem understanding what sensitivity Hall Effect Sensors to get, what strength and size magnet(s) to get, and how to go about figuring how they relate to each other. Essentially, I don't want the magnet too close to the 6 Hall Sensors, nor do I want a huge, expensive magnet. I have 216 neodymium buckeyballs I can encircle the shaft with, if I used them would it matter which polarity I had them arranged in? If I used a single magnet, would I place the poles alongside or perpendicular to the rod? How would I go about ball-parking the mT of the magnetic field 50mm (or whatever distance) down the rod, away from the magnet to get an idea of the sensitivity (rated in mV/mT for the hall effect sensors)? How does a magnetic field propagate through a conductor? How would I position the magnet(s) to maximize the mT down the rod of my shifter? How do I place the Hall Effect Sensors (which read mT perpendicular to their face) to maximize the readings? Ideally, I'm hoping to place the magnet(s) far enough away that what I'm reading is the transmitted 'magnetism' of the rod itself, is this an improper way to look at it (or even possible)? If it's not, is it the case that I have to bring the actual magnets near the hall effect sensors, and I can't 'transfer' it to the rod?


title: Radioactivity and quantum superpositions

text: In the Schrödinger's cat experiment 'there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays'. The rest of the experiment magnifies this into a macroscopic superposition, but I want to know more about the claim that the radioactive decay produces a superposition. Firstly, has this been experimentally tested? Something along the lines of accelerating radioactive ions so there is a chance that they will decay while in flight (and so change trajectory), and then combining the decayed and undecayed parts to look for interference. Secondly, the tiny bit of radioactive substance will still contain large numbers of atoms. Won't this cause problems? If the atoms were in a Bose- Einstein condensate, then I would expect that there could be a superposition of 'one (unspecified) atom decayed' and 'no atoms decayed', but they're not, so a specific atom will decay. Won't that mess things up?


title: How to produce a loss-free combination of two "identical" beams?

text: This is for anyone with experience in optics/imaging/photography as well as anyone who likes to puzzle over tricky physics problems. As the title suggests, this is about combining two (for all practical purposes) identical light beams in an optical system to one beam of twice the intensity. Mind you, I'm not talking about monochromatic laser beams, although the underlying problem would be the same. As an example, imagine a fancy imaging system that you've constructed and with which you look at objects, which are fairly dim. Therefore, you'd like to enhance the image quality by collecting as much light as possible coming from that source by using not one, but multiple copies of your fancy device. You then project the beams from those device onto, let's say, a single CCD chip and thereby end up with a higher signal-to-noise ratio. You only have one camera available, so just buying a few extra cams and superposing the images on your PC is NOT an option. Now, the crux of this problem is: How does one combine multiple identical beams into one, while keeping the intensity loss (that one can certainly expect) to a minimum? In general, there seems to be two basic approaches to tackle this problem:   1. Don't bother with beam combining, instead, project the beams from different angles onto the CCD and somehow deal with the varying distortion/defocussing of the resulting images caused by the different angles of incident.    2. Try to combine the beams into one. You then won't have to deal with the troubles arising from different angles as in the first strategy.  Intuitively, I prefer option 2, but after pondering on it for a week, I found the problem of combining identical beams surprisingly non-trivial. Maybe anyone of you guys here has had to deal with a similar problem or maybe you just happen to have a really nice idea how to solve it. Let me know what you think, I will also try to explain some of the (flawed) ideas I had a bit later!


title: Quantum Quench Problem

text: I read about the quantum quench problem in condensed matter physics. But what does really mean? Has anybody a good explanation about the origin of quantum quench problem?


title: How does Kepler's laws and Newtons universal gravitation for two bodies come together?

text: Does Newton's laws of gravitation and Kepler's laws give exactly the same orbit for two bodies? Could someone please explain the derivation if so?


title: Four-current, Induced Charge and Magnetic Flux

text: I'm studying Jackiw's "Fractional Charge and Zero Modes for Planar Systems in a Magnetic Field" DOI: 10.1103/PhysRevD.33.2500 but I have difficulties at some points. One of the problems is $$\langle j^0\rangle=\pm\frac{e}{4\pi}B$$ where $j$ is four-current, $B$ is magnetic field. How can I derive this result (and why we used only $j^0$ component)?.


title: Can a single molecule have a temperature?

text: A show on the weather channel said that as a water molecule ascends in the atmosphere it cools. Does it make sense to talk about the temperature of a single molecule?


title: Can a magnet or a magnetic field push gravity?

text: I have been asking around at my school and at the high school and at EWU but no one can answer this question: can a magnet or a magnetic field push gravity?


title: Dispersion Relation (e vs. k) clarification (crystal momentum or electron momentum)

text: If we get the dispersion relation from the Fourier transform of the lattice vectors then how do we get electrons information? Specifically, for the $k=0$ point of the graph, does this mean the electron has zero momentum(I am pretty sure that electrons don't have zero momentum in that case due to Heisenberg's uncertainty principle)? I was thinking (since crystal momentum and electron momentum are different) that the $k$ is how the overall electrons wave packets move in regards to crystal momentum, or that crystal momentum dictates the electrons momentum. As you can probably tell I am still very shaky on this, so anything is really appreciated!


title: Why Thermodynamic cycles and no single process

text: Why Thermodynamic cycles are used to obtain work for example carnot engine rather than single isothermal process which is part of cycle and can be used to obtain more work.And why isothermal process do not violate second law even when there is no friction or any irreversibility.I know they violate second law in actual world due to friction .But in theory reversible processes are possible which do not violate second law,so why it doesn't.


title: What's wrong with Schwarzschild equations?

text: I don't know much about black holes physics and so I find the Schwarzschild equations with a few contradictions. In particular I am trying to understand this little puzzle. The Schwarzschild Newtonian gravitational field equation is expressed as follows (see http://en.wikipedia.org/wiki/Schwarzschild_radius): $\frac { r^2 }{r_s} \frac {g}{c^2} = \frac {1}{2}$ So once a particle is close to the event horizon such that $r\to r_s$ the equation becomes: $ r \frac {g}{c^2} = \frac {1}{2}$ But then at that point light cannot escape so I would think that $g\to c/t$ where $t=1 sec$. So the equation would now approximate to: $r = \frac {c/t}{2}$ But this implies that $r$ is generalized for all black holes regardless the mass. If $r$ is indeed $r\equiv r_s$ then that contradicts the other Schwarzschild formula where $r$ depends on $m$: $r_s = \frac {2 G M} {c^2}$ Also based on what we know about $r_s$ in massive black holes, a radius of 150,000 km is quite small. What's wrong with this picture?


title: How to analyse data that is in four dimension?

text: I have obtained a series of data that is about density distribution of liquid in three dimensions, density$=f(x,y,z)$. How can I know the detail information about the way that density changes with $x$ and $y$ and $z$? And how should I do to get the positions of minimum and maximum of liquid density?


title: How is black hole affected by gravity of nearby bodies?

text: I run into wikipedia articles about ergosphere of rotating black holes. What if some massive body passes nearby some black hole: is something like ergosphere produced, or is the event horizon distorted by the gravity of the passing body?


title: Calculation for force generated by a rotating rectangular blade

text: When trying to calculate the lift force generated by a simple rectangular blade, I've found the following equation: $$F = \omega^2 L^2 l\rho\sin^2\phi$$ in which $\omega$ is the angular velocity, $L$ is the length of the helix, $l$ is the width of the helix (both in meters), $\rho$ is the air density at normal conditions, and $\phi$ is the angular deviation of the helix related to the rotating axis. So a 4-helix propeller would lead to $F=4\omega^2 L^2 l\rho\sin^2\phi$ and so on. However, when I substitute the variables with real values, it seems to me very unreal. For example, if the 4-blades propeller works at $13000 RPM$, $\rho=1.293 kg/m^3$, $\phi=1^\circ$, $l=10^{-2}m$, $L=5\times 10^{-2}m$, leads to $$F=4\times(120\pi\times13000)^2\times(5\times10^{-2})^2\times(10^{-2})\times1.293\times(\sin1^\circ)^2$$$$\therefore F=9.46\times10^5N$$ So in this case, a simple $1cm\times 5cm$ propeller would carry $946 tons$ is surely wrong. So, where is the issue in the formulae? **Update** There was a mistake of my calculation, mr. @Mark Eichenlaub made me see this. The right calculation is $$F=4\times(2\pi\times13000/60)^2\times(5\times10^{-2})^2\times(10^{-2})\times1.293\times(\sin1^\circ)^2$$$$\therefore F=0.072995N$$ which is quite reasonable. So, for lifting a $0.5 kg$ load ($\implies P=9.81\times 0.5=4.9N$) we should get longer blades or change the $\phi$ inclination. Thanks.


title: Nano-particle or Molecule?

text: What's the difference between something being labeled a "nano-particle" or it being called a "molecule"?


title: Is a phase difference of 180 degree possible between emf and current?

text: While studying alternating currents I could read and observe through an oscilloscope that there can be phase difference between emf and current. But, is a phase difference of 180 degrees possible in a series LCR circuit?


title: Chosing a reference frame in which the earth is at rest and doesn't rotate

text: We may choose a non-rotating earth as our reference frame and ask ourselves: how about the planetary and stellar motions. A star at a distance of 10 million light years would turn around the earth in 24h with a velocity of 10^18 m/s. A friend once told me that actually articles have been published delving into this problem, e.g. to prove that fictitious forces emerge from the choice of such a bizar reference frame that ensure that the earth is still (somewhat) flattened at it's poles. Questions: 1) Does anybody know of such a publication? 2) I know that even such speeds of 10^18 m/s are not in contradiction with relativity because a limiting velocity only exists for exchange of information, which apparantly does not occur.   Still: could anybody explain why such bizar velocities are allowed?


title: What is the electrical field of a capacitor plate as a charge approaches

text: The electrical field for a charge density $\varrho(r)$ is $${\bf E}({\bf r})=\frac{1}{4\pi\varepsilon_0}\int \varrho({\bf r}')\frac{{\bf r}-{\bf r}'}{\hspace{.1cm }|{\bf r}-{\bf r}'|^3} \mathrm d^3r'.$$ Given a single particle of charge $q_C$ fixed in the centre of the coordinate system, a test charge $q_T$ feels a field which goes as $\propto\frac{1}{r^2}$. This field diverges as one gets closer (${\bf r}\to{\bf 0}$). On the other hand, if we have a big wall of charges with density $\varrho_W$, then its electrical field is constant and doesn't diverge as I get closer ($z\to0$) - for example imagine a capacitor place in the xy- plane. Say I have a charge $q_T$ at position ${\bf x}(0):=(0,0,d)$ above charged plate in the xy-plane. It's eighter infinitely big of or radius $R$. Now I start moving the particle along the given trajectory ${\bf x}(t):=(0,0,d-v\ t)$. Here $d$ and $v$ are fixed constants. What is the value of ${\bf E}({\bf x}(t))$? What is the electrical field in the case where I have a capacitor plane containing many charges, one of which is perfectly fixed at ${\bf 0}$?


title: The most challenging physical phenomena

text: What are examples of endeavors, in the history of mankind, to understand physical phenomena with models which were proved to be incorrect later, reformed significantly, or are still under development?


title: What is anti-matter?

text: Matter-- I guess I know what it is ;) somehow, at least intuitively. So, I can feel it in terms of the weight when picking something up. It may be explained by gravity which is itself is defined by definition of the matter! What is anti-matter? Can you explain it to me?   * Conceptually simplified   * Real world evidence


How do the Planets and Sun get their initial rotation? Why do Venus and Mercury rotate so slowly compared to other planets and why does Venus rotate in a different direction to Mercury, Earth and Mars?


title: Representations in quantum mechanics

text: This might be a very simple question. I just want someone to point me the right direction to understand things like this: $$ \langle x|x'\rangle=\delta(x-x') \\\ \psi(x)=\langle x|\psi\rangle \\\ \tilde{\psi}(p) = \langle p|\psi\rangle \\\ \langle x|p\rangle=\frac{1}{\sqrt{2\pi \hbar}}\exp(ipx/\hbar) $$ I am using Griffiths textbook, but it's too confusing. Where (on the internet) can I find a easy approach to understand these representations?


title: A question about defining a classical CFT

text: This is kind of related to this, Defining a CFT using beta-functions So what would be the right definition of a CFT even classically?   * Is it true that classically one will call a theory scale invariant only if the action is invariant under scale transformations? (and not by the Lagrangian density)  For example under the scale transformations $x' = \lambda x$, in $3+1$ the scalar field goes as $\phi'(x') = \lambda \phi(x)$ and in $1+1$ it goes as $\phi'(x') = \phi (x)$. This means that in $3+1$ the action of the massless scalar field is not scale invariant but in $1+1$ it is but the Lagrangian density goes the otherway. But from the point of view of beta-functions isn't it more consistent to call the $1+1$ theory as a CFT but not the one in $3+1$? Isn't a massless scalar field theory in $3+1$ guaranteed to produce mass by RG flow whereas the $1+1$ theory will not?


title: Where is the magnetic self energy term in $L$ for a charged particle in an electromagnetic field?

text: In the Lagrangian for a charged particle in an electromagnetic field $$L = \frac{1}{2}mu^2 - q(\phi - \frac{\vec{A}}{c}\cdot \vec{u})$$ the energy of the particle is contained in the kinetic term, the rest being interaction terms of the particle with the electromagnetic field. If it's travelling at some velocity, then it will generate its own magnetic field and therefore possess a magnetic self energy, so which term in $L$ contains this?


title: How do you determine the Lagrangian?

text: I have always been puzzled by how do you arrive at Lagrangians? That is, how do you know that the functional you need to get Newton's equations is $L$ = $T-V(x)$ Do you derive the Lagrangian first somehow or do you just guess the one which would satisfy the action to give equation's of motion?(because then you would need to know the equations of motion first) Also, is the Lagrangian always equivalent to something resembling $T-V$, or there are other ways to determine it? More generally, _is the action known before you know the equations of motion, or vice versa_? What I really wish to know is, was the Einstein Hilbert action discovered before field equations were? If so, _how_? ( _My major doubt is how do you come across the Lagrangian if you don't know the equations of motion, and you can't guess $L$ then_ )


title: Don't heavier objects actually fall faster because they exert their own gravity?

text: The common understanding is that, setting air resistance aside, all objects dropped to Earth fall at the same rate. This is often demonstrated through the thought experiment of cutting a large object in half, the halves of which clearly can't then fall more slowly just by being sliced in two. However, I believe the answer is that when two objects fall together, attached or not, they do "fall" faster than an object of less mass alone does. This is because not only does the Earth accelerate the objects toward itself but the objects also accelerate the Earth toward themselves. Considering the formula: $F_g = G m_1 m_2/d^2$ We can see that the force of gravity is dependent on **both** the masses, not just that of the more massive object. Of course in everyday situations, we can for all practical purposes treat objects as falling at the same speed. But I'm hoping not for a discussion of practicality or what's measurable or observable, but what we think is actually happening. Am I right or wrong? What really clinched this for me was considering dropping a small Moon-massed object close to the Earth and a small Earth-massed object close to the Earth. This made me realize that falling isn't one object moving toward some fixed frame of reference, but that the Earth is just another object, and falling consists of _multiple objects mutually attracting in space_.


title: Radial fall in a Newtonian gravitational field

text: Suppose an object of mass $m$ starts at rest at a radial distance $ r_0$ from a perfectly spherical mass $M$ (where $m << M$), $r_0 > R =$ radius of $M$. Can we analytically determine when $m$ will hit the surface of the $M$? In other words, can we analytically solve this initial value problem: $$ \frac{d^2r}{dt^2} ~=~ - \frac{GM}{r^2} ,$$ $$ \dot{r}(0) ~=~ 0 ,$$ $$ r(0) ~=~ r_0? $$


title: Do heavier objects fall faster?

text: This question has been asked multiple times here and all over the internet yet I can't find a conclusive answer:   * Some claim that heavier objects do fall faster: Don't heavier objects actually fall faster because they exert their own gravity?   * Others claim that all objects fall at the same speed regardless of their mass: Free falling of object with no air resistance Which one is the right one?


title: Gravity question

text: > **Possible Duplicate:**   >  Don’t heavier objects actually fall faster because they exert their own > gravity? When true: The force pulling the "heavy" object down is greater BUT it also takes more force to accelerate a heavy object. These two effects cancel out. As I heard, the bigger mass/size an object the bigger attraction force between each other, then, why the big mass object did not accelerate faster due to the attraction force is greater than light object.


title: Falling from Earth's sphere of influence

text: How can I make a graph of an object falling from say, the Earth's sphere of influence, where acceleration(,a) is the real force of gravity at the objects radius? ie, using $$s=ut+\frac{1}{2}at^2$$ I can find the position s after a time t due to acceleration, a. This does not account for any gravity gradient, which is what I want to account for. Basically, $$ s=ut+\frac{1}{2}(\frac{GM}{r^2})t^2 $$ But there is a problem, firstly, I don't think that would work as it still only uses a constant acceleration, also there is a circular dependancy with r and s basically having the same meaning. (s + r would be the original radius at t=0) I'm not sure how helpful this will be, but recall (Hopefully accurately) that the area under an acceleration time graph is the distance travelled. Currently I have a function for the force at any radius [f(x)=GM/r^2], and a function for the position with the acceleration for a point r in it. In my case, it is [s(x)=ux+1/2 f(r) x^2] **Edit:** What I have realised is that when I calculate the position it returns s=ut+1/2 at^2 (duh...) So every point on the graph is the distance travelled had the object been accelerating for time,x all the way from the starting distance, rather than accelerating from the last point. Hope that makes it clearer, is there a way to get around this? P.S. In the graph, the actual force is not what I want and I am assuming that the object has a mass of 1kg, thus the force is the acceleration. Thanks in advance, Leo


title: Distance traveled in a simple two body problem

text: I'm trying to program an $N$-body simulation and I'd like to be able to test it with a known solution to a simple, two-body problem. I've looked at multiple sources, but I just don't know how to apply it to my simple test case. Two objects at rest placed 10 meters apart with mass of 1. The force between them is a modified gravitational force of F = 10 * m1 * m2 / r^2. How long will it take for each object to travel 4 meters?


title: If an object fell from the moon

text: Ignoring the moons gravity, if an object sitting still (relative to the Earth, i.e. not in orbit) was dropped from the moon. How long would it take to hit the Earth?


title: One dimensional motion with changing acceleration. Falling to a large body from a great distance

text: > **Possible Duplicate:**   >  Radial fall in a Newtonian gravitational field My math and physics are rusty. I am trying to calculate the time an object takes to fall to a large body. Before you answer $1/2at^2$, the conditions where $1/2at^2$ apply is where $a$ is a constant. Constant acceleration is a fine approximation when the distance the object falls is $<<$ than the distance to the center of the large body. i.e. 100 meters on the surface of the Earth. I'm looking at problems where distance fallen is 50% or more of the distance between objects. Gravity varies with the inverse square of distance. Given two bodies, $m_s$ and $m_l$. $$ F = m_sa = m_la $$ $$ F = Gm_sm_l/r^2 $$ $$ m_sa = Gm_sm_l/r^2 $$ $$ a = Gm_l/r^2 $$ Thus acceleration of $m_s$ varies with the inverse square of the distance to the center of $m_l$, and versa visa. Given R is the radius of the $m_l$, defining the surface of $m_l$. Given $h$ is the distance $m_s$ is above $m_l$'s surface, subsitute $R+h$ for $r$. $$ a = Gm_l/(R+h)^2 $$ This is as discussed at stackexchange 35878. Given the initial velocity of $m_s$ is zero, what is the time, $t$, it takes $m_s$ to fall distance $h$? An alternative question is give a $t$, how far with $m_s$ fall? This is where I'm rusty. I don't believe one can't simply substitute $Gm_l/(R+h)^2$ for $a$ in $1/2at^2$, but I don't know what else to do. The stackexchange articles, 15587 and 41741, discuss $a(x)$ where $a$ changes linearly with distance. Here $a$ changes with the inverse square of the distance. I did a lot of web searching and did not find this topic discussed. The discussions are with $a$ being constant or changing in a linear manner. Thanks for the help.


title: What's an equation for two astronomical entities both of 4000 tonnes in weight, colliding?

text: I have next to no knowledge of any physics, but would be happy if you could answer my question... I want to know an equation for two astronomical entities such as the star Sirius (2.02 solar mass) colliding.


title: Basic question about law of gravitation

text: > **Possible Duplicate:**   >  Radial fall in a Newtonian gravitational field This is how Wikipedia defines Newton's law of Gravitation: > Every point mass attracts every single other point mass by a force pointing > along the line intersecting both points. The force is proportional to the > product of the two masses and inversely proportional to the square of the > distance between them: > > $F=G\frac{m1m2}{r^2}$ > > where > >   * F is the force between the masses, >   * G is the gravitational constant, >   * m1 is the first mass, >   * m2 is the second mass, and >   * r is the distance between the centers of the masses. > Now, say 2 spheres, one the size of the earth and the other the size of a ping pong ball are placed say 10 km apart. There are no other forces acting on the system other than gravitation. If I've understood rightly, then _both_ the ball & the earth sized sphere will be pulled towards each other with the same huge force. My question is- how can we calculate when the 2 spheres will meet? And while calculating that shouldn't we consider the fact that the force is changing every moment because the distance between them $r$ changes every moment? How can I include this factor into my calculations? Further, since the force is changing every moment, are the spheres undergoing acceleration or _accelerated_ acceleration?? (Forgive me if my terminology is improper. I'm a beginner.) Is there any name for such forces & accelerations which change at a predictable rate as in this question?


title: Determining impact velocity over long distances

text: Everything I have found concerning impact velocity from a given height deals with constant acceleration due to gravity. I would like to know how to work in varying acceleration into the equation. So, time for the question... How does one go about determining the velocity at which an object with negligible mass $m$ and radius $a$ will hit the surface of a much larger object with mass $M$ and radius $r$ from a initial distance $R$? To be a bit more specific, let's say we have a closed system with two objects, one comparable to the moon and another with a small mass, let's say a basketball. The problem I have with this situation is the acceleration due to gravity is not constant at any given distance. Newton's equation for this is: $$g = GM / R^2.$$ Ideas?


title: Can I use two SI prefexes

text: Is it ok to say $145\,{\rm k\,MPa}$ for $145\, {\rm GPa}$. We are so used to comparing stresses in ${\rm MPa}$ that I want to keep things relative to this unit. So would it be a no-no to do so.


title: Is there any problem a quantum finite state machine can do faster than a classical finite state machine?

text: All of the quantum algorithms I've seen so far require a turing-complete quantum computer, at least as far as I can tell. Are there any quantum algorithms that require only a quantum finite automaton? If so, how does their asymptotic complexity compare to the classical versions of those algorithms?


title: How do you calculate heat flux (Kw/m2) at the focal point of a mirror?

text: can anyone help me to determine the heat flux (Kw/m2) on a focal point of a parabolic dish having a diameter of 1.5 meter and a focal length 60 cm ??? please awaiting your soonest reply for my senior project :( Regards


title: 'hypersurface orthogonal' component of covariant derivative of normal vector

text: I believe that answer to my question is rather trivial but I can't seem to get my head around it. In context of ADM formulation of gravity (or any other differential geometry context, I guess) the covariant derivative of a normal vector to the hypersurface/foliation/slice, in any direction within the hypersurface gives extrinsic curvature. In components K_ij would be e.g. covariant derivative of normal vector in direction "i" projected to direction "j" where both basis vectors "i" and "j" lie in the hypersurface. My question is, how come that vector which is covariant derivative of the normal vector along one of these "i"'s always has orthogonal component equal to zero? **I.e. how come the covariant derivative of normal vector in direction "i" projected to the normal vector itself always equals zero?** It isn't true for any other vector, as a matter of fact, using compatibility of a metric from definition of extrinsic curvature K_ij=(cov(n,i)|j) we can easily see that (n|cov(j,i))=K_ij so that covariant derivative of any other vector "j" along "i" does have a component along normal "n" and it is exactly the extrinsic curvature. Consequently, I'd assume that the above property of not having an orthogonal component of covariant derivative is kind of a defining property of a normal vector. I just wonder where does this follow from. Thank you! Cheers!


title: Generalized Coulomb's Law

text: This question is about the generalization of Coulomb's law to continuous bodies of charge. The basic statement of Coulomb's Law involves two discrete charges $q_1$ an $q_2$: $$\vec{F}_i = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{12}} \hat{r}_i $$ Here $i$ represents the charge on which the force is exerted, and $\hat{r}_i$ represents the unit displacement vector between the other charge and the charge $i$. Many treatment of electrostatics extend this law to the case that one charge is not discrete, but rather a continuous body. The force on the discrete charge $Q$ is then: $$\vec{F} = \frac{Q}{4 \pi \epsilon_0} \int \frac{dq}{r^2} \hat{r} $$ Here $dq$ is the infinitesimal charge element of the continuous body, while $r$ and $\hat{r}$ represent the distance and displacement vectors between $dq$ and $Q$. Continuing this way, we could probably propose an expression for force between two continuous bodies of charge, like so: $$\vec{F} = \frac{1}{4 \pi \epsilon_0} \int \int \frac{dq_1 dq_2}{r^2} \hat{r}$$ However, I have not really seen this expression in the literature/treatments of electrostatics. Does anyone know why this is the case? Is the expression not useful, or are there no applications demanding the above expression?


title: Why Higgs particle is the root of all elementary particles?

text: The Higgs boson is a hypothetical elementary particle predicted by the Standard Model (SM) of particle physics. It belongs to a class of particles known as bosons What Will Happens If physicist Find the Higgs Particle that thought to be fundamental is not fundamental?


title: Stability of the vacuum state of interacting quantum fields

text: "Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is _not_ bounded below for thermal sectors, however, but thermal states are nonetheless taken to be stable because they satisfy thermodynamic constraints. In classical Physics, we would say that the thermal state has lowest _free energy_ , which is a thermodynamic concept distinct from Hamiltonian operators that generate time-like translations. The entropy component of free energy, meanwhile, is a _nonlinear_ functional of the quantum state (presuming that the definition of entropy in quantum field theory would be at least this much like von Neumann's definition in terms of density operators), so we can reasonably expect the sum of the energy and entropy components to have a minimum in the state of greatest symmetry, as we see for thermal states. [It seems particularly notable in this context that the entropy is not an observable in the usual quantum mechanical sense of a linear functional of the quantum state.] The presence of irreducible randomness in quantum mechanics presumably puts quantum field theory as much in the conceptual space of thermodynamics as in the conceptual space of classical mechanics, despite the quasi-functorial relationship of "quantization", so _perhaps_ we should expect there to be some relevance of thermodynamic concepts. Given this background (assuming, indeed, that no part of it is _too_ tendentious), **why should we think that requiring the Hamiltonian to have a spectrum that is bounded below should have anything to do with stability in the case of an interacting field?** The fact that we can construct a vacuum sector for free fields in which the spectrum of the Hamiltonian is bounded below does not seem enough justification for interacting fields that introduce nontrivial biases towards statistically more complex states. This question is partly motivated by John Baez' discussion of "quantropy" on Azimuth. I am also interested in the idea that if we release ourselves from the requirement that the Hamiltonian of interacting fields must have a spectrum that is bounded below, then we will have to look for analogues of the KMS condition for thermal states that restore some kind of analytic structure for interacting fields. I asked a related Question here, almost a year ago. I don't see an answer to the present Question in the citations given in Tim van Beek's Answer there.


title: Triangulation for Astronomical Distances

text: How can triangulation be used to calculate the approximate distance to very distant celestial bodies like stars, globular clusters, etc.? And can it be used to measure the distance to a Black Hole? (Can someone please help me with tags?)


title: Limitations in using FLEX as a DMFT solver

text: When using the fluctuating exchange approximation (FLEX) as a dynamical mean field theory (DMFT) solver, Kotliar, et al. (p. 898) suggest that it is only reliable for when the interaction strength, $U$, is less than half the bandwidth. How would one verify this? Also, is there a general technique for establishing this type of limit? To clarify, DMFT is an approximation to the Anderson impurity model, and FLEX is a perturbative expansion in the interaction strength about the band, low interaction strength limit.


title: Sympletic structure of General Relativity

text: Inspired by physics.SE: http://physics.stackexchange.com/questions/15571/does- the-dimensionality-of-phase-space-go-up-as-the-universe-expands/15613 It made me wonder about symplectic structures in GR, specifically, is there something like a Louiville form? In my dilettante understanding, the existence of the ADM formulation essentially answers that for generic cases, but it is unclear to me how boundaries change this. Specifically, I know that if one has an interior boundary, then generally the evolution is not hamiltonian; on the other hand, if the interior boundary is an isolated horizon, then the it is hamiltonian iff the first law of blackhole thermodynamics is obeyed (see http://arxiv.org/abs/gr-qc/0407042). The sharper form of the question is thus what happens cosmologically? (And as usual for a research level (?) question: what are the Google-able search terms to find out more about this?)


title: How to obtain the constant $a^g$ in Eq.(2.7.19) in Polchinski's string theory book

text: Excuse me, I have calculated $a^g$ a lot of times, using the relation between $:\;:$ and ${}^{{}_\circ}_{{}^\circ} \; {}^{{}_\circ}_{{}^\circ}$. But I can't get the same result with the book. It is not too hard to get $$ :b(z)c(z'):-{}^{{}_\circ}_{{}^\circ} b(z)c(z'){}^{{}_\circ}_{{}^\circ} = \frac{\left(\frac{z'}{z}\right)^{\lambda-1}-1}{z-z'}. $$ Which can be found in Problem 2.13 on $P_{76}$. Take the limit $z\rightarrow z'$, we find $$ :b(z)c(z):-{}^{{}_\circ}_{{}^\circ} b(z)c(z){}^{{}_\circ}_{{}^\circ} = \lim_{z\rightarrow z'}\frac{\left(\frac{z'}{z}\right)^{\lambda-1}-1}{z-z'}=\lim_{z\rightarrow z'}\frac{\left(1-\frac{z-z'}{z}\right)^{\lambda-1}-1}{z-z'}=\lim_{z\rightarrow z'}\frac{\left(1-(\lambda-1)\frac{z-z'}{z}\right)-1}{z-z'} =\frac{1-\lambda}{z}. $$ $$ \partial (:b(z)c(z):)-\partial ({}^{{}_\circ}_{{}^\circ} b(z)c(z){}^{{}_\circ}_{{}^\circ}) = -\frac{1-\lambda}{z^2} $$ and $$ :\partial b(z)c(z):-{}^{{}_\circ}_{{}^\circ} \partial b(z)c(z){}^{{}_\circ}_{{}^\circ} = \lim_{z\rightarrow z'}\partial\frac{\left(\frac{z'}{z}\right)^{\lambda-1}-1}{z-z'} =\lim_{z\rightarrow z'}\left(-\frac{\left(\frac{z'}{z}\right)^{\lambda-1}-1}{(z-z')^2}+\frac{(1-\lambda)\left(\frac{z'}{z}\right)^{\lambda-1}}{z(z-z')}\right) =\frac{(\lambda-1)^2}{z^2}. $$ The energy-momentum tensor is $T(z)=:(\partial b)c:-\lambda\partial(:bc:)$. Using the above results, we can express $T(z)$ in _creation-annihilation normal ordering_ ${}^{{}_\circ}_{{}^\circ}\;{}^{{}_\circ}_{{}^\circ}$ $$ T(z)={}^{{}_\circ}_{{}^\circ} \partial b(z)c(z){}^{{}_\circ}_{{}^\circ}+\frac{(\lambda-1)^2}{z^2}-\lambda\left(\partial ({}^{{}_\circ}_{{}^\circ} b(z)c(z){}^{{}_\circ}_{{}^\circ})-\frac{1-\lambda}{z^2}\right) ={}^{{}_\circ}_{{}^\circ} \partial b(z)c(z){}^{{}_\circ}_{{}^\circ}-\lambda\partial ({}^{{}_\circ}_{{}^\circ} b(z)c(z){}^{{}_\circ}_{{}^\circ})+\frac{1-\lambda}{z^2} $$ $$ \Rightarrow a^g=1-\lambda $$ But in Polchinski's book,$a^g=\frac{1}{2}\lambda(1-\lambda)$. What wrong with my derivation?


title: On-shell symmetry from a path integral point of view

text: Normally supersymmetric quantum field theories have Lagrangians which are supersymmetric only on-shell, i.e. with the field equations imposed. In many cases this can be solved by introducing auxilary fields (field which don't carry dynamical degrees of freedom, i.e. which on-shell become a function of the other fields). However, there are cases where no such formulation is known, e.g. N=4 super-Yang-Mills in 4D. Since the path integral is an integral over all field configurations, most of them off-shell, naively there is no reason for it to preserve the on-shell symmetry. Nevertheless the symmetry is preserved in the quantum theory. Of course it is possible to avoid the problem by resorting to a "Hamiltonian" approach. That is, the space of on-shell field configurations is the phase space of the theory and it is (at least formally) possible to quantize it. However, one would like to have an understanding of the symmetries survival in a path integral approach. So: > How can we understand the presence of on-shell symmetry after quantization > from a path integral point of view?


title: Does turbulence violate Galilean relativity?

text: Fluid flows become turbulent beyond a certain velocity. The velocity is almost always with respect to a fixed boundary. However, an observer in a frame of reference travelling with the fluid will also experience turbulence when the velocity of fluid with respect to the boundary exceeds a certain value. Does this indicate that fluid flow is not invariant under a Galilean transformation?


title: May molecules of ideal gases have an inner structure?

text: The following question is probably very elementary: **whether molecules ofideal gases may have optic properties?** As far as I understand, when one discusses optic properties, one assumes that molecules of the material have some inner structure, in particular different energy levels. **The question is whether existence of such an inner structure may contradict the assumption that the gas is ideal.**


title: Why doesn't a block rotate due to friction?

text: In a horizontal surface, a block (cube) is sliding due to a sudden push. When the block slides, there is frictional force which is acting on the block. Frictional force will have a torque around the center of mass, so why does the block not rotate/roll around (a horizontal axis through) the center of mass instead of sliding?


title: Relation between decay probability and the energy of particle

text: Is there any way to find the energy of a particle through its decay probability?


title: Why are there only perfectly anti-correlated quantum states, not perfectly correlated?

text: The singlet state of two qubits is anticorrelated in every basis. For example, in the Pauli bases, it can be expressed, $\frac{1}{\sqrt{2}} ( | 01 \rangle - | 10 \rangle) = \frac{1}{\sqrt{2}} ( | +- \rangle - | -+ \rangle) = \frac{1}{\sqrt{2}} ( | \circlearrowright \circlearrowleft \rangle - | \circlearrowleft\circlearrowright \rangle)$. However, there is no state that is correlated in every basis. The best we can get is correlation in two Pauli bases, and anti-correlation in the third. For example, $\frac{1}{\sqrt{2}} ( | 00 \rangle + | 11 \rangle) = \frac{1}{\sqrt{2}} ( | ++ \rangle + | -- \rangle) = \frac{1}{\sqrt{2}} ( | \circlearrowright \circlearrowleft \rangle + | \circlearrowleft\circlearrowright \rangle)$. Why is this? Would it violate some principal, like allowing for superluminal communication?


title: Does the Fundamental Frequency in a Vibrating String NOT Necessarily Have the Strongest Amplitude?

text: I am doing some experiments on musical strings (guitar, piano, etc.). After performing a Fourier Transform on the sound recorded from those string vibrations, I find that the fundamental frequency is not absolutely the component with the largest amplitude (or energy). I learnt from introductory physics courses that fundamental frequency is the "major" component of a vibrating string. So why does it sometimes does not possess the highest amplitude?


title: Counting degrees of freedom of gauge bosons

text: Gauge bosons are represented by $A_{\mu}$, where $\mu = 0,1,2,3$. So in general there are 4 degrees of freedom. But in reality, a photon (gauge boson) has two degrees of freedom (two polarization states). So, when someone asks about on-shell and off-shell degrees of freedom, I thought they are 2 and 4. But I read that the off-shell d.of. are 3. And my question is how to see this?


title: The physical interpretation of limit of ratio of two functions

text: Imagine we have two different differentiable functions $f(t)$ and $g(t)$ where $t$ generally represents the time, if there exists the following limit as $$ \lim\limits_{t\rightarrow \infty } \frac{\| \dot{f}(t) \|}{\|\dot{g}(t)\|}=c$$ Then, is there any appropriate physical explanation for this limit ? If ignore the limit, the $\frac{\| \dot{f}(t) \|}{\|\dot{g}(t)\|}$ is sort of instantaneous reletive absolute rate of change of $f(t)$ over $g(t)$, but what is that when limit involves in ?


title: Where do photons get their energy from?

text: If energy required to accelerate a particle to the speed of light is infinite then where do they get it from? But first if photon's are massless, then why do they collide to some other thing and get reflected as in our daily life or get deflected after colliding to an atom in the sun and just move inside the sun for a long time before escaping it?


title: Why does the Dopfer EPR experiment require coincidence counting?

text: Dopfer Momentum-EPR experiment (1998) seems to provide a interesting tweak in the EPR experiment. To read more details on this experiment, see: http://www.hep.yorku.ca/menary/courses/phys2040/misc/foundations.pdf (page S290) http://www.physics.ohio-state.edu/~lisa/CramerSymposium/talks/Cramer.pdf (page 11) Also, a discussion of the experiment, the coincidence counter, and how the conditions of the no-signaling theorems might not apply to this setup: http://casimirinstitute.net/coherence/Jensen.pdf In summary, the experiment sends two entangled photons A and B toward two separate arms. Arm A has a lens and a Heisenberg detector, which can be placed either at the focal plane or the image plane. Arm B is sent on a two-slit filter. The observed results of this experiment are as follows: 1) if the Heisenberg detector at arm A is placed at the focal plane, the output of the two-slit filter at arm B is an interference pattern 2) if the Heisenberg detector at arm A is placed at the image plane (twice the focal plane) the output of the two-slit filter at arm B is an incoherent sum of intensities from each slit As suggested in the 3rd paper link I posted, if you use time bins, there really doesn't seem to be _any need at all_ to rely on the coincidence counter, as you can study the interference pattern on each time bin in isolation from photons received in other time bins Am I confused? How is the coincidence count being used at all? notice that the interference pattern is spatial, not temporal!


title: Is a plasma a distinct phase of matter?

text: Long ago I learned that a plasma was a distinct state of matter after solid, liquid and gas, and also that it was achieved by imparting heat to a the matter. But most references describe a plasma as an ionized gas. So I'm having trouble understanding, what then, does it mean to be a distinct phase of matter? Is ionization, as opposed to heat, all that's required to make a gas a plasma? If so, what makes a plasma more distinguished than, say, an ionized liquid?


title: Why there's a whirl when you drain the bathtub?

text: At first I thought it's because of Coriolis, but then someone told me that at the bathtub scale that's not the predominant force in this phenomenon.


title: What causes a whirlpool to form in a bathtub?

text: I mean, when you have a full bathtub and then let it empty, under what conditions does a whirlpool form? Could we devise an experiment and measure this effect? When it comes to fluids, I don't know why I can't think of anything to test a hypothesis.


title: Is it possible to estimate the speed of wind by the sound emitted by a cable of an overhead power line?

text: I was near ($\approx40m$) an overhead power line and I heard a sound coming from the cables of the power line; I think the sound was made by the vibrations of the power cables due to the wind but I am not sure. The wind was very light. The sound was not the "buzz" asked about here. ![enter image description here](http://i.stack.imgur.com/azt0a.jpg) My question is: assuming the sound was generated by the wind, is it possible to estimate the speed of wind from the sound properties (i.e. its spectrogram) and the mechanical properties of the cable? If yes, how accurate will be the estimate? If yes, can you provide some back-of-the-envelope calculation?


title: How to get the new direction of 2 disks colliding?

text: I'm developing a 2D game including collisions between many disks. I would like to know how I can get the angle corresponding to the new direction of each disk. For every disk I have this information : **direction** (integer), **speed** (float), and **position** ($x$;$y$, which are both integers). Of course I know that the new direction will be the opposite of where the collision happens (disk hit on the bottom-left will go to the top-right), but I don't know how to calculate exactly the new angle.


title: How to size an electromagnet

text: How can I size an electromagnet? For example if I would to attract a mass of $x$ kg what are the calculations that I must do to size the ferromagnetic core and of course the solenoid? And thus, how can I compute the force of the magnetic field generated?   * Current: AC 230V @ 50Hz.   * Material: Iron.   * Distance: 30 cm.


title: Black body radiation

text: **I have a few questions related to the emission of electromagnetic radiation by black bodies.** * * * Consider the following image: ![fig.1](http://s22.postimg.org/77bujyudt/image.png) On the above image I have drawn the rays of light that are emmited by black bodies assuming that they have only 8 points of emmision (They are marked with red dots).   _Which of these two images shows the real situation? The single point emits the radiation in all directions or only in one direction?_ * * * If my intuition is not wrong and the image on the right is correct consider the next image where I assume that there is only one point of emmission on the object: ![fig.1](http://s23.postimg.org/m87phx7dn/image.png)   * _Is the intensity of radiation the same in every direction?_   * _Does the radiation in each direction have the same intensity-wavelength distribution (presented in the image below)?_ ![fig.3](http://s24.postimg.org/b53ar97ad/image.png)


title: Is something beyond the material needed to solve the Von Neumann Chain?

text: A problem has been presented that goes like this: Particles normally exist as several mathematical possibilities rather than one actual object. It is said that in the absence of observation, particles exist in a superposition of possibilities rather than one actual thing. But when we look they are not in such an indefinite state. The problem states that the way to solve finding out why there is something definite when we look is decoherence. But it is said that this doesn't really solve the problem because whatever particles were used to collapse another, what was used to collapse that particle? And so on and on. And the reason for this is because the wave function of a particle cannot be unentangled from that of whatever is used to measure it. When one photon is measured by another they entangle. If one particle measures another, it inherits part of its wave function, and that particle which is supposed to be measuring, cannot be fully explained without what it is measuring. So you need another measuring device to collapse that initial measuring particle to a definite state. But then you need something else to collapse that measuring apparatus as well, and so on and so on. This creates a chain of material objects in a superposition of measuring, which is known as a Von Neumann chain. Since quantum laws are what describe all material objects, some other particles or measuring apparatus is always needed to collapse the next one in line. You keep going back until you get to something nonlocal. Outside the entire material system, which escapes this chain by not being bound by the same physical laws, and is able to cause final collapse of everything in the chain, which is argued to be a conscious observer. Something beyond the material with the ability to collapse the entire physical system. Is this true? If not, why not.


title: Photons and uncertainty principle

text: Let's assume we have a perfect single-photon source: a device emitting exactly one photon at a time, with defined energy and direction. Let's shoot a photon: we know exactly the position of the photon (starting point and time, velocity) and it's momentum (energy and velocity). Would such a device violate uncertainty principle? Where is the trap? * * * Just to clarify things, my question essentially is: _a particle (e.g., a photon) prepared in an eigenstate of momentum can be found everywhere (at least along the direction of momentum)?_


title: Calculating velocities using Reference frames

text: Suppose an object A is traveling at a velocity of 100 m/s, and another object B is traveling at 105 m/s. With both the objects traveling through the same direction, taking A as a reference frame, the velocity of B would be 5 m/s (Is this actually right?). But, when they're traveling in opposite directions, how would one measure the velocity of B (with A as reference frame)..? Does it actually take a negative sign? - Sorry, if I have a misunderstanding...


title: What is the difference between "at all times" and "at any particular time"?

text: Morrison writes in "Morrison, Michael A. : Understanding quantum physics : a user's manual" > $ |\Psi(x,t)|^2 \xrightarrow[x\rightarrow\pm \infty ]{} 0$ at all times _t_ > [bound state] > > $ |\Psi(x,t)|^2 \xrightarrow[x\rightarrow\pm \infty ]{} 0$ at any particular > time _t_ [unbound state] So I can imagine that "all" means the entirety of all times, but do I not get "all" when summing over all particular states? I also understand that in a bound state, the wave is never at the infinity position, but the wave of an unbound state may exist there.


title: Why can glass absorb ultraviolet light?

text: Please see the following photos. (I cannot post them...) http://i1163.photobucket.com/albums/q554/startanewww/CIMG4545.jpg http://i1163.photobucket.com/albums/q554/startanewww/CIMG4546.jpg From the first photo, the book mentioned _Don't cover the paper with glass because glass absorbs enough ultraviolet light to slow the damage process._ (line 8) My questions:   * Why can glass absorb ultraviolet light?   * Will papers with dark colours fade fastest? Why is that the case? (see the second last paragraph)


title: Showing Dirac Hamiltonian is hermitian

text: I'm trying to show that $H_D = -i\boldsymbol{\alpha}.\nabla+\beta m$ is hermitian. Its given that $$ \gamma^{0\dagger}=\gamma^0 $$ $$ \boldsymbol\gamma^\dagger=-\boldsymbol\gamma $$ What i've done is: $$ H_D^\dagger = +i\boldsymbol\alpha^\dagger.\nabla+\beta^\dagger m $$ $$ =+i(\gamma^0\boldsymbol\gamma)^\dagger.\nabla+\beta m $$ $$ =+i(\boldsymbol\gamma^\dagger\gamma^{0\dagger}).\nabla+\beta m $$ $$=-i(\boldsymbol\gamma\gamma^0).\nabla+\beta m $$ Well clearly i'm doing somthing wrong because $\boldsymbol\gamma\gamma^0\neq\gamma^0\boldsymbol\gamma$


title: Design of atomic bomb

text: Please see the following photo. (I cannot post it) http://i1163.photobucket.com/albums/q554/startanewww/CIMG4548.jpg Why is atomic bomb in a "fish-like" shape? (I don't know how to describe it) Is it specially designed for some purposes? Thanks a lot.


title: Why does the aligning of magnetic dipoles in a material cause its heat capacity to decrease?

text: This is with regards to adiabatic magnetisation.


title: Field quanta- infinite in extent?

text: > **Possible Duplicate:**   >  confusion on quantum field theory Are field quanta infinite in extent as stated in Art Hobsons paper? What does this even mean? I've not seen any electrons or atoms that are infinite in size? Am I getting something wrong somewhere?


title: re-defining the question, field quanta size in field theory?

text: > **Possible Duplicate:**   >  confusion on quantum field theory I asked are field quanta infinite in extent and I keep getting back that its the probabibility distribution. But this is a normal quantum mechanics answer. In terms of quantum field theory, what is meant by saying a field quanta of an electron field is infinite in extent? does it mean the quanta is infinite in size? Art Hobson has said its energy can be spread across light years which surely means the field quanta of the field is massive in size? if we assume the wavefunction is real and doesn't collapse then each quanta is a wave spread across the whole of space, correct?


title: Why is there a photon every millimeter on earth coming from a star millions of light years away?

text: I've been having this confusing thought for so long now it would be amazing if someone could answer me. Imagine this asterisk * . As you see, from the center point, lines go outwards, just like a sun will emit rays of light in all direction. BUT, theoretically, there should be a "finite" amount of photons it sends in space, which means that the farther you are from that sun, let's say 1 million light years, the less likely are your eyes of catching the photons emitted from the source? So does this make the theory of the photon bad? Since we can see a star millions of light years away, no matter where we stand on the ground of this planet. This means that the star can emit at least one photon every millimeter or less millions of light years away so this would mean that it would need an "impossible" density of photons sent at the source on the sun's surface in every direction of the cosmos. How's this possible?


title: Number of supersymmetric charge and the meaning of $\cal N$

text: I have been thinking about the definition of the notation $\cal N$ and its relation to the number of supercharges in SUSY, but still feel a little confused. In dimension 2, we usually denote, for example, $\cal N = (2,2)$ supersymmetry, where we have 2 chiral supercharge and 2 anti-chiral supercharge; but in higher dimensions we just refer to $\cal N = 1$, etc. What is the difference and why we make such different notation? Also, I would appreciate of one can explain the exact meaning of $\cal N$, for example in 4 dimensions, and how they are related to number of supercharge $Q$ and independent spinors.


title: Do particles rotate around themselves or they just move while the object rotates?

text: In this question, I'm not talking about particle spin. I guess, when an object rotates, its atoms also rotate. When an atom rotates, its particles must move in space. I wonder that if the particles have a direction. Can they rotate or do they just move position around the axis (middle) of a proton so we consider that the proton rotates? Let's think about single particles like electron instead of composite particles like hadrons. Can electrons rotate ? Edit : I think this is a simple and good question but I couldn't get a sufficient answer yet .


title: Gravity and acceleration

text: I've imagined this little scenario to help me conceptualize things. Let's say we have a doughnut-shaped object with a hole whose diameter is greater than that of a sphere. Let's say that the sphere is vertically aligned with the center of the doughnut and is horizontally gravitating towards it according to Newton's law of universal gravitation. What will happen? 1) The sphere will pass through the doughnut, travel a certain distance (but how far) and accelerate back towards the doughnut (and oscillate back and forward). 2) The sphere will stop as it reaches the center of the doughnut. The reasoning behind this is that the distance between the two objects will be zero and hence the acceleration which is inversely proportional to the distance will be infinity (but in both directions?). This doesn't sound right. 3) Something else


title: If the Moon had gravity as good as the Earth and a magnetic field could it have supported life?

text: If the Moon had gravity as good as Earth and a magnetic field could it have supported life? Because if the Moon had gravity, it could have retained water more than is present today on the surface. If the Earth is in the habitable zone, does the Moon also lie in the habitable zone?


title: How to achieve Gigavolts?

text: I was searching the internet when I found this article http://arxiv.org/abs/0804.1764, about achieving high voltage and power to ignite thermonuclear reaction by inertial confinement, the plan was to achieve it in a ultra vacuum and something that have to do with "taylor flow " which includes quantum physics which I really dont know anything about. So I searched more and all the sites ( including wikipedia ) where talking about maximum voltage related to gas surrounding, why can't we surround it with liquid with a much higher dielectric strength?


title: Slowdown rate of rotating body due to friction force

text: This isn't a homework question, but it might as well be. The problem I have been pondering is: > If a disc (or children's roundabout if you like), of radius r, mass m, is > spun around it's center with an initial force F, and thereafter there is the > friction force (of either the axle or air resistance or both) of f, then how > long will it take to come to a stop? I have thought about it and have come up with not much. My first way is thus: $F = ma$, so $a = F/m$, the initial acceleration ( or should that be $(F-f)/m$ ?). And then the deceleration is $a = -f/m$. I'm not sure how to calculate the initial linear velocity, but assuming I have it, $u$, say, then I could say that after time $t$ the velocity is $v = u -at = u -ft/m$, where f is the friction force. So then the disc would stop spinning when $ t= um/f$. I am aware that this is wrong (well, it might work if we were dealing with linear motion). Straight away it seems wrong because it doesn't take into account the radius of the disc and also the slow down seems linear, when from observation it seems rotating discs slow down and taper off to a standstill. But that is as far as I got. I have tried to use angular motion equations (well $\omega r = v$) but I am stuck at this point, and of course, finding the initial velocity. Any help is appreciated.


title: In what order should unit symbols appear?

text: I am trying to represent the result of a dimensional analysis calculation and I can't find an official document that lists the order that unit symbols should appear. For example, when I google $5\text{ m}\times 2\text{ kg}$ or $2\text{ kg}\times 5\text{ m}$ the result is always meters first, or $10\text{ m kg}$. But when I plug both of those calculations into Wolfram Alpha the result has kilograms first, or $10\text{ kg m}$. I would assume that Wolfram Alpha would take more care in displaying a mathematical results than Google but I would like an **official reference (at least for SI)** explaining the order unit symbols should appear and if possible other formatting rules. EDIT: I (as a human) will not be doing the rearranging of the symbols so I am looking for a spec that will produce the same output every time.


title: How is a Majorana fermion created when a s-wave superconductors is in proximity to a topological insulator (e.g. via an antidot)

text: Kane and Fu proposed a few geometries how to create Majorana zero modes using a s-wave superconductor in proximity to a 3D topological insulator (TI). -> http://www.physics.upenn.edu/~kane/pubs/p56.pdf I understand that we need the superconductor to induce the particle-hole symmetry and we need the topological insulator to get a protected edge state at zero energy. But overall I must admit that I have no intuitive description for this process. Especially the importance of the Berry phase, the vortex or the magnetic flux quantum is not clear to me. Especially in the so called Antidot-experiment, where there's a hole in a s-wave superconductor on top of a TI and a magnetic flux quantum through this hole creates a Majorana zero mode. It seems like a big question, but maybe someone can give a simple intuitive answer why we need all these ingredients and end up with a Majorana zero mode.


title: What is a $p_x + i p_y$ superconductor? Relation to topological superconductors

text: I often read about s-wave and p-wave superconductors. In particular a $p_x + i p_y$ superconductor - often mentioned in combination with topological superconductors. I understand that the overall Cooper pair wavefunction may have orbital momentum = 0 (s-wave) or orbital momentum = 1 (p-wave) where the first one is spherically symmetric. Now what does the splitting in a real ($p_x$) and imaginary ($p_y$) part mean? Why is it written in this form and why is that important (e.g. for zero Majorana modes) ?


title: Electric field around charged cylinder

text: This is a homework question, so please don't give me the answer outright. I just need help conceptually. "A cylindrical shell of length 190 m and radius 4 cm carries a uniform surface charge density of σ = 12 nC/m2. (a) What is the total charge on the shell? Find the electric field at the ends of the following radial distances from the long axis of the cylinder. (b) r = 2 cm" To part (a) I answered 573nC circumference*length*(charge density)=(2pi*.04)*190*12E-9=573E-9 Part b is obviously very difficult to calculate absolutely correctly, since there is no obvious gaussian surface perfectly orthogonal to the electric field at every point. However, it seems to me that a short cylinder with its axis aligned with the charged cylindrical surface would make a good approximation, and I believe that is what is expected of me in solving this problem. So I'll do it with a cylinder of length 1m for simplicity's sake. Since (to a good approximation) the field will be orthogonal to the cylinder's curved surface at all points, and the flux through the ends will be 0, the flux through the curved survace will equal the field strength times the surface area of this surface, which will also equal the charge enclosed over epsilon naught (natural permittivity of space, I'll write this e0). E*A=Q/e0 E=Q/(e0*A) So the charge enclosed will simply be the charge in a 1m section of the charged cylinder. Q=(2pi*.04)*12E-9 The surface area of my Gaussian surface is... A=(2pi*.02) (ends not included because the flux through the ends of the cylinder is 0) E=.04*12E-9/(en*.02)=2710.581760219553 When I put this answer into Webassign (online homework, graded immediately) it is marked as wrong. My answer to part (a) is, however, correct. What is my problem?


title: A good theoretical approximation for a magnetically damped pendulum

text: In a laboratory course we had to perform an experiment with a pendulum (just an iron weight on a wire) and play around for some time with its wire's length and so on. This was quite boring and we decided to make something more interesting: We took two magnets (like this one) an tied one on the previously mentioned wire (which is made of plastic), and placed the other one on the surface of the table (I've tried to create a schematic). We tried to create a regular damped oscillator but the lab's staff told us it's not a good approximation, the problem is that we've only had one semester of mechanics and we've just began electricity. So my question is what what be a good relatively easy to understand theory which we actually apply to our measurements (we've measured the amplitude , the angle the time we've just video taped the whole motion).


title: Do Photons interfere when it passes through a slit (one)?

text: When a light (photons) goes through two slits it creates interference patterns. if the light goes through a "single" slit, does it create interference patterns or does it behave like particles (photons)? is the pattern same for both particles and light waves if it is a "single slit"? In the double slit experiment, if you close one slit (or observe) it is said that light behave as particles (bullets) which means that through one slit light exactly behaves as stream of particles??


title: Why incoherent source of waves have to be passed though a single slit for double slit interference pattern to occur?

text: Thomas Young used a single slit between the light source and the double slits. I can't understand why did he used the single slit, since the light from only one source is coherent already or isn't it? Does the narrow single slit make incoherent source coherent?


title: Bremsstrahlung vs energy conservation

text: From Wikipedia: > Bremsstrahlung is electromagnetic radiation produced by the deceleration of > a charged particle when deflected by another charged particle, typically an > electron by an atomic nucleus. The moving particle loses kinetic energy, > which is converted into a photon because energy is conserved. Isn't energy conserved for the moving particle in an electrostatic potential, $E_{kinetic} + E_{potential} = \frac{mv^2}{2}+\frac{kqQ}{r}$? If so, where does the extra energy for photons come from? Why don't electrons in atoms radiate away their energy?


title: What happens with a tunneling particle when its momentum is imaginary in QM?

text: In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to escape the potential through a process call quantum tunneling. This seems extraordinary from the point of classical mechanics because it implies the particle must cross a zone where it has imaginary momentum. I understand that from the point of view of quantum mechanics there is a non zero probability for the particle to be in such zones. What is it know about the behaviour of the particle in this zone? Links to research experiments or papers would be appreciated.


title: Why wire filament shakes inside a light bulb?

text: My light bulb cast a clear light toward adjacent wall and I can clearly see, that wire filament inside bulb shakes, though lamp itself does not moves even an inch What is causing this? Is it a permanent effect, happening all the time? Or is it a syndrome of near end of life of this current light bulb?


title: Is it possible to "cook" pasta at room temperature with low enough pressure?

text: It is known fact, that boiling point of water decreases by decreasing of pressure. So there is a pressure at which water boils at room temperature. Would it be possible to cook e.g. pasta at room temperature in vacuum chamber with low enough pressure? Or "magic" of cooking pasta is not in boiling and we would be able to cook pasta at 100°C without boiling water (at high pressure)?


title: How is the integrand concluded to be identically zero?

text: In expanding the classical Klein-Gordon field in Fourier space to write it in terms of $\phi(\mathbf{p})$ instead of $\phi(\mathbf{x})$, I reached the following result. $$\int \mathrm{d}^3p\exp({i\mathbf{p}\cdot\mathbf{x}})\left[\frac{\partial^2}{\partial \mathrm{t}^2}+|\mathbf{p}|^2 + m^2\right]\phi(\mathbf{p},t) =0$$ Now, how is it concluded that $$\left[\frac{\partial^2}{\partial \mathrm{t}^2}+|\mathbf{p}|^2 + m^2\right]\phi(\mathbf{p},t) =0.$$ I suspect there is a physical rather than mathematical reasoning for this, since, at least apparently, the integrand could have the whole complex plane as its range. (Or is the assumption that $\phi(\mathbf{x})$ is real, and therefore $\phi ^*(\mathbf{p})=\phi(\mathbf{-p})$, relevant?)


title: Accelerating masses lose energy?

text: If I understand this correctly, accelerating charges lose energy in the form of EM waves because they change the electric and magnetic fields, which "costs" energy. Does that mean that accelerating masses lose energy too, because they change the gravitational field (i.e. curve spacetime)?


title: Dimensionless entropy interpretation

text: Measuring temperature in joules instead in the artificial units of Kelvin would render entropy as a dimensionless quantity. This is quite appealing since entropy has always been quite a misterious quantity: it is used a measure of the disorder in a system but its units are J/K, which makes it really hard to interpret. The reason why entropy and temperature were defined this way is because they were studied before the athomical composition of matter was completeley accepted. You can read more about this in these posts: Why isn't temperature measured in Joules? Should entropy have units and temperature in terms of energy? Arieh-Ben Naim, a chemistry from Israel, has really good books in this topic such "Entropy demystified". He is one the main defenders that entropy should be a unitless quantity. I have always like to understand the gist of things, and the first step to understand a magnitud like entropy is understanding how it can be measured. For instance, I think I know what a speed is because I can reason in terms of space and time. But in entropy, as the way is normally defined, this is hard and tricky, and all the explanations I have heard so far seem to me like quite far-fetched. So here it goes my question. Let's accept for the sake of argument that we are considering entropy a dimensionless quantity. Now we heat a gas, and we calculate the entropy associate to this process. The result would be a number, whatever. Let us say that number is going to be 100. **How to interpret this number? What would it be measuring?** And finally, **do you agree with this vision of temperature units?**


title: Is centrifugal force equal in magnitude to the centripetal force in the frame of a body undergoing circular motion?

text: I was working out the minimum tangential velocity required for a swing to complete a full revolution and assumed the centripetal force is equal to the centrifugal force, so that I could set the weight force equal to the formula for centripetal (i.e. net force 0 at the top so swing won't fall). I'm pretty sure the answer is correct but doubt my reasoning.


title: Effects of high frequency lighting on human vision?

text: I have a couple of different LED flashlights. One of them has three different "modes" of brightness, and the way it controls it is via pulse width modulation (PWM). Here is a picture that illustrates how it works: ![enter image description here](http://i.stack.imgur.com/GF3LQ.gif) I know that this particular flashlight's PWM circuit operates at about 120Hz. What this means is that when you move something very quickly under it, when running a low duty cycle, it produces a strobe-light effect, where you'll see many "copies" of the moving object. It reminds me of the way video-games are rendered, and it actually creates a really neat effect because you only "see" very small time-slices. Watching running water this way is absolutely fascinating. From empirical observation I determine that on the lowest setting it seems to be on about a 2-5% duty cycle. The ghost-images produced are remarkably sharp. On Medium, I reckon it's about 25 to 30%. Something I've noticed very recently is that when I use this flashlight under dark-adjusted conditions, the brightness that is perceived definitely doesn't seem to scale linearly. I have no scientific light intensity equipment to perform measurements with, but I am more or less convinced that a 1000 lumen light on a 2% square-wave duty cycle appears brighter than a 20 lumen light, all else being equal (which would include incident light energy). I think there may be some biological explanation for this. Is this an effect that has been observed by others?


title: Why does a parachute decrease terminal velocity?

text: Terminal Velocity depends on two things- surface area and speed. These are inversely proportionate. If both these variables affect terminal velocity, why do parachutes slow you down? Initially you had a small surface area but a fast speed- with the parachute you have a larger surface area but lower speed. You have increased one variable but decreased the other. Therefore why do parachutes decrease speed?


title: Relationship between classical electromagnetic wave frequency and quantum wave function + de broglie frequency

text: As it is. As I study through classical mechanics and quantum mechanics, I began to wonder whether there is a relationship between classical electromagnetic wave frequency and quantum wave function and de broglie frequency). I think this is somehow related to quantum electrodynamics...but anyway.


title: How does the Kinect device work?

text: Some explanations of the device base it on a simple echo of light: "The camera transmits invisible near-infrared light and measures its “time of flight” after it reflects off the objects. Time-of-flight works like sonar: If you know how long the light takes to return, you know how far away an object is." (wired.com). Is it so easy? On other hand, the developers, Primesense, speak about "a sophisticated parallel computational algorithm to decipher the received light coding". And they claim to avoid noise from ambiance light and to be able to obtain a resolution of 1cm at 2 meters. A motivation to ask this here in physics is that some other questions were asking for measurement of light speed with household devices.


title: The Black Hole Problem

text: Consider a spherical body of uniform density $\rho$ and initial radius R. You can imagine this body containing another sphere of radius R/2 which touches the center and the periphery of the larger sphere. The smaller sphere has 8 times less mass, since the mass goes as the radius cubed. If you let the big sphere collapse gravitationally along with the smaller one, keeping the density uniform, the whole thing just shrinks proportionally. The Schwarzschild radius is proportional to the mass, so $R_S= 2GM/c^2$ for the larger mass, and for the smaller sphere $r_S= 2GM/8c^2$, one eigth as big. So when the large mass collapses, the smaller one hasn’t. It follows that the smaller sphere can still communicate with things outside, but the larger sphere should prevent it from doing so. The outgoing world lines at P due to the smaller sphere must be trapped by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems that the remaining larger irregular shaped mass has a greater attractive power than the regular shape of greater mass at specific points like P.Is it really so? For a sphere of a larger fraction of the size, say 3/5R, which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere, the smaller Schwarzschild radius is about .2 of the larger Schwarzschild radius. When the larger sphere collapses the smaller one has not collapsed---it has world lines in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion? Related question: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed? [QM effects are not being considered in this problem]


title: Is this really how a capacitor works? Why doesn't it behave like a resistor?

text: My book says a capacitor is two conducts being connected by an insulator. Now let's take a parallel plate capacitor to simplify the problem I have. Suppose I got two parallel plate capacitor in series and I hook the circuit up with a battery. ![enter image description here](http://i.stack.imgur.com/YWnG8.jpg) As soon as I hook it up, electrons flow (forget conventional current for now) into on the right plate and builds up on that capacitor (and spreads on the surface of conducting plate) and remains stuck there because there is an insulator that blocks the electrons from going anywhere. Now here is my confusion, how does the left plate of $\ C_1$ even build the positive charges and how do the current even run through the circuit if there an insulator blocking the electrons from moving? Is there even current through the circuit?


title: Gravitational field with cavity removed

text: I'm just struggling a little with this question: A uniform sphere, of radius $R$, contains a spherical cavity of radius $R/4$, whose centre is $3R/8$ from the surface. The diameter passing through the centres of the sphere and cavity meets the surface at points $X$ and $Y$. Find the ratio of the gravitational field at $X$ and $Y$. My attempt at the solution goes something like this: Using the superposition principle, the gravitation field due to the whole mass is equal to the sum of the gravitational fields due to the remaining mass and the removed mass. The gravitational field due to a uniform solid sphere is zero at its centre. Therefore, the gravitational field due to the removed mass is zero at its centre. The gravitational field due to the solid sphere is equal to the gravitational field due to the remaining mass. Now we know g acts towards the centre of the sphere. As such, both the gravitational field of the combination of the sphere and removed mass and the gravitational field of the sphere only act in the same direction, so we can use the scalar form of the equation. Therefore the gravitational field is given by $g=GMr/R^2$. Then insert $r=-R$ and $R$ for the gravitational field at $X$ and $Y$. But this doesn't seem to be correct as it is just the same as if the removed mass wasn't there..... have I gone wrong in my logic somewhere?


title: Calculating mass of object by lifting edge

text: Assuming a solid rectangular plate, hinged along one edge. How does one calculate the mass of the plate if the force necessary to lift the opposite edge is known?


title: Existence Of Electric Field Lines

text: Can an Electric Field with field lines Like So Exist: ![](http://puu.sh/tWkJ) One Of my friends said it couldn't as the field lines here are not conservative ; so it cannot exist ; Is he right? Or can it be made to exist


title: Photon source for Bell test

text: Wiki tells us that _In practice most actual experiments have used light, assumed to be emitted in the form of particle-like photons (produced by atomic cascade or spontaneous parametric down conversion), rather than the atoms that Bell originally had in mind. The property of interest is, in the best known experiments, the polarisation direction_ What device can actually be used for that source which creates a photon pair with entangled polarisations?


title: Contact angle formula still holds for liquid liquid interface?

text: ![enter image description here](http://i.stack.imgur.com/zubVb.jpg) I have seen in http://books.google.fr/books/about/Molecular_theory_of_capillarity.html?id=_ydSF_XUVeEC&redir_esc=y that there is a formula for the contact angle with a solid wall of a liquid- gas interface. The formula is $$ \cos \theta=\frac{ \sigma_{liquid-solid}-\sigma_{gas-solid}}{\sigma_{gas- liquid}}$$ where $\sigma_{AB}$ are the surface tensions between $A$ and $B$. > Does this formula work also in the case where instead of gas we have another > liquid?


title: Can action of the weak and strong forces be reduced to action of electromagnetic force?

text: It is known that electromagnetic (EM) fields action on particles is limited to the Lorentz force action. In terms of spinors and currents, the EM field: (i) rotates the Dirac current around the direction of the field $B$ to the angle proportional to the magnitude of $B$, and (ii) "accelerates" the Dirac current in the direction of $E$ to the extent proportional to the magnitude of $E$. Action of Lorentz force exhausts all possible rotations and boosts. In fact, nothing else could "happen" to the Dirac current (which is a Minkowski space 4-vector) except (a) rotation and boost described above, and (b) change in magnitude of the Dirac current vector prohibited by conservation of charge and/or mass. Unless the action of weak and strong forces is always limited to change of mass/charge of the particle, is it possible to consider the effect of these forces on particles as a kind of "special" electromagnetic action?


title: Is the universe finite and discrete?

text: Is the universe finite, both in the sense of being a closed spacetime manifold, as viewed from the macro level, but also in the sense of being fully discrete and finite in all of its intricate quantum level construction? The most popular current research, i.e. string theory, builds a machinery on top of a continous notion of spacetime. Would a more accurate model of the physical world have to build on top of a finite, discrete, network like, relational spacetime model?


title: Why doesn't the water spill out?

text: In this experiment, a number of coins are put into a cup _full_ of water, without spilling it. http://www.youtube.com/watch?v=N2mKpZHnEzw Firstly, let me clarify one thing. > If you fill up a cup of water to the brim, in such a way that even another > _drop_ of water will cause it to overflow, **_can this cup take a coin, > instead of a water-drop_**?   >  \- If no, then it doesn't matter and there's no point to this question.   >  \- If yes, then my question is this: _why another coin_ and not another > water-drop? **\---This part exists only if the answer to the question above is yes---** They say it's because of surface tension, but I still don't get how that explains it. If the surface tension can hold together _another coin_ , then why not **_another drop_** (which actually has less volume than a coin)? The only reason I can think of is that the adhesion between the water and the coin is high, which sorta pulls the water molecules towards the coin, increasing the density of water immediately around the coin - thereby making up for the extra space the coin takes.   _(But thinking about that, that doesn't seem to make much sense either. The coin is at the bottom, and I don't know if adhesive forces can produce such increases in density.)_ So: what _is_ the reason for this? Why a coin and not another water-drop?


title: Invariance of Maxwell's Equations under inverting variables - Reference and use

text: Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I think "inverting" may have been the word the author used.) The paper was in one of the endorsed groups (not General Physics), and seemed quite authoritative. But I've never seen this property mentioned elsewhere, and wanted to know:   1. A reference, as stupidly I didn't note the paper's ArXiv code at the time (The reference needn't be to that or another ArXiv paper of course - Quite likely this is better explained in some other source such as a textbook.)   2. Whether this is considered just a curiosity with no known use or, like the Lorentz transforms, which are another well-known Maxwell Equations invariant, does it have any practical application?


title: Oldest population 1 star system?

text: While reading Stanislaw Lem's essays on advanced civilizations, I had a question: When did the earliest generation of population 1 star systems form? How much older could they reasonably be than our star system?


title: Optical laser pumping and reflectors

text: Let's say we are building Nd:YAG laser. It is optically pumped by some linear xenon flash lamps, it absorbs light around 750nm and 800nm, and emitted light is at 1064nm. The question is why doesn't 1064nm emission from the flash lamps interfere with laser operation? Why doesn't 1064nm photons emitted in the Nd:YAG at 'wrong' directions (not coaxially to the resonator path) and reflected back and forth from the cylindrical/oval reflector (for the flashlights) interfere with the laser emission? As far as I see it, both these factors should consume precious atoms in excited state, and probably require some 1064nm filter around the Nd:YAG rod...


title: Mathematical concept of supersymmetry

text: I wish to study supersymmetry in field theory(sometime in december). However, I am quite not sure what is needed for its study. In supersymmetry, I just want to get the mathematical idea, such as its algebra. I will finish a course in QM this semester. I have studied some lie algebra (Cahn, Georgi). I also have some knowledge about classical field theory such as E-L equations, yang- mills theory, gauge invariance, symmetry breaking, higgs mechanism which I acquired through the study of solitons. I DONT HAVE ANY KNOWLEDGE OF QUANTUM FIELD THEORY. Is this knowledge enough to study supersymmetry? What exactly in supersymmetry can I hope to learn in addition to the mathematics? WOuld it be possible for me to apply it to the standard model? Hope this will not be closed as too specific. I am looking for brief information on what exactly can one study in supersymmetry and its prerequisites.


title: On the atomic level, how is incandescent light structured?

text: I want to know from the smallest possible originating structures how the light I see generated from heat is made by atoms themselves.


title: Why would a layer of ice prevent frost damage to fruit?

text: I know a family that grows fruit such as blueberries in a climate that frosts on occasion. When this happens, they turn on sprinklers which covers the buds and fruit with a layer of water which turns to ice. Why would this layer of ice prevent damage to the plants/fruit? Perhaps it insulates them, keeping temperature at 0 degrees but now below it?


At CMB recombination (z=1090), what is the radial extent of the last scattering "shell"? a) Delta(z) = .... b) Delta(comoving angular distance)= ....Mpc The WMAP first-year parameters give Delta(z) = 195. Is this still correct?


title: What's going on along the "sides" of an Alcubierre warp bubble?

text: The models/depictions I've seen of warp bubbles show space compressed ahead of the bubble and expanded behind, so that the space inside the bubble moves with respect to the space outside. If that is so, then what is happening at the sides? It would seem that there is some sort of shear taking place between the space inside and outside. Is that correct, or is that based on a misinterpretation of the model?


title: Good place/supervisor for PhD in Theory of Condensed matter

text: I am currently finishing my undegraduate degree in physics and would like to do PhD in Theory of Condensed Matter field. Could you give advice on which are good groups/supervisors in the field. Please, justify by adding citations to important research papers they have produced, any awards received etc.


title: Bound State of Only Massless Particles? Follows a Time-Like Trajectory?

text: Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light- like trajectory, or would the interaction energy cause it to travel on a time- like trajectory?


title: Flow of liquid among branches

text: If water is flowing through big pipe is branched into 4 branches of small pipe. Lets say the flow is around 4 m/sec. I have the following questions:     1. What will be the flow rate in each of the pipes? I would be knowing diameter, height of the pipes. Considering all pipes are rigid.     2. What will be the flow rate in each of the pipes, if I close one pipe of the 4 branches? Will water flow speed increase in other 3 pipes? If yes, how we can calculate the gain of speed of flow?     3. What if the pipes are non-rigid, will that have any effect?


title: Speed of light is not fixed?

text: In my research, I found that the speed of light is not fixed. IS it true? Namely, We know that light refracts when the medium it travels through changes. Actually, light travels in the same medium without refraction . This is a relative motion in two dimension. However, in the medium light up to ‘’(△v)t ’’ is behind of observer. The wavelength of the light entering the medium, shortened according to the wavelength in vacuum ( such as a compressed spring). Observed by the observer's motion a relative movement. According to v > v2. (v2 =c ). In water do not refracted light only according to the observer, up to (△v)t been remains behind in time. So, speed of the observer is greater than speed of light in the medium. Electromagnetic waves loses speed while passing inside medium. I tested it several times, it is possible to explain with equations of relative motion in two dimension. This mean is that; speed of our universe is ''c'' and same direction spherical wave and this speed creates time. ( All masses are moving in the same direction with speed of ''c'', this way we can not observe this speed) I also observed this; the light coming from upright to x and y coordinates ( Normal) do not refract, but shorter (We observe an object a higher position than initial position in water) . Is this right? We can explain this with the equations of relative motion in two dimention. How can we, assuming the Fermat and snell says true? How can I explain it with the equations of relative motion in two dimensions? If I am wrong, could you please explain me why.


title: The AntiBonding Orbital with Shrinking Interatomic Distance

text: I guess this is more of a chemistry question, but whatever. I think it's interesting. Suppose you had two bare atomic nuclei. For concreteness, lets assume the nuclei are the same with atomic number $Z$. Lets bring in a single electron and focus on the ground states of the nuclei. When the nuclei are far apart, the ground states are degenerate. When we bring the nuclei together, the ground state splits into the bonding and anti-bonding orbitals. Let $\Delta E$ represent some measure of the energy difference between the bonding and anti-bonding orbitals. From intuition, I would expect $\Delta E$ to increase with decreasing internuclear distance $R$. What happens as $R$ shrinks to zero? I expect the bonding orbital to become the ground state of an "atom" with charge $2Z$. Is that correct? More importantly, what happens to the anti- bonding orbital? This isn't an exercise in the Born-Oppenheimer Approximation. I magically hold the nuclei at a distance $R$, so their repulsion doesn't matter. Also, electron-electron repulsion doesn't matter because I only introduce one electron.


title: What Observations could undeniably support string theory?

text: What experiments could provide observable "stringy" effects. All valid experiments are acceptable (also theoretical experiments).


title: How many orders of magnitude in energy spans the Standard Model phenomenological spectrum?

text: I am wondering if it makes sense to state that the upper limit is roughly 1012 eV (up to know the physics probed by the LHC seems to be pretty consistent with the SM) and the lower one is ... the upper bound for the photon mass (somewhere between 10-14 and 10-26 eV according to http://arxiv.org/pdf/hep- ph/0306245v2.pdf).   If I understand well the argument in this article, one could say the larger value 10-14 eV comes from the Standard Model of particles (the photon would acquire mass by the Higgs mechanism, its large-scale behavior beeing eﬀectively Maxwellian) while the smaller value 10-26 eV would come from the standard model of cosmology (the value of the galactic field today leading to this value from the hypothesis of a "Proca regime for all scales" ??). Edit 06/12/13: I removed the expression : "domain of validity" that sounds too much like a mathematical closed interval. It is not adapted to the Standard Model because it is not a theory. I have chosen the formulation "phenomenological spectrum" to insist on the fact that this spectrum can be enriched with new particles whose masses are in the same energy range as the old ones.


title: Practical method to weigh human limbs with common household items?

text: What methods could be used to determine ( _or_ estimate within a _reasonable_ margin of error) the mass of a living human's limbs, short of cutting them off? And more interestingly, how can this be done without any high tech equipment, just with the means commonly found in households? A scale for example is allowed. An MRI isn't ;)


title: Having trouble seeing the similarity between these two energy-momentum tensors

text: Leonard Suskind gives the following formulation of the energy-momentum tensor in his Stanford lectures on GR (#10, I believe): $$T_{\mu \nu}=\partial_{\mu}\phi \partial_{\nu}\phi-\frac{1}{2}g_{\mu \nu}\partial_{\sigma}\phi \partial^{\sigma}\phi$$ In an intro to GR book I find this formulation of the same: $$T^{\mu \nu}=[\rho+\frac{P}{c^2}]u^{\mu}u^{\nu}+g^{\mu \nu}P$$ I'm having trouble seeing how they are describing the same thing. Is $\partial_{\sigma}\phi \partial^{\sigma}\phi$ equal to $P$? In the book equation, $u^{\nu}$ and $u^{\mu}$ are four velocities differentiated w.r.t. time. Where do these appear in Suskind's equation? What happens to the factor of $\frac{1}{2}$? If I understand the lectures correctly, $\rho$ is essentially the $T^{00}$ component of the tensor in the Newtonian limit. I don't see how the second equation reduces to $\rho$ in that limit (slow and flat). I appreciate your help.


title: Is it possible to split a single light beam into two beams of opposite circular polarization?

text: A properly oriented calcite crystal will separate an unpolarized beam into two beams, one vertically polarized and one horizontally polarized. Other polarizers pass just one polarization and absorb the perpendicular one.   Is there a device that splits an unpolarized light beam into a right circulaly polarized one and a left circularly polarized one, instead of just absorbing one or the other?   (If so, please tell me where I can buy one.)   If not, is this theoretically impossible?


title: Constant Volume vs. Constant Pressure?

text: Approaching the following question: > Consider two experiments in which 2 moles of a monatomic ideal gas are > heated from temperature $T$ to temperature $T + \Delta T$: in the first > experiment the volume $V$ is kept constant, in the second experiment the > pressure $p$ is kept constant. How much more heat is needed in the second > experiment than in the first experiment to raise the temperature by the > given amount $\Delta T$? The answer is $2 R \Delta T$. The origin of the problem may be found here under _Question 14_. I am confused as to home to come to this conclusion. I believe I am able to utilize $pV = N k_B T$ and $VT^\alpha = const$, $pV^\gamma = const$ but I am unsure of how the two constants apply to this. Do both constant apply to each of the experiments? How do I manipulate these equations to achieve my desired result?


title: Total radiation flux from a star

text: I'm looking around the net to find good resources on how to compute total radiation flux from a given star at a given orbiting distance. Ideally I'd like to get not just the $W/m^2$ of the star, but also the expected high-energy particles, EM, thermal, solar wind pressure.. well, the works. Everywhere I looked they seem to compute these values for our Sun and at 1AU, then I'm left to wonder how this relates to stellar mass, composition type, luminosity, distances, etc. In the end, I'm trying to quantify a sort of habitability range around a given star. Much in the way of saying: well, given this blue-hypergiant you could get close to about $40$ $AU$ before you get toasted in your puny spacecraft. Or, habitable planets could exist between $100$ AU and $120$ AU.etc.. I would have thought this would have been more common around sf projects, but radiation seems to go unnoticed in most sf themes.


title: Relation between comoving distance and conformal time?

text: In cosmology, we have two quantities and I want to understand the physical relation between these two : $\chi = \int_{t_e}^{t_0}c\frac{dt'}{a(t')}$ : the comoving distance with $t_e$ the time at emission and $t_0$ the current cosmic time $\eta_0 = \int_{0}^{t_0}\frac{dt'}{a(t')}$ : the conformal time with $0$ the time at Big-Bang and $t_0$ the current cosmic time My question are : 1) Is it possible to know the conformal time of a galaxy only knowing its comoving distance from us 2) What are the physical meaning difference between $\eta$ and $\frac{\chi}{c}$ ? 3) What are the physical meaning difference between $\chi$ and $c \eta$ ? Than you very much !