My mind has been busy recently by this question: What is physics of Collision between solid and liquid (or gas)? What is Conservation law's of such Collision? Why, when we drop a solid object in water, water shows an Strange behavior (infact what is Conservation law's of energy and momentum when we drop a solid object in water )? Figure 1: Strange behavior of water after impact ![Strange behavior of water after impact](http://wp.streetwise.co/wp- content/uploads/2012/05/water-drop.jpg)


title: Storing kinetic energy in bonds

text: Let's assume a setup with a static linear molecule with three identical atoms connected by bonds and a single atom, identical to the other three, being shot at the molecule. Let's also assume that everything happens in 1D and can therefore be illustrated by this simple scheme:               (projectile) A ->    A-A-A (molecule)      Where the direction of the arrow is the direction of motion of the projectile and the dash signs in the molecule are the bonds between atoms. Assuming a low-energy, non-relativistic, perfectly elastic collision, the projectile will stop dead in its track while the molecule will be set in motion at 1/3rd of the projectile's speed, as it has 3 times the projectile's mass (conservation of Momentum). Balancing also the equations for the Kinetic Energy easily reveals that 2/3rds of projectile's kinetic energy must have been locked away in internal vibrations of the molecule. Now, it's easy for us to calculate these numbers by considering the projectile and the molecule as just two separate systems and conveniently attaching a total mass to each. But in reality the universe doesn't group atoms into molecules, does it? Each bond in the setup doesn't "know" about the existence of the other bond and each atom could be said to be unaware of all but the atoms bonded or colliding with it. In this context, not "knowing" total masses, how does the universe "calculates" that in this case the molecule must store 2/3rds of the projectile kinetic energy into internal vibrations, no more, no less?


title: How to show isotropy of $SU(2)$ Yang Mills stress energy tensor?

text: When I vary the action of the YM Lagrangian density $$L = -\frac{1}{4} F^a_{\mu \nu}F^{\mu \nu}_a + J_a^\mu A^a_\mu$$ with respect to the metric, I obtain: $$T_{\mu \nu} = \frac{-2}{\sqrt{|g|}} \frac{\partial}{\partial g^{\mu \nu}} \left( \sqrt{|g|} L \right) = \frac{1}{4} g_{\mu \nu} F^a_{\sigma \alpha} g^{\alpha \beta} F^a_{\beta \rho} g^{\rho \sigma} - F^a_{\mu \alpha} g^{\alpha \beta} F^a_{\beta \nu} ,$$ where $$F^a_{\mu \nu} = \partial_\mu A^a_\nu - \partial_\nu A^a_\mu +f^a_{jk} A^j_\mu A^k_\nu. $$ $f^a_{jk}$ being the structure constant that embodies the properties of the symmetry group under consideration, here $SU(2)$ so that the index $a$ can run over three different values. My question is, how do I go about showing that this stress energy tensor is invariant under rotations? I was able to show this for the $U(1)$ case with a scalar field, where I got $$T'_{\mu \nu} = R_{\mu i} R_{\nu j} T_{ij} = T_{\mu \nu}$$ using the FLRW metric in its cartesian coordinate form, and assuming that the time component of the scalar field was zero and $A^a_i = \phi(t) \delta^a_i$ so that the terms arising from taking its derivative only yield diagonal elements. Note that the rotation matrix used was a standard 4 by 4 matrix with 1 as its (1,1) element and sine/cosine on the remaining 3 by 3 block. Can I do something similar for the above tensor, that is, use the same rotation matrix?


title: Jupiter Core is Solid Hydrogen

text: I was watching a show on the science channel about gas giants; there is something I do not understand. I am not a scientist, so this may be obvious to some. I learned that there a three states of an given physical object; solid, liquid, and gas depending on how cold or hot the object is. An easy example is ice, water and steam from coldest to hottest. So the theory is that Jupiter has a super-heated solid and very dense core that is made up of hydrogen. How does a gas like hydrogen become a solid while being super-heated? Is it that the pressure is so much that the gas is compressed into a solid? If so how much pressure does it take to compress hydrogen into a solid? How does the heat play into the equation?


title: Why the dangling bonds at the edge terminated by hydrogen atoms give no contribution to the electronic states near the Fermi level

text: How about changing H atom to other kinds of atoms?


title: Elastic Collision

text: A cube has a side length of 20 cm. An atom in the gas moves around the cube as shown. It continually bounces off the four lateral walls of the cube. The atom has a mass of 6.6×10−27 kg. Because of the elastic collisions with the walls, the atom maintains its speed of 300 m/s as it moves around. The figure below shows the view from above looking down into the cube at the path of the atom. The repeated hits cause there to be a force applied to each of the four lateral faces. Find the force (in Newtons) that it applies to Face 1. Find the force it applies to Face 2.![enter image description here](http://i.stack.imgur.com/mrgk6.jpg) I have tried the thing as F=change in momentum w.r.t time for face 1 chnge inn momentum is 2mv sin(60') how to calculate change in time? or is there any other approach to the problem??


title: Minimum possible Kinetic Energy of a confined electron

text: The problem is this: > Consider an electron confined in a region of nuclear dimensions (about 5 > fm). Find its minimum possible kinetic energy in MeV. Treat this problem as > one-dimensional, and use the relativistic relation between E and p. From Heisenberg's uncertainty relation for position and momentum $\Delta x \Delta p\geq\frac{ℏ}{2}$, $\Delta pc= \frac{ℏc}{2\Delta x}=39.4\text{ MeV}$ where $2\Delta x=5\text{ fm}$ is the width of the region. Plugging this into the relativistic energy-momentum relation $E^2=(mc^2)^2+(pc)^2$, $E=39.4\text{ MeV}$ which is the correct answer. However, in my book there is also an equation for the zero-point energy which is defined as the lowest possible kinetic energy for a quantum particle confined in a region (one-dimensional) of width $a$ and is given by $\langle K \rangle= \frac{ℏ^2}{2ma^2}$ and the answer I get here is about $1.52\text{ GeV}$. Why are/should these answers be so different? Also the questions says "The large value you will find is a strong argument against the presence of electrons inside nuclei, since no known mechanism could contain an electron with this much energy." How is this argument made exactly?


title: DO the condensed photon particles-waves-longitudinal-waves exist?

text: This is kind of hard to explain, because weird as it sounds, i have experienced a phenomenon that i would like to see if it exists and if i can explain it mathematically. The longitudinal waves of photons( visible light spectrum) had a density and pressure. It could be sound waves if they can produce light effects in the space( visible,white light), i dont know i am speculating ?.. but for this to happen, i quess, there would have to be very high frequencies of sound waves, which i quess would damage a living organism? I dont know. I am sorry, for not being very specific, but this is everything i got. So, my question is : Can there exist a longitudinal wave of light( white light) with density and pressure, that can be felt? Thank you for your time.


title: Huygens Principle and principal of rectilinear propagation of light

text: Suppose I have an wave source and light waves are radiating from it. If I have a point source, then after a time t, with a radius of ct I will have a circular wave front.By Huygens principle each point on the wave front acts like a secondary source. From this point again light can travel in all directions. So isn't the principle of rectilinear propagation of light violated?![enter image description here](http://i.stack.imgur.com/ipOCi.png) Consider the light following the specified path shown with the arrow head.


title: Is the density operator a mathematical convenience or a 'fundamental' aspect of quantum mechanics?

text: In quantum mechanics, one makes the distinction between mixed states and pure states. A classic example of a mixed state is a beam of photons in which 50% have spin in the positive $z$-direction and 50% have spin in the positive $x$-direction. Note that this is not the same as a beam of photons, 100% of which are in the state $$ \frac{1}{\sqrt{2}}[\lvert z,+\rangle + \lvert x,+\rangle]. $$ It seems, however, that at least in principle, we could describe this beam of particles as a single pure state in a 'very large' Hilbert space, namely the Hilbert space that is the tensor product of all the $\sim 10^{23}$ particles (I think that's the proper order of magnitude at least). So then, is the density operator a mathematical convenience, or are there other aspects of quantum mechanics that truly require the density operator to be a 'fundamental' object of the theory? (If what I mean by this is at all unclear, please let me know in the comments, and I will do my best to clarify.)


title: How much energy is necessary to set a year to exactly 360 days

text: How much energy would be necessary to slow down Earth rotation such that a year was 360 days long? In the same spirit: how much energy would be necessary to make the Earth rotate faster around the Sun such that a year was 360 days long? _(Just for fun: how would you do it practically?)_


title: Is there any relation between weak and strong fields, similar to electric and magnetic fields?

text: Is it possible to unify the strong, weak, electric and magnetic field just by Maxwellian type equations? (Maxwell by adding a small change - unified electric and magnetic field, then Einstein's equations - use it to create special and general theory of relativity, now maybe all we need is a little more change to unify all fields,) When $B$ and $E$ are known magnetic and electric fields, then $W$ and $S$ are weak and strong fields, what are their units?


title: How to calculate the electric field at a point in space

text: Let's say I have a uniformly-charged wire bent into a semi-circle around the origin. How can I find the electric field (magnitude and direction) I'm not even sure if I should use Coulomb's or Gauss' law either. Kind of stuck setting up a solution and starting somewhere.


title: A space train falls front first into a black hole

text: A long space train's HAL 2000 computer goes wacko and drives the ship and its sleeping crew front first straight into a Black Hole. As it nears/crosses the event horizon, does the space train break up due to gravitational stretching from the rear first, the front first, or evenly ? Contrary to depictions on YouTube which suggest the closest parts break up first, my quick calculations put the rear under most stress due to huge momentum forces from it being accelerated forward in its weaker gravitational field by the front of the train, as opposed to the front which is in free fall except for being held back by the rest of the space train's increasing momentum. Think of a merry go round which simulates the increasing gravitational field. A long heavy rubber Bungy stretches more at the centre of the MGR where it is tethered than at the loose end because the tethered end carries the full weight of the Bungy. If it goes around fast enough the Bungy will break off at the tether not at the loose end or in the middle. Am I correct?


I got asked this question for my physics course at college, i'm not the best at airspeed velocities... > What is the airspeed velocity of an unladen swallow? I still can't find anything to help me, i'm quite stuck and have been googling and asking about on a few forums. Best help I found was this page on the subject. Thank you.


title: Can the new results (about photonic time travel) make quantum computers feasible?

text: New results published about photonic time travel, reference here make quantum computers a reality in the near future? These results seem to indicate that there can be qubits that can exhibit nonlinear behaviour, and this in turn may have deep implications to quantum cryptography, and possible profound effects on the nature of unitary interaction, and the influence of decoherence.


title: Does the Bohr van Leeuwen Theorem also apply to ferromagnetism?

text: I know that the Bohr-van Leeuwen theorem shows that there could be not consistent pure classical explanation of dia- and paramagnetism. Does the same theorem also rule out a consistent classical theory of ferromagnetism? Do you have any realiable references for this?


title: What is the intuition behind $gt^2/2$ equalling the distance something falls after $t$ seconds?

text: Let's say $g=10\ \text{m/s}^2$ and it drops for $3$ seconds. For the first second it will drop $10\ \text{m}$, the second it will drop $20\ \text{m}$ ($10 + 10$) and the third second it will drop $30\ \text{m}$. Then if we add $10+20+30$ it equals $60$ but if you use the equation it equals $45$. Whats the flaw in my thinking?


title: Effect of aircraft speed on barometer

text: Many aircrafts depend on several types of static pressure sensors (barometers) to find the altitude. I assume this sensor need to be located outside the aircraft main body, so that it has a contact with the outside atmosphere to measure its pressure. Now, won't the speed of the aircraft has an effect on this barometer? The fastest you are, the faster is the airflow in contact with the pressure sensor, which would cause (erroneous) increased pressure reading.


title: Output of a beamsplitter with photon number (Fock) state inputs

text: Given a beamsplitter drawn below, where $\hat{a}$ and $\hat{b}$ are input modal annihilation operators, transmissivity is $\tau\in[0,1]$, and output modal annihilation operators are $\hat{c}=\sqrt{\tau}\hat{a}+\sqrt{1-\tau}\hat{b}$ and $\hat{d}=\sqrt{1-\tau}\hat{a}+\sqrt{\tau}\hat{b}$, suppose the inputs $\hat{a}$ and $\hat{b}$ are in photon number (Fock) states $|m\rangle$ and $|n\rangle$, respectively. What are the states of the outputs $\hat{c}$ and $\hat{d}$? ![beamsplitter](http://i.stack.imgur.com/KKwVy.png) I understand that if one of the inputs is a vacuum state $|0\rangle$, then the output states are binomial mixtures of photon number states, with "probability of success" parameter being either $\tau$ or $1-\tau$ and the "number of trials" parameter being the photon number $n$ of the non-vacuum input (so, if $|0\rangle$ was input on mode $\hat{a}$ and $|n\rangle$ on mode $\hat{b}$, then mode $\hat{c}$ is in the state $\sum_{k=0}^n\binom{n}{k}(1-\tau)^k\tau^{n-k}|k\rangle$ and mode $\hat{d}$ is in the state $\sum_{k=0}^n\binom{n}{k}\tau^k(1-\tau)^{n-k}|k\rangle$). I am wondering how this generalizes to both input modes being in the non-vacuum states.


title: Point of rotation appears as an ellipse when calculated from gps coordinates

text: First question here. Feel free to write if I posted in the wrong place. While rotating a ship as accurately as we can around some point within the ship, we can calculate the point of rotation from GPS data collected by a GPS receiver on the ship (the GPS is positioned some distance away from the point of rotation). From the GPS data we gather, we find the point of rotation to be an ellipse. Of course due to inaccuracy we cannot find the exact point of rotation from GPS satellites, but is there some physical explanation as to why the point of rotation is an ellipse and not a circle? For reference we used a Dynamic Positioning system to calculate the point of rotation. This was a circle.


title: Moving coil contradiction of Faraday Induction

text: In Faraday's Induction Experiment, the e.m.f. induced in the induction coil becomes zero when the relative velocity of the coil and the magnet becomes zero. But one can also argue from a stationary observer's reference frame. Let's assume the magnet and the coil to be moving at an equal velocity. For a stationary observer (who measures the induction apparatus in motion), there will be an induced e.m.f. in the region of space around the moving magnet, since there will be a relative velocity between any point in surrounding space and the magnet. Now since the coil moves through this region of space, it should therefore possesses an induced electric field as well. I totally trust Relativity, and therefore this means that the stationary observer should compute a reverse e.m.f. that exactly cancels out the e.m.f. caused by the moving magnet, or maybe I am on the whole absurdly wrong (in which case I would like to know where my thought experiment went wrong).


title: Can a neutron star compress until it's converted to a black hole?

text: The Universe's densest objects are black holes. In the second place, there are neutron stars. So, if a neutron star compresses to its Schwarzschild radius, would it appear as a black hole? That black hole would be one of the most dense objects in the universe?


title: Understanding the Eötvös experiment

text: The aim of the Eötvös experiment was to "prove" that for every (massive) particle, the quotient $\frac{m_g}{m_i}$ is constant, where $m_g$ is the gravitational mass and $m_i$ is the inertial mass. **The experiment:** Consider two objects with coordinates $x(t)$, $y(t)$ and with masses $M_i$, $M_g$, $m_i$, $m_g$ (on the earth where the gravitational field $\mathbf g$ can be considered constant), connected by a rod of length $r$, and suspended in a horizontal orientation by a fine wire. The Newton's second law says that $$\ddot {\mathbf{x}}(t)=-\frac{M_g}{M_i}\mathbf g$$ $$\ddot {\mathbf{y}}(t)=-\frac{m_g}{m_i}\mathbf g$$ so if we experiment that the quantity $\eta:=\frac{2|\ddot {\mathbf x}(t)-\ddot{\mathbf y}(t)|} {|\ddot {\mathbf x}(t)+\ddot{\mathbf y}(t)|}$ is very small, then when can conclude that $\frac{M_g}{M_i}=\frac{m_g}{m_i}$ and so we are done. Now textbooks say that if $\ddot {\mathbf{x}}(t)\neq\ddot {\mathbf{y}}(t)$ then we will have a torque $$N=\eta\, r(\mathbf g\times \mathbf{e_2})\cdot \mathbf{e_1}$$ and misuring this torque we can give an estimation of $\eta$. ![enter image description here](http://i.stack.imgur.com/F39RI.jpg) **My problem:** Even if the two accelerations are different, I don't understand where is the torque, the point ${\mathbf{x}}(t)$ will move down and ${\mathbf{y}}(t)$ will move up in my opinion. The angular momentum is along $\mathbf{e_3}$, so the rotation is in the plane $\left<\mathbf{e_1},\mathbf{e_2}\right>$.


title: What to consider before taking a physics course (given a mathematical background)?

text: I'm a Computer Engineering major, but when I was in high school I was a very poor student. I didn't pay attention and I didn't think I was capable of succeeding in classes like Math and Science so I just didn't care. I'm much older now and a bit wiser, and because I'm back in school, I realize I may have some potential. I've always loved science and math but never appreciated it. I left high school knowing only pre-algebra. Now 8 years later I taught myself Algebra through reading and practice, and started attending a community college and placed directly into their Pre-calc class without any Algebra classes. I successfully passed Pre-Calc, Calculus 1 and currently in Calculus 2 all with A's. I've never taken a Physics course before, but I'm extremely interested in the topic. Will my success in Math translate into success with my upcoming physics courses (calculus based physics is where I'll be starting)? Is there anyway to prepare to learn physics so that I have a higher chance of succeeding in the course? How much of understanding physics is just natural ability?


title: Negative g-force: difference between gravity and centrifugal force?

text: I was having a discussion with a friend about human tolerances of g-force. He believed that the maximum human tolerance of negative g-force is low, in the order of .5 g. I countered, saying that you're able to stand on your head and do not die. An interesting discussion ensued but there was one thing that we couldn't figure out: Is there any difference between the negative g-force when you are standing on your head (i.e. you're stationary on the ground, just upside down, experiencing gravity) and negative g-force when you're in motion? For example, like when you are riding a roller coaster that has a bump in the track, and you're forced up from your seat?


title: Does the canonical commutation relation fix the form of the momentum operator?

text: For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar $$ Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on coordinate or momentum representation, but I don't know if that statement constitutes a proof. Moreover if we choose $\hat{x}\psi=x\psi$ is the answer of the following question yes? For the second one $$(\hat{x}\hat{p}-\hat{p}\hat{x})\psi=x\hat{p}\psi-\hat{p}x\psi=i\hbar\psi $$ but I don't see how can I say that $\hat{p}$ must be proportional to $\frac{\partial}{\partial x}$. I don't know if trying to see that $\hat{p}$ must satisfy the Leibniz rule and thus it should be proportional to the $x$ derivative could help. Or using the fact that $\hat{x}$ and $\hat{p}$ must be hermitian Any hint will be appreciated.


title: Is there an "authoritative" source for ephemeris data?

text: I find some variation in the values reported for ephemeris by the various sources I have access to. For example for 2012-11-27T03:31:55 UTC I get solar declination values of -21.1828°, -21.18296°, -21.1814°, -21.1834°, -21.1906° and (again) -21.1814°. Are the differences among these values meaningful? Is there an "authoritative" source (ideally online) for ephemeris data?


title: Does closing curtains 'make your home warmer'?

text: I mean, in the sense that the act of closing curtains would somehow reduce the amount of heat loss of the house to the outside, thus making it warmer _for a given supply of heating_.


title: Symmetry breaking under isothermal expansion

text: Is there any example of a symmetry breaking phase transition in a system of particles under isothermal expansion?


title: Why I think tension should be twice the force in a tug of war

text: I'm going to provide my argument for why I think the tension in a rope should be twice the force exerted on either side of it. First, let's consider a different example. Say, there is a person named `A` and a block in space. `A` pushes on the block with a force of 100 N. Then, the block will also push `A` with a force of 100 N by Newton's third law. Now, consider the case where instead of the block, there is a person `B` who is also pushing on `A` with a force of 100 N while `A` is pushing on him. `A` will experience a force of 100 N because he pushed on `B`, AND another 100 N because he is being pushed by `B`. Hence he will experience a force of 200 N. Similarly, `B` also experiences 200 N of force. Now, back to the original problem. There are two people `A` and `B` in space with a taut rope (no tension currently) in between them. If only `A` is pulling and `B` is not, then I agree that the tension is equal to the force `A` exerts. This situation (in my opinion) becomes analogous to the above if `B` is also pulling. So, say both of them pull from either side with a force of 100 N. Then the rope at the end of `B` will pull `B` with a force of 100 N (this pull is caused by `A`). By Newton's third law, the rope will experience a pull of 100 N. But `B` is also pulling his end of the rope with 100 N. Therefore, the tension should be 200 N. Similarly, the end of the rope at `A` must pull `A` with 100 N of force (because `B` is pulling from the other side) and hence experience a force of 100 N itself by Newton's third law plus another 100 N because `A` is pulling on the rope. Apparently, the answer is not this (according to my searching on the web). So, could anyone tell me why this reasoning is wrong? Thanks. **EDIT :** So apparently people don't agree with my first example, leave alone the second. This is to the downvoters and the upvoters of the highest-rated answer: You all agree that if only `A` pushes `B` with a force of 100 N, then `A` and `B` both will get pushed by a force of 100 N in opposite directions, right? Then, in the case where `B` is also pushing with a force of 100 N, it doesn't make sense that the answer would be exactly the same. It doesn't seem right that no matter what `B` does, `B` and `A` will always experience the same force as they would have if `B` hadn't applied any force. **EDIT 2 :** I'm going to provide here a link to a question that I posted: Two people pushing off each other According to the answer and the comments there, **the reason as to why my first example is incorrect is different to the one provided here**. So maybe you should all read the answer and the comments provided by the person and reconsider what you think.


title: Tension when two connected blocks are pulled in opposite directions

text: Suppose there exist two blocks A and B connected by a massless, inextensible cord. Both A and B have equal masses and are acted upon by equal forces in opposite directions. So, is the tension in the string the sum of the two forces, the resultant of the two forces or something else?                     <-F--  A _________ CORD__________B   --F->


title: How to reconstruct information from a graph of an oscillation?

text: We are given a graph of the position of a wave (amplitude). How can we calculate the wavelength, frequency and the maximum speed of a particle attached to that wave? We have _Speed = wave length $\times$ frequency_ , _$W=2 \pi \times$ frequency_ , $V_{max}=A\times W$. So how to calculate A? ![enter image description here](http://i.stack.imgur.com/9vkUA.png)


title: Are a quantum mechanical system a chaotic (yet deterministic) system?

text: The title is slightly misleading. I really want to know if the randomness and probabilities observed in quantum mechanics is really just the result of a chaotic (yet deterministic) system. If it is not simply a chaotic system, how do we know?


title: Is time the rate at which one moves through space

text: I'll start out with the cliche attempt in a protective shield of my dignity. I am a young highschool kid just eager to learn and understand. If I'm way off or this is already a known idea, or maybe this post is in the wrong area, I would appreciate a nonchalant and informative correction. When I imagine space-time as a 3D fabric, I see actual threads of fabric, each weave is a certain length that can stretch or shrink. I'd also like to point out that I see space and distance as different things. As in a meter can still be a meter if no space-time fabric exists. So my question is; is time the rate at which one moves through the threads? I have many reasons for why I thought this, I'll name a few:   1. The universe (including space-time) is expanding, so if it is stretching and moving then that could be what causes time to flow forward.   2. When going the speed of light, time stops apparently, with my idea, I figured the speed of light could be = to the speed of the expanding space-time. Therefore if you move at the speed of light and are moving in-sync with space, then the rate at which you move through space is 0, meaning time is 0.   3. The speed of light could be constant relative to us inside the universe as $x = k/y$ where x = the speed of the expansion of space and y = time.   4. When approaching a black-hole, time slows down. This could be because it stretches space(the threads stretch out) making the same distance cover less threads, making a slower time. perhaps: $time = \frac{threads}{distance}$ and $(speed of expansion of space) = \frac{(speed of light)(distance)}{(threads)}$ Ultimately my idea (not all here) has come to the conclusion that we live in a black hole. I really just don't have anyone to discuss my physics questions with, so I would like to know what you all think, why this doesn't work, or really just any input. Thanks


title: Controlling the outcome of a quantum measurement through translational entanglement

text: According to the paper: A. S. Parkins and H. J. Kimble, Phys. Rev. A 61, 52104 (2000). http://pra.aps.org/abstract/PRA/v61/i5/e052104 You can entangle position and momenta of two atoms by using entangled light. Atoms A and B are located at sites A and B. You get entangled light by parametric-down-conversion and send one photon to atom A and the corresponding entangled photon to atom B. You keep on sending entangled pairs until atom A and B come to a steady-state and they will be entangled with each other. Essentially what is happening is that "entanglement is transferred from a pair of quantum-correlated light fields to a pair of trapped atoms in a process of quantum state exchange." ![enter image description here](http://i.stack.imgur.com/ou0PZ.png) The atom is trapped in the x direction. The atom is stuck in a harmonic potential. The entanglement is only in x direction. position are anti-correlated between two atoms: (q1 = -q2) and momentum are correlated (p1 = p2) You can measure the position and momenta of each particle using homodyne measurement techniques. So, if I were to measure the position of atom A very very precisely, then its momentum would be very uncertain. Its distribution would be so smeared out that it'd be approaching a uniform distribution of momentum, if position is a sharp delta function. _At this point, there would exist a probability that the momentum is very large, and thus its kinetic energy would be very large too! KE = p^2/2m._ (Need a checking here) **Would there be a non-negligible probability that the energy of the atom would be so large it would escape the harmonic oscillator trap?!** Since the two atoms are entangled, p1 = p2, thus atom B would also have correlated momentum which translates to correlated kinetic energy. Atom B would also have enough energy to escape the harmonic trap as well. If everything I have stated is correct, haven't I found a method to communicate via translational entanglement, because I can control the outcome of the measurement? (Unlike spin...) Let's say we have an ensemble of these entangled atoms. A scientist at Lab A can send a binary message by choosing to measure the position of an atom at Lab A to high precision thereby causing the atom at Lab B to escape the harmonic trap. Not measuring would keep the atoms trapped. The presence or absence would correspond to a 1 or a 0. Since there would exist chances that the momentum would not be large enough to cause an escape, then we could have batches of entangled atoms that would represent one bit. Very costly, but you can interact instantaneously over large distances...


title: Questions regarding solving the Brachistochrone problem using Lagrangian

text: brachistochrone problem: Suppose that there is a rollercoaster. There is point 1 ($0,0$) and point 2 ($x_2, y_2)$. Point 1 is at the higher place when compared to the point 2, so the rollercoaster rolls down from point 1 to point 2. Assuming no friction, we want to build a rollercoaster path from point 1 to point 2, so that the rollercoaster will reach point 2 from point 1 in shortest time. So, time taken would be defined as $$\text{time (1} \rightarrow 2) = \int_1^2 \frac{ds}{v}$$ Then, the textbook says that v=$\sqrt{2gy}$. Then, $ds = \sqrt{dx^2+dy^2} = \sqrt{x'(y)^2 +1} \, \, dy$ Then, $$\text{time (1} \rightarrow 2) = \frac{1}{\sqrt{2g}} \int_0^{y_2} \frac{\sqrt{x'(y)^2 + 1}}{\sqrt{y}} \, dy$$ Then, $f(x,x',y)$ is defined as $$f(x,x',y)=\frac{\sqrt{x'(y)^2 + 1}}{\sqrt{y}}$$ As per Euler-Lagrange equation, $$\frac{\partial f}{\partial x} = \frac{d}{dy}\frac{\partial f}{\partial x'}$$ The left-hand would be zero, so $$\frac{\partial f}{\partial x'} = \text{constant} = \frac{1}{2a}$$ Then $$x' = \sqrt{\frac{y}{2a-y}}$$ and $$x = \int \sqrt{\frac{y}{2a-y}} \, dy$$ The textbook then says that substituting $y=a(1-\cos\theta)$ would aid solving the integral. How does this make sense?


title: How do I integrate $\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$

text: How do I integrate the following? $$\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$$ where $C$ is a constant. I'm supposed to get a Gaussian function out of the above by integrating but don't know how to proceed.


title: Electrons and energy

text: I'm an a-level student. While studying quantum physics I came across this statement:"According to electromagnetic theory an accelerating charge emits energy". The bottom-line was that an electron (which is an accelerating charge in an atom) should, according to this, emit electromagnetic radiation, but it does not. Can someone please explain the electromagmetic theory and why the electron does not emit energy? Please keep in mind I'm only an a-level student.


title: Atomic gravitational field?

text: This might be a silly question, but if every atom has its own gravitational force could atoms or molecules be attracted to each other over vast distances in the void of space if there were no other greater forces being applied? Is this similar to the cooling/slowing theory?


title: What is the most general expression for the coordinate representation of momentum operator?

text: I have a question about deriving the coordinate representation of momentum operator from the commutation relation, $[x,p]= i$. One derivation (ref W. Greiner's Quantum Mechanics: An Introduction, 4th edi, p442) is as following: $$ \langle x|[x,p]|y \rangle = \langle x|xp-px|y \rangle = (x-y) \langle x|p|y \rangle. $$ On the other hand, $ \langle x|[x,p]|y \rangle = i \langle x|y \rangle = i \delta (x-y)$. Thus $$ (x-y) \langle x|p|y \rangle = i \delta(x-y). \tag{1} $$ We use $(x-y) \delta(x-y) = 0$. Take the derivative with respect to $x$; we have $\delta(x-y) + (x-y) \delta'(x-y) = 0$. Thus $$ (x-y) \delta'(x-y) = - \delta(x-y). \tag{2} $$ Comparing Eqs. (1) and (2), we identify $$ \langle x|p|y \rangle = -i \delta'(x-y). \tag{3} $$ In addition, we can add $\alpha \delta(x-y)$ on the right-hand side of Eq. (3), i.e. $$ \langle x|p|y \rangle = -i \delta'(x-y) + \alpha \delta(x-y), $$ and $[x,p] = i$ is still satisfied. We can also add $$ \frac{\beta}{\sqrt{|x-y|}}\delta(x-y)$$ on the RHS of Eq. (3). Here $\alpha$ and $\beta$ are two real numbers. My question is, what is the most general expression of $\langle x|p|y \rangle$? Can we always absorb the additional term into a phase factor like Dirac's quantum mechanics book did? Thank you very much in advance.


title: Meaning of terms and interpretation in the electric multipole expansion

text: In section 3.4.1 of Griffiths' _Introduction to Electrodynamics_ , he discusses electric multipole expansion. He derives the formula or the electric potential of a dipole, which I follow, but right after, he begins talking about the electric potential at a large distance, which is as follows: $$V( \vec{r}) = \frac{1}{4 \pi \epsilon _{0}} \int \frac{\rho (\vec{r}')}{ℛ} dV$$ $ℛ$ is from some point inside the charge distribution to the point P. **What exactly does $\vec{r}'$ denote?** Is it the distance from the center of the charge distribution? Next, he uses law of cosines to find the expression for $ℛ^{2} = r^{2}+(r')^{2}-2rr'\cos\theta'$. This gives the same question as above, what does the symbol $r'$ mean? Then he defines $ℛ = r(1+ \epsilon)^{1/2}$, where $\epsilon \equiv \left(\frac{r'}{r}\right)^{2}\left(\frac{r'}{r}-2\cos\theta^\prime\right)$. The proceeding part is where I really get lost: > For points well outside the charge distribution, $\epsilon$ is much less > than 1, and this invites a binomial expansion. $$\frac{1}{ℛ} = > \frac{1}{r}\left[1- (1/2) \epsilon+ (3/8) \epsilon ^{2} - (5/16) \epsilon > ^{3}+\ldots\right]$$ **What is going on in this last step?** And finally, we eventually derive the formula $$V(\vec{r}) = \frac{1}{4 \pi \epsilon _{0}} \sum ^{\infty}_{n=0}\frac{1}{r^{n+1}} \int(r')^n\,P_{n}(\cos \theta)\,\rho( \vec{r}')dV $$ Why did we go for all this trouble? If this is supposed to be the electric potential at a large distance, **couldn't we have just used $V( \vec{r}) = \frac{1}{4 \pi \epsilon _{0}} \int \frac{\rho (\vec{r}')}{ℛ} dV$**? I don't understand what this equation _actually means_ in physical terms. And in regards to the actual equation, **what is $P_{n}$**? Any help is much appreciated.


title: relative phase/sign in $\Psi$ after exchange of composite particles with angular momenta

text: I'm reading _Quantum Liquids_ by A.J. Leggett and became confused by the following statement in the first chapter. > Consider now a pair of such identical atoms. In the absence of appreciable > coupling between the hyperfine and (atomic center-of-mass) orbital degrees > of freedom, the energy eigenfunctions can always be written as a product of > a “spin” function (i.e. a function of the hyperfine degrees of freedom) and > an orbital function (i.e. a function of the coordinates of the atomic > nuclei). The symmetry of the orbital wave function under exchange of the two > atoms is $ (−1)^L $ where $L$ is the relative orbital angular momentum. As > to the spin wave function, the combination of two atomic (intrinsic) angular > momenta each equal to $F$ yields possible values of the total dimer > intrinsic angular momentum $K \equiv \left| F_1 + F_2 \right| $ equal to $0, > 1, \ldots , 2F$. $F$ here is the total atomic spin. ~~I have trouble understanding how the relative phase of the wave function results from the _difference_ between the magnitude of the angular momenta when their $z$-projections ($z$ being the quantization axis) are not known.~~ ~~Does anyone know how $L$ and $K$ are determined?~~ Ok, so "relative" here had to do with "relative motion" and not "difference".   Now... does anyone know the reasoning behind the factor of $(-1)^L$ ?


title: How is energy extracted from fusion?

text: I understand that combining deuterium and tritium will form helium and a neutron. There are three methods to do this (1) tokamak (2) lasers and (3) cold fusion. I would like to know after helium is formed. How is that energy extracted from tokamak and stored?


title: What is wrong in this representation of relative reference systems?

text: Up until now I've explained relative time to myself as looking at the 3D world from different four-dimensional perspectives, analogous to how looking at a 2D-ish object (eg. a sheet of paper) from different angles makes it appear to change shape. Also, I've used this representation below to explain how the time at which an event occurs could change depending on the body's reference system. This representation uses two bodies that move relative to each other, $B1$ and $B2$, to represent the time of occurrence of events $E1$ and $E2$. ![](http://i.stack.imgur.com/KsZ2r.png) ( _Not very precise -- blame MS Paint :P -- but my intent should be clear._) I am not sure, but as far as I know $t(E1) \le t(E2)$ should hold true for any reference system (order should be preserved), which means that the drawing is correct. But I just realized that in certain cases, it is possible for $E2$ to occur before $E1$ (according to my representation): ![](http://i.stack.imgur.com/8X5n9.png) Here you can see that $B3$ and $B2$ have entirely different perceptions on the order of the two events, but that would break causality, so it cannot be true. What is wrong in my representation of relative systems of reference?


title: Bariometric formula derivation

text: I don't understand the following reasoning that I found in a set of lecture notes from a physics course, it's about Perrin's stimate on $N_{a}$ Avogadro's number via the bariometric formula In order to stablish that formula, the reasoning begins with Boltzmann distribution $$\frac{n(E)}{n(0)}=\exp\left(-\frac{E}{k_{B}T} \right) $$ For a single particle, under the action of the Earth's gravitational field $$E=\frac{p^2}{2m}-mgz $$ In the equilibrium $$E=-mgz$$ substitution upon Boltzmann's distribution $$\frac{n(z)}{n(0)}=\exp\left(-\frac{-(mgz)}{k_{B}T} \right) \propto \exp(z) $$ completely wrong In the lectures notes that problematic minus sign is omitted. Where is (are) the error(s)?


title: Topological order vs. Symmetry breaking: what does (non-)local order parameter mean?

text: Topological order are sometimes defined in opposition with the order parameter originating from a symmetry breaking. The latter one being possibly described by a Landau theory, with an order parameter. Then, one of the distinctions would be to say that _topological order can not be described by a **local** order parameter_, as _e.g._ in this answer by Prof. Wen. I thus suppose that a Landau theory describes a _local order parameter_. I have deep difficulties to understand what does _local_ mean ? Does it mean that the order parameter can be inhomogeneous (explicit position dependency), as $\Delta\left(x\right)$ ? Does it mean that one can measure $\Delta$ at any point of the system (say using a STM tip for instance) ? (The two previous proposals are intimately related to each other.) Something else ? A subsidiary question (going along the previous one of course) -> What is the opposite of _local_ : is it _non-local_ or _global_ ? (Something else ?) What would _non-local_ mean ? Any suggestion to improve the question is warm welcome.


title: What evidence refutes a "pre-eternally existent cosmic egg"?

text: I've seen many Young-Earth Creationists attempt to discredit Big Bang cosmology. For example, an article by Cal Thomas in the 1990's stated that it meant there was a "pre-eternally existing 'cosmic egg' that decided to explode." A new refrain I keep hearing that there was pre-eternally existent energy. My layman's understanding of Big Bang cosmology is that there was a "start" to matter, space, time, **and energy**. The Young Earth retelling, in contrast, would say "pre-eternally existent energy, then turning into these other things." Even the theme song for Big Bang Theory says: > Our whole universe was in a hot dense state, > > Then nearly fourteen billion years ago expansion started, wait Which, seems to be a popular re-telling of what I presumed was the YEC distortion of the Big Bang model itself. Temperature and density pre-existed, according to the song. **QUESTION: What references or very short articles explicitly define the Big Bang model in terms of "what-was-before"? _Was there energy sitting around?_**


title: Why singularity in a black hole, and not just "very dense"?

text: Why does there have to be a singularity in a black hole, and not just a very dense lump of matter of finite size? If there's any such thing as granularity of space, couldn't the "singularity" be just the smallest possible size?


title: Is this a simple system in which no heat transfer is possible?

text: Let's say that a hot gas is trapped in a metal box. This metal box is magnetically suspended in another structure with a low temperature. The inner box does not touch anything. And there is a void in the structure. To me there seems to be no way for heat transfer to occur. Will the gas change its temperature with time?


title: Stern Gerlach Experiment

text: Since l=0 for a valence electron in 5s state of silver, L=0 and therefore magnetic dipole moment is also 0 which means that the beam should not have deflected at all. So, we introduced the property of an electron called spin which explains the deflection. However, my problem is How the introduction of spin explains the splitting of beam into two parts ?


title: What does the Higgs boson have to do with the uncertainty principle and quantum oscillations?

text: I was looking in New Scientist the other day when I saw something to do with the Higgs boson, energy levels, entropy, space/time, quantum oscillations and many other things. It was in a feature to do with symmetry. I have read up about this and I know that the magazine does not accept original works, so I guess that this is mainstream physics. ![higher energy levels are brighter](http://i61.tinypic.com/28sltnm.jpg) The above is a diagram of what I'm talking about. This is how it appears in the magazine: ![Their diagram...](https://scontent-b-lhr.xx.fbcdn.net/hphotos- xfp1/t1.0-9/q71/s720x720/10255610_10152371905339589_1518379512515532344_n.jpg) According to NS, a ball (like the blue one above) that is sitting at the top of a piece of space/time warped like this has an unstable energy level and position. Given the slightest nudge, it will "fall" into a lower energy state and quantum oscillations (which occur as is "rolls" up and down the "pit") caused by the uncertainty principle create Higgs bosons in the Higgs field. I have pondered this repetitively, and it still looks like nonsense (even in the eyes of quantum physics). What I want to know is: has this been regarded as true or is this "complete nonsense"? And if so, how can the uncertainty principle cause such things to happen? \--ADDITION TO QUESTION-- What I do not understand is how a vacuum generates Higgs particles if it has no mass - unless it's trading it with energy. What is actually happening (the magazine hasn't described it in enough detail for me to understand)? (It's hard for me to visualise; it's an entirely new concept to visualise for me.)


title: Truss Analysis with multiple moments creates linear combinations

text: So in my engineering statics course we have been doing a great deal of work with trusses and machines, and a part of the physics behind it has really been confusing me. Just as a note, I also have been trying to use matrices/inversion once I have my family of equations since I also like trying to use linear algebra to solve problems. While I find this topic interesting I keep having problems creating my family of equations to solve from. One thing in particular I noticed that if I try to use 2 moments from one of my free body diagrams and I start trying to solve my equations I typically get a singular matrix. For example: ![enter image description here](http://i.stack.imgur.com/FpKpQ.png) Determine reactions on member ABCD at A and D. If I take this whole body as a FBD, I did the sum of the x-component forces, y-component forces, and the moment about F. However, since this has 2 reactions at A an d2 at F I need four equations to solve the final FBD. But when I tried using the moment about A I get a linear combination of the other variables, and when I tried the moment about E the same result occurred. I might be making a mistake in the following way, but if not then theres an even bigger question at hand: I have simplified the pressures into resultant forces that gives the total magnitude of force applied, and placing this force at the center of application (@ point E for the uppoer 2kN m rectangle and @ point C for the 2kN m triangle). Are these resultant forces not usable for moment calculations? currently I had these equations I was using (sorry don't know latex yet)               sum Fx = Ax - Fx + 3kN = 0          sum Fy = Ay + Fy - 4kN = 0          sum Mf = -Ay - 3kN*2m - 4kN*1m = 0          sum Ma = 1m*Fy - 3kN*2m = 0          sum Me = -Fx*3m + Ax*3m - 3kN*1m - Ay = 0      only 1 moment equation provides any new information to the system. If I am not making a mistake the core question I have is why? Why does looking at a different moment not yield any new information about the system?


title: Amount of fluid that moves along a path

text: Let suppose that $\vec{F}$ is the velocity vector field of of a fluid in space, and $\vec{s}$ is a straight path of arbitrary length. Let's suppose that $\vec{F}$ and $\vec{s}$ are parallels and point in the same direction, so that $\vec{F} \cdot \vec{s} = F s$. How can we account for the total amount of fluid that moves along the path (per unit of time). **Related question**


title: Dragon Ball Z: Hyperbolic Time Chamber *(also increased gravity training)

text: Firstly, I am sorry if this seems like a joke. It is not.       I have always loved the Dragon Ball series, so this question has been on my mind for a while. Can any of you figure out why time would move slower in a " 'hyperbolic' time chamber?" (this seems like a relevant physics question for a fan of the show). Does it have anything to do with the fact that hyperbolic inverse tangent is utilized in special relativity? In addition, if one could survive for months in 10x earth's gravity, would one actually get that much stronger? It does seem like they would, just by drawing a free body diagram.. But would this ever be a logical method to use for strength training? Would your entire body get proportionally stronger? (also, all of my tags are just guesswork for this question, as any of them may apply)


title: What does a wing do that an engine can't?

text: This isn't a question of how a wing works -- vortex flow, Bernoulli's principle, all of that jazz. Instead, it's a question of why we need a wing at all. A wing produces lift, but why is that necessary? I got to this by thinking of an airplane at a coarse level. The wing produces lift through some interesting physics, but it needs energy to do this. The engine is what ultimately provides all of this energy (let's assume no headwind, and in "ultimately" I'm not including chemical energy in the fuel, yadda yadda "it all comes from the sun"). That means the engine pushes enough air, and fast enough, to (a) offset gravity and (b) still propel the plane forward. So the question is: **why can't we just angle the engine down a bit and get the same effect?** To slightly reword: why do wings help us divert part of an engine's energy downward in a way that's more efficient than just angling the engine? One answer is that we can do exactly that; I'm guessing it's what helicopters and VTOL airplanes like the Harrier do. But that's less efficient. Why? One analogy that comes to mind is that of a car moving uphill. The engine doesn't have the strength to do it alone, so we use gears; for every ~2.5 rotations the engine makes, the wheel makes one, stronger rotation. This makes intuitive sense to me: in layman's terms, the gears convert some of the engine's speed-energy into strength-energy. Is this analogy applicable -- is the wing on a plane like the gearbox in my transmission? And if so, what's the wing doing, more concretely? If a gear converts angular speed to increased force, what X does a wing convert to what Y? None of the answers I could guess at satisfied my intuition. If the wing converts horizontal speed to vertical speed, tipping the engine downward would seem to have the same effect. If it's changing the volume/speed of the air (more air blown slower, or less air blown faster), it would still have to obey the conservation of energy, meaning that the total amount of kinetic energy of the air is the same -- again suggesting that the engine could just be tipped down. **EDIT** In thinking about this more from the answers provided, I've narrowed down my question. Let's say we want a certain amount of forward force $S$ (to combat friction and maintain speed) and a certain amount of lift $L$ (to combat gravity and maintain altitude). If we tilt our engine, the forces required look like this: ![vectored thrust](http://i.stack.imgur.com/lIIVr.png) The total amount of force required is $F = \sqrt{S^2 + L^2}$. That seems pretty efficient to me; how can a horizontal engine + wing produce the same $S$ and $L$ with a smaller $F'$?


title: Quantum Mechanics and Entanglement

text: I'm hearing a guy ( Tom Cassidy ), which supposedly has a master in physics, saying that what we expect in a physical experiment ( for example, observing some particle ) can actually interefere with the workings of the experiment. Is he distorting quantum mechanics terms and facts to use it with his purpose ( what we think internally can actually interfere with the external world ) ? Here is more or less of what he said : We can measure an electron to be at two different places at the same time.And we can also observe an electron as a particle or as a wave depending on what we set the experiment to observe.. It makes no sense but WHAT we are actually looking for, creates the result. Because its all the experiment, it's not humans thinking "oh, it would be nice if the results came that way ... ". What we expect to see, we see ... then we design the experiment in a different way and expect something else ... and thats what we see ! It makes no sense, thats why we don't understand Quantum Mechanics. The scientists know this. When you are doing a quantum mechanics experiment, you are looking to observe somthing as a particle, you open up a box ( figurative ) and what you see is a particle. What you are looking for, it knows you are looking for .. thats how quantum mechanics works .. An electron will exist in the bottom of an energy well, it has really low probability of getting outside of that energy well ( the energy required is insane ) but every so often electroncs magically tunnel into the walls ( energy walls ) .. Why do they do it ? I don't know ... and anyone who says they know why it works, they are lying ... they don't know, nobody knows why quantum mechanics is the way it is ... Then some people might directly think that Quantum Mechanics is like Law of attraction : "You think and it happens ". But it's not as simple as that.What we found is that this is the way of how results are found in quantum mechanics. Quantum mechanics works for the very very very very small , but recently , just last week i was reading a study which says that Quantum Mechanical entanglement effects have been observed in much larger things ... groups of atoms as high as fifty. Last week, there was a study in the New Scientist in the UK which reported that quantum mechanical effects have been observed between pairs of diamond crystals. And the relation of size between Diamond crystals and our brain is a lot smaller than the difference between particles and diamond crystals. Now, the final question is ... how big are thoughts ? It's so when you start thinking " its actually real ". You talk of people between the law of attraction and they say, oh its so mambo-jambo, now they can think its ideas are actually based on science ... So, is there at least some truth to it ( even if its not true that quantum mechanical effects work for a pair of diamonds ) ? Thanks a lot in advance. EDIT : Just did some search and it seems like the final part of the top answer in this link Quantum Entanglement - What's the big deal? might suggest some kind of influence of one electron in another electron, physically distant from it"


What does it take to become a top physicist? Why do so many extremely talented young upstarts totally flop as they move to more advanced physics?


title: Understanding 1D Kinematics and Uniform Acceleration?

text: So I was given the following homework problem: > You land on an unknown planet somewhere in the universe that clearly has > weaker gravity than Earth. To measure g on this planet you do the following > experiment: A ball is thrown upward from the ground. It passes a windowsill > 15.0 m above ground and is seen to pass by the same windowsill 2.00 s after > it went by on its way up. It reaches the ground again 5.00 s after it was > thrown. Calculate the magnitude of g (the acceleration due to gravity) at > the surface of this planet. I found a solution on answers.yahoo.com, but I still don't really understand it as well as I would like. I drew a picture and know that after 15m it takes 2secs to fall back to 15m and then an additional 5secs until it hits the ground. I can't assume that the velocity is uniform for entire trip can I? (e.g. 6secs travel time going both up and down/quadratic curve, for total 12secs) I have the 4 equations of kinematics and usually I just look where I can plug in values and simply get the answer, but obviously that's not going to help me to solve slightly more advanced problems such as this! Could someone please give me advice on how to approach this problem (and/or physics problems in general). Anything that can help me conceptualize these better. I just want to be able to solve these without staring at it for 5hrs...Thanks in advanced.


title: Astronomical detection significance from magnitude error

text: At this website: http://heasarc.gsfc.nasa.gov/docs/swift/analysis/threads/uvot_thread_afterglows.html The passage at the bottom states that a V-band magnitude of 17.62, with an error $\pm$0.02 is a 49.4-$\sigma$ detection significance. How is this value calculated? Could you provide the working? I have a similar problem, with a set of magnitudes and errors, and would like to know at what magnitude limit I can claim a statistically significant (6-sigma) detection. Thanks


Are strange metals described by a quantum critical theory?


title: Mass is rigidity?

text: In General Relativity, a totally rigid body cannot be accelerated. It will behave like something of infinite mass. Similarly a body of two separated particles which connected to each other with a highly rigid bond, will be difficult to accelerate. The more rigid bond is, the more difficult will it be to accelerate the system. As such, my question is, can any particle's mass be a measure of rigidity of the bonds of its fundamental components?


title: How to prove that Weyl tensor is invariant under conformal transformations?

text: I need to verify that the solution for vanishing Weyl tensor is conformally flat metric $g_{\mu\nu} = e^{2\varphi}\eta_{\mu\nu}$. The most convenient way to show this is to prove that Weyl tensor is invariant under conformal transformation of the metric. How to prove this fast? I have the idea to build 4-rank tensor which include terms with curvature tensor, Ricci tensor and scalar curvature and then use the requirement on invariance under infinitesimal conformal transformations. If I can show that it is Weyl tensor, I can also prove the statement. But do some alternatives exist?


title: Selection rules in Stark effect

text: The energy level of an electron could be shifted by an electric field. $\langle n, l,m|[L_z,z]|n^{\prime},l^{\prime},m^{\prime}\rangle=(m-m^{\prime})\hbar \langle n, l,m|z|n^{\prime},l^{\prime},m^{\prime}\rangle$. Because $[L_z,z]=0$, we must have $m= m^{\prime}$ for non-vanishing $\langle n, l,m|z|n^{\prime},l^{\prime},m^{\prime}\rangle$. This is one selection rule in Stark effect. Then how to rigorously prove $l^{\prime}=l\pm1$ is the other selection rule for $\langle n, l,m|z|n^{\prime},l^{\prime},m^{\prime}\rangle\neq0$?


title: How can we measure time?

text: If we cannot define a proper time (or synchronize clocks in different positions) in an inertial frame (independent with the theory of relativity), there seems to be no direct way to confirm the 2 postulates of Einstein. Is that true? Consider an inertial frame, which is associated with a proper coordinate $(t,x,y,z)$. It seems like there is no way for observers in different positions of this frame to synchronize their clocks. If they move to 1 position to do so, they must accelerate, and they have completely destroyed their inertial frame. If there is no way one can measure the time in different positions of an inertial frame, how real is the $t$ coordinate of the frame? Is there any convention to measure such $t$? If there is, how true it is compared with the "real" inertial time? However, in the end I feel like there is no way we can measure $t$ in different positions without destroying the inertial frame. Therefore it seems like we cannot truly measure the velocity of anything. I ask this question because there may be a request for proving the constancy of the speed of light, and to measure the speed of light (from A to B) we have to synchronize 2 clocks, which is a very subtle process.


title: Mass-spring system on an incline

text: ![block-spring system](http://i.stack.imgur.com/oCVEr.jpg) I am reviewing for an exam next week, and this is one of the questions I am stuck on. I have the mass-spring system above with spring constant $k$ on a frictionless incline. I would like to find the total energy of the system at any time $t$. I know that the total energy of the system is going to be the sum $E = K + U_g + U_s $ My first question is that I am confused about how to approach the problem. If I take my axes along the ramp, then the problem becomes one dimensional. My idea was set up my coordinate system like that so I could describe the displacement of the mass around it's equilibrium position on the ramp so I could find $K + U_s$, and then switch back to a more traditional coordinate system where I take my axes along the perpendicular sides of the ramp to find $U_g$. Does this approach work? If not what should I be doing?


title: What properties are used to quantify the odds of a star harboring earth-like life?

text: Say you start with a list of stars. What properties do we believe to be critical in the present existence or future formation of earth-like life in those star systems? How can one reasonably pare down such a list? To be clear, I'm specifically interested in life as we understand it, on a planet, orbiting a star. Intelligence or complexity isn't necessary to the question. If a star could have planets resembling a young earth, with very simple life, that's fine.


title: Landau Mechanics: why does adding Lagrangians remove the indefiniteness of multiplying each Lagrangian by a different constant?

text: In Landau Mechanics (third edition page 4), why does adding Lagrangians of two non interacting parts remove the indefiniteness of multiplying each Lagrangian by a different constant? If both systems are completely non-interacting, I can perfectly create a new Lagrangian L = a*L1 + b*L2 and still maintain validity of the Euler-Lagrange equations and make the action integral perfectly stationary, with a and b different. Can't I? Here's the original statement: > It is evident that the multiplication of the Lagrangian of a mechanical > system by an arbitrary constant has no effect on the equations of motion. > From this, it might seem, the following property of arbitrariness can be > deduced: the Lagrangians of different isolated mechanical systems may be > multiplied by different arbitrary constants. The additive property, however, > removes this indefiniteness, since it admits only the simultaneous > multiplication of the Lagrangians of all the systems by the same constant. I kind of understand that, of course, after you create L = L1 + L2, xL = xL1 + xL2 but nothing stops me from multiplying each Lagrangian of each non interacting part by _different_ constants a and b and _then_ summing, like: xL = xaL1 + xbL2 So the statement seems without meaning for me. Could anyone clarify? Thanks! One addition: I see that, if both systems are interacting externally, the constants must be equal (and the proportion of masses becomes relevant). My goal is exactly that: to understand, conceptually, how he derives the role of ration of masses later on in page 7. Going back to the text, what confused me is that the whole thing starts with the assumption that both system are _closed_ so any external interaction is dismissed: > Let a mechanical system consist of two parts which, if closed (..), and the > interaction between them may be neglected, the Lagrangian of the whole > system tends to: lim L = La + Lb.


title: Will the rms current be affected by inserting dielectric in the capacitor in an LCR circuit?

text: MY thoughts: I think it will not be as the expression for RMS value is dependent only on the peak value of current. Is my thinking correct?


title: What characterizes a metallic sound, and why do metals have a metallic sound?

text: We know that when we strike a metal, it usually has a characteristic "sharp" sound, unlike when we strike wood, say. What characterizes this "metallic sound"? Does it have a well-defined power spectrum? What are its generic properties? Also, why do metals have a metallic sound? My best guess would be that metals have high Young's / Bulk modulus and so the resonances for typically sized metals should be at fairly high frequencies, and since they are very elastic, they wouldn't dissipate energy all that easily, so the resonances would have small FWHM and hence be sharp. So my guess is that a "metallic sound" has distinct resonance peaks in its power spectrum, whereas for a piece of wood, for example, these peaks merge into each other to create a continuum.


title: Why might the normal force on a box not be equal to its weight?

text: Very simple homework question which I managed to get wrong: > "The weight of a box sitting on the floor points directly down. The normal > force of the floor on the box points directly up. Need these two forces have > the same magnitude? (y/N)" My answer was yes, the correct answer is no. I must be missing some important concept here, may someone help me think of a realistic scenario in which the magnitudes are not equal?


title: How to approximate acceleration from a trajectory's coordinates?

text: If I only know $x$- and $y$- coordinates of every point on a trajectory without knowledge of time information, is there any way to approximate Cartesian acceleration angle at each point? Time interval between every two points is very small, ~0.03 second.


title: Double-slit-experiment but with unobserved alternating opening of slits. Does an interference pattern still arise?

text: Step #1 Imagine one preforms an electron based Double-slit-experiment and one does so with only one electron being fired at a time. Step#2 Also included in the experiment is an unobserved alternating opening of the double slits such that there is only one slit open at a time, and that each individual alternating ( the single process of closing of 1 slit and the opening of the other ) occurs during the gap time period that is present between the individual electrons being fired. Knowledge of which slit each electron goes through is therefore NOT being observed. Thus does an interference pattern still arise over time here to ? If so, could you please present any data concerning proof of this in particular experiment, thus in turn eliminating any assumption. Note: _Time is required to accumulate an interference pattern in the double slit experiment, just like it is in the Kim et al Delayed Choice Quantum Eraser experiment of the year 2000._ _But in this Delayed Choice Quantum Eraser experiment, what makes the experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler was not made until 8 ns after the position of the signal photon had already been measured by detector D0._ _Thus this Delayed choice experiment raised questions about time and time sequences._ _Two separate events, the position detecting of the signal photon and the determining of the which-path information of the idler photon, occurred at two different times, yet despite being separated by time, both were taken into account to produce a single final outcome._ _Thus my above double-slit experiment arises. Does one electron interfere with another electron despite being displaced by time, or does a single electron interfere only with itself._


title: Importance of MHV amplitudes

text: Why are MHV amplitudes so important? How/where are they used and why do people keep trying to rederive them in many different ways?


title: Question about Origins in Galilean transformation

text: I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, $y'=y$, $z'=z$, $t'=t$. My question involves the $x'$ term. Don't these equations assume that frames $S$ and $S'$ align together (origins $O$ and $O'$ are the same point) at $t=0$? This assumption is not explicitly stated in my textbooks, and it seems like the general formula should be $x'=x-x_0-vt$, where $x_0$ is the distance (in $x$-direction) the $S'$ frame is away from the $S$ frame (along the $x$-axis) ath $t=0$. This wouldn't change the velocity transformation formula, because $x_0$ is constant. Am I right about this? If so, why doesn't the canonical form for a galilean transformation include this initial displacement term?


title: Earth moving over the Sun instead of around

text: Let's say you are observing the movement of the Sun and Earth from very far away. After year 1, the Earth creates an orbital plane around the Sun. Since the objects in the universe induce forces of different magnitudes on the Earth and Sun, you will observe the Sun and Earth moving differently, although the Earth will always orbit the Sun. My question is, what is the time frame under which the Earth moves out of the orbital plane it created after year 1. After how long does this orbital plane rotate? Will this change in orbital plane have any visual or physical effect for an observer on the Earth?


title: Can someone please qualitatively explain unitary group from a physics perspective?

text: Unitary Groups is the most mysterious thing for me when studying physics. All my physics endeavor ends when author starts talking about unitary groups. This is often the case because in a lot of the texts or papers the author would throw terms like $SU(3)$, $SU(5)$ without any background motivation. When you search for some more answers online, you will often get a purely mathematical treatment (i.e. Wiki article: http://en.wikipedia.org/wiki/Special_unitary_group) or something related to quantum field theory. Now remind me how many years of studying physics will one reach QFT? Could someone qualitatively explain or provide a good article that motivates the concept of unitary group with examples drawn from ... every day experience or basic physics. Could someone at least explain what an element of an unitary group physically mean?


title: Gravity on the International Space Station

text: We created a table in my physics class which contained the strength of gravity on different planet and objects in space. At altitude 0(earth), the gravitational strength is 100%. On the moon at altitude 240,000 miles, it's .028%. And on the International Space Station at 4,250 miles, the gravitational strength compared to the surface of the earth is 89%. Here's my question: Why is the strength of gravity compared to the surface of the earth 89% even though it appears like the ISS has no gravity since we see astronauts just "floating" around?


title: What is the space between galactic arms called?

text: Is there a term referring to space that is inside the plane of a galaxy, but not part of the center/bar/arms/spurs, etc? What's the filler called? The space between two spiral arms (if it isn't a spur or anything) would be called... I really feel like there should be a word for this, but I can't find one.


title: Determine the acceleration and angular acceleration of a disc

text: The question is: > A 90kg disc is floating in a frictionless vacuum. A 150N force is applied to > the outer rim of the disc. The disc has a radius of 0.25m and a radius of > gyration of 0.16m. What is the acceleration and angular acceleration of this > disc? To solve it I set up these equations: \begin{equation} \mathbf{F}_{a} = \mathbf{m}\times\mathbf{a}\tag{1} \end{equation} \begin{equation} \mathbf{F}_{\alpha} = \frac{\mathbf{I}\times\mathbf{\alpha}}{0.25}\tag{2} \end{equation} \begin{equation} \mathbf{F}_{a}+\mathbf{F}_{\alpha} = 150 N\tag{3} \end{equation} You can find I and plug it in along with m, but that still leaves 4 unknowns and only 3 equations. I need a 4th equation but I'm not sure what else is known about the problem.


title: Solenoid pull force & Velocity calculation

text: So I am building a circular accelerator (like a slightly oversimplified model version of CERN) as a physics project, and I'm at a dead end. I believe I need to know how to work out differential equations to answer this, but I'd like to know if there's any other way to get the answer. Okay. I am calculating the velocity of a projectile after passing through a solenoid. I have a system using an photo-interrupter to switch the coil on when a projectile passes through it. I know the force of a solenoid can be calculated using $F = (NI)^2\mu_0A/2g^2$ So the first part of my question should be fairly simple I believe. Since the gap between projectile and coil ($g$) changes as the projectile accelerates, the force acting on the projectile become stronger (because the magnetic field diminishes with the square of the distance.) Can I use the average distance between coil and projectile or must I learn how to work differential equations? My second question involves the length of time the force from the solenoid is applied. As I have my formulas set up, I know the distance between the photo- interrupter and the coils, I know my starting velocity, and I know the acceleration applied to the projectile (assuming I can use the average force applied). I made a python program to run through the equation for displacement as a function of time, adding a set amount of time in each run-through, until the displacement was equal to the distance between my interrupter and my coils. I then had it record the number of second it took, rearranged $F=ma$ to get $\frac{F}{m}=a$, used this instead of $a$ in $V = \frac{a}{\Delta t}$ to get $$V=\frac{\frac{F = (NI)^2\mu_0A/2(g_{avg})^2}{\text{Mass of projectile}}}{\Delta t} \,.$$ Is this an accurate way to calculate the velocity?


title: In what way do passive circuit elements change the functional form of the voltage?

text: I heard capacitors affect the valleys and mounds of voltage sine curves, so that you get DC from AC. It's related to Graetz bridge, flipping signs of sine waves and seemingly afterwards smoothing sharp points, see pictures below. How can that be derived and interpreted from electronics? What is the math behind capacitors in a parallel configuration of an AC source $U_\text{ext}$ leveling to give flater the output voltage? For example the images suggest the capacitor provides the current at the right time, but I don't know why. If charges when the current is high, but how to compute the current at the vertex at the parallel capacitor and the partition to the three paths. The picture suggest the process is periodic and so I guess there might be a closed form for the time behaviour of the relevant functions. * * * ![enter image description here](http://i.imgur.com/yEt8IMe.gif) * * * ![enter image description here](http://i.imgur.com/sw5QI7u.gif) * * * My approach: $I_{U_\text{ext}}=I_C+I_R$ $U_R=I_R\ R$ $U_C=\frac{1}{C}\int I_C \mathrm dt$ $U_\text{ext}\overset{?}{=}I_{U_\text{ext}}\cdot \frac{1}{1/Z_C^{???}+1/R}$ $U_\text{ext}\overset{?}{=}\pm U_C\overset{?}{=}\pm U_R$ $U_R=\ ???$


title: How do we know that weak isospin is an exact symmetry while strong isospin is not?

text: It is said in textbooks that if the $SU(2)_f$ or $SU(3)_f$ flavor symmetry were exact for sstrong isospin, then all members of the multiplets would be exactly equally massive. By looking at quark masses then one can conclude that the symmetry is not exact. But how does the argument work with the weak force ? It is said to be an exact symmetry, yet electron and neutrino have different masses even though they are in the same doublet. What is the difference ?


title: Element of area in 4-dimensional space-time

text: How would you proof that $$ \mathrm {Tr} (\mathbf{S\cdot \bar S })=0$$ where $\mathbf S$ is an element of area delimited for the 4-vectors $\mathbf u$ and $\mathbf v$ given by $$S^{\alpha \beta}\equiv u^\alpha v^\beta-u^\beta v^\alpha$$ and $$\bar S^{\alpha \beta}\equiv \frac{1}{2}\epsilon^{\alpha \beta \gamma \delta} S_{\gamma \delta}$$ is the dual of $\mathbf S$. I used an analogy with the Maxwell field tensor $\mathbf T$. I know that $\mathrm {Tr} (\mathbf{T\cdot \bar T })=\frac{4}{c}\mathbf E \cdot \mathbf B$. Building the analog vectors $\mathbf E$ and $\mathbf B$ but with $\mathbf S$ I get that $ \mathrm {Tr} (\mathbf{S\cdot \bar S })=0$. But I'm looking for a more ilustrative solution to this problem. Any ideas?


title: Mechanics Question: Energy, Work and Power

text: I'm a pure mathematician by trade, and have been trying to teach myself A-level mechanics. (This _is not_ homework, it is purely self-study.) I've been working through the exercises and have come up against a stubborn problem. Here it is: **Question** A train of mass 150 tonnes is moving up a straight track which is inclined to 2$^{\circ}$ to the horizontal. The resistance to the motion of the train from non-gravitational forces has magnitude 6 kN and the train's engine is working at a constant rate of 350 kW. `Calculate the maximum speed of the train.` The track now becomes horizontal. The engine continues to work at 350 kW and the resistance to motion remains 6 kN `Find the initial acceleration of the train.` **Answers** `Calculate the maximum speed of the train.` This is straightforward. When the train reaches its maximum velocity it will have zero net acceleration, i.e. the force from the engine must neutralise the force from resistance. The gravitational resistance has a magnitude of $150000g\sin 2$ and so the total resistance is $(6 + 150g\sin 2)\times 10^3.$ Using this with the formula $P = Fv$ we get $3.5 \times 10^5 = (6 + 150g\sin 2)v\times 10^3$ and so $$v = \frac{350}{6 + 150g\sin 2} \approx 6.11 \, \text{m/s} \, .$$ `Find the initial acceleration of the train.` This is where I come unstuck. The question asks for the "initial" velocity straight after telling you that the hill levels out. As such I assume it wants the "initial" acceleration right after reaching the peak of the hill. Since the train is on level ground, the only resistance is the 6 kN non- gravitational resistance. (No value for $\mu$, the coefficient of friction, is given and I assume there is no friction.) We also know that the engine works at a rate of 350 kW. Using the formula $P = Fv$ we get: $$ 350000 = F \times \frac{350}{6 + 150g \sin 2} \iff F = 1000(6 + 150g\sin 2) \, . $$ Finally, we use the formula $F = ma$ to give $1000(6+150g\sin 2) = 150000a$, and in turn: $$ a = \frac{6+150g\sin 2}{150} \approx 0.382 \ \text{m/s}^2 \, . $$ This is not the answer in the book. It is very close, but it is slightly out. I feel that either I am misreading the question or the question is under- determined. For example, the maximum possible climbing speed of the train is around $6.11 \ \text{m/s}$, but there is no mention in the question that the train spends a sufficient amount of time climbing in order to reach that speed. I would be pleased to see your ideas about how to resolve this problem. My misunderstanding is not mathematical, but conceptual; don't worry about using a lot of maths. But please try to explain the physical phenomena in a lucid fashion. Thanks in advance.


title: How do I deal with a quantum field in the denominator?

text: I am wondering how to deal with an expression like $$ \int d^4\theta \frac{1}{T + T^\dagger} \big( \dots \big) $$ If the denominator was of the form $1 + T + T^\dagger$, I could assume that $T \ll 1$ and expand the denominator in a Taylor series. If more context helps, this expression pops up in $5D$ SuGra abelian gauge theory (http://arxiv.org/abs/hep-th/0106256, eq. (5) on page 2). The authors of the above mentioned paper assume the modulus to be stable ($<T> \equiv R$) before performing the superspace integration. I do not want to do this and keep the dependence on the modulus.


title: What entities in Quantum Mechanics are known to be "not quantized"?

text: Since all the traditional "continuous" quantities like time, energy, momentum, etc. are taken to be quantized implying that derived quantities will also be quantized, I was wondering if Quantum Physicists agree upon any quantity not being quantized? I couldn't think of a single thing, until I came across this: Why position is not quantized in quantum mechanics?


title: Is there another way to calculate the work done by air resistance?

text: > A ball of mass $0.37\text{ kg}$ is thrown upward along the vertical with a > initial speed of $14\text{ m/s}$, and reaches a maximum height of $8.4\text{ > m}$. > > a) What is the work done by air resistance on the ball? I came up with $$F \times\text{Distance}(8.4) = .5 \times\text{Weight}(.37)\times(0-14^2)$$ But my answer doesn't match with the book's answer which is $-5.8\text{ J}$. Not sure if I"m doing this wrong; if there's some special way to calculate air resistance that _isn't_ the formula $W = .5(\text{Mass})(v_f^2-v_i^2)$, with $v_f$ being the final speed and $v_i$ being initial speed. Part B = Assume that air resistance does about the same work on the downward trip. Estimate the speed of the ball as it returns to its starting point.


title: Centrality and collision parameter b

text: Can someone tell me what does it 20-30% collision centrality mean in terms of impact parameter b?


title: Why are distant galaxies not actually tiny bits of matter?

text: Distant galaxies are said to be moving away from the Milky Way (and us) at speeds approaching the speed of light. Since Special Relativity tells us that any object moving away from us at a velocity of near the speed of light will increase in mass in our observations, i.e. it will appear to be much more massive than its rest mass, approaching infinity as the speed approaches the speed of light. If we observe very large masses (like galaxies) moving away from us at near light speed, wouldn't their rest masses be tiny? So why do we not think these distant galaxies are actually just specks of matter in terms of their actual rest masses? And if that is the case then are we not just looking at what may be sub-atomic particles moving away from us at near light speed? ...The expanding universe explanation is the standard one. The balloon example is perhaps suggestive but not correct. If you occupied one point on the surface of a balloon, and you had a friend next to you and the balloon expanded, your friend would move away from you at a relative velocity v. Einstein's equations would obviously still apply. I see no easy way to explain why when I look at measurements of relative velocity between distant recessive galaxies, those velocities are somehow not what are measured and quoted but something very different because the universe is expanding. Velocity is defined (for Einstein too) as distance divided by the time to travel that distance. And we are talking about objects with mass; not a reflective beam from a searchlight or something like that. Even if the universe expands, velocity is still what it is. And if it is not what it is, then why do astrophysicists state that distant galaxies are moving away from us at nearly light speed? I guess I would like to see the intuitive argument with equations included which must be there but no one knows how to do it. I suppose it took a while before time dilation could be explained on the back of an envelope too.


title: What is the Hubbard-Holstein model?

text: Please explain as simply as possible what the Hubbard-Holtstein model is and what it is used for.


title: XX coupling vs Heisenberg coupling

text: I am going through CURVATURE OF SPIN NETWORKS by Jonckheere et al. The first line of the abstract mentions XX coupling and Heisenberg coupling. What is the difference between these two couplings?


title: how can electromagnetic waves reach a cell phone in faraday cage?

text: is there any way to make electromagnetic waves reach a cell phone in faraday cage although conductor surround cell phone everywhere , can we pass current through conductor to make charges move as a trick then if electromagnetic field reach the conductor then no charge can prevent electric field as they are mobile not static charges


title: How long does it take a black hole to eat a star?

text: I presume the answer is that it depends on the mass and size of the star and black hole, but I was wondering if somebody could provide some rough bounds (e.g. hours vs thousands of years). By "eating" I mean the time it takes a star to go through the event horizon of the black hole, although maybe there are other easier-to-detect or more relevant events one can measure?


title: References for conceptual issues in Quantum Field Theory

text: I realize this question is very broad but may be I will still get a helpful answers. References and textbooks for the development of the technical and mathematical aspects of QFT abound. However, I never came across a source dealing with the conceptual issues of QFT. I am interested in stuff like,   * the meaning of Gauge symmetry,    * Spontaneous symmetry breaking,    * interpretation of renormalization group,    * etc.  Are there any reference that deals with these issues mainly?


title: Einstein's box - unclear about Bohr's retort

text: I was reading a book on the history of Quantum Mechanics and I got intrigued by the _gendankenexperiment_ proposed by Einstein to Bohr at the 6th Solvay conference in 1930. For context, the thought experiment is a failed attempt by Einstein to disprove Heisenberg's Uncertainty Principle. ![Einstein's box as drawn by Bohr](http://upload.wikimedia.org/wikipedia/en/6/65/Ebohr4.gif) > Einstein considers a box (called Einstein's box; see figure) containing > electromagnetic radiation and a clock which controls the opening of a > shutter which covers a hole made in one of the walls of the box. The shutter > uncovers the hole for a time Δt which can be chosen arbitrarily. During the > opening, we are to suppose that a photon, from among those inside the box, > escapes through the hole. In this way a wave of limited spatial extension > has been created, following the explanation given above. In order to > challenge the indeterminacy relation between time and energy, it is > necessary to find a way to determine with adequate precision the energy that > the photon has brought with it. At this point, Einstein turns to his > celebrated relation between mass and energy of special relativity: $E = > mc^2$. From this it follows that knowledge of the mass of an object provides > a precise indication about its energy.   >  \--source Bohr's response was quite surprising: there was uncertainty in the time because the clock changed position in a gravitational field and thus it's rate could not be measured precisely. > Bohr showed that [...] the box would have to be suspended on a spring in the > middle of a gravitational field. [...] After the release of a photon, > weights could be added to the box to restore it to its original position and > this would allow us to determine the weight. [...] The inevitable > uncertainty of the position of the box translates into an uncertainty in the > position of the pointer and of the determination of weight and therefore of > energy. On the other hand, since the system is immersed in a gravitational > field which varies with the position, according to the principle of > equivalence the uncertainty in the position of the clock implies an > uncertainty with respect to its measurement of time and therefore of the > value of the interval Δt. **Question:** How can Bohr invoke a General Relativity concept when Quantum Mechanics is notoriously incompatible with it? Shouldn't HUP hold up with only the support of (relativistic) quantum mechanics? Clarifying a bit what my doubt is/was: I thought that HUP was intrinsic to QM, a derived principle from operator non-commutability. QM shouldn't need GR concepts to be self consistent. In other words - if GR did not exist, relativistic QM would be a perfectly happy theory. I was surprised it's not the case.


title: How much of a star falls into a black hole?

text: http://blogs.discovermagazine.com/badastronomy/2011/04/05/astronomers-may- have-witnessed-a-star-torn-apart-by-a-black-hole/ A lot of the star in the disc, a lot of the star in the jets, precisely how much of the star actually falls into the black hole?


title: What's wrong with this simple derivation of energy flux in a photon gas?

text: In a photon gas, we know that pressure, $P$, and energy density, $u$, are related by: $$P=\frac{u}{3}$$ We also know from relativity that the momentum of a photon is $$p=\frac{E}{c}$$ Finally, the pressure can usually be thought of as the flux of momentum through a surface, but that would imply that the flux of energy through that surface is: $$E_{e}=Pc=\frac{u}{3} c$$ However, the standard formula, from kinetic theory, is: $$E_{e}=\frac{u}{4} c$$ I guess the assumption which is most probably wrong is identifying this sort of thermodynamic pressure with momentum flux, but I'm not sure how this comes about.


title: What are the patterns appear after kernel averaging?

text: Having a `2D map` filled `uniformly by random values` ( _Figure:top-left_ ) to demonstrate a disordered phenomena, the next maps are kernel averaged with a kernel of sizes 3x3, 5x5, ..., 11x11.   **The questions are:**   What are the patterns appeared in the kernel averaged maps?   What is the physical explanation of existence of such patterns? For image please see this link. **Note:**   To generate the maps a kernel based averaging system type **C** was applied on the original data.


title: Surface tension and capillarity

text: The cause of surface tension is said to be asymmetry in the forces experienced by the molecules at the surface due to different interactions with air and liquid, but then the same argument also applies for all other surfaces, where the fluid is in contact with the container then why isn't all strange surface tension phenomenon seen at those surfaces? And how can surface tension be described as perpendicular forces to an imaginary line at the surface, isn't it supposed to act in all direction?? Regarding capillarity, in deriving the equation $ \gamma= \frac{r h \rho g}{2 \cos \theta_Y}$, we use the relation of excess(over the pressure on convex side) pressure on the concave side which is derived only for spherical bubbles or drops. then how can we assume the meniscus formed will be spherical and not defined by some other function?


title: Can Joule's First Law of Thermodynamics be Applied to Atomic Charges?

text: James Joule established that all forms of energy were basically the same and interchangeable. My question is if thas law is relevant in particle physics. Can a positive charge and a negative charge be interchangeable? Will the force carrying particles allow it?


title: How would you go about finding the natural frequencies (resonance frequency)

text: How would you go about finding the natural frequencies of solid materials like wood (e.g., teak, pine), stone (e.g., marble, granite) liquid, etc?


title: Nuclear Compton Scattering Data

text: Is there a repository where one can find unpolarized nuclear Compton scattering data $\gamma (Z,N)\rightarrow \gamma (Z,N)$ for specific nuclei $(Z,N)$? or even some parametrization of structure functions that loosely follows the data?


title: How is black hole complementarity derived from path integrals or string theory?

text: How is the black hole complementarity version of the holographic principle derived from path integrals and/or string theory? That has never been obvious to me. Can someone show me how to do it step by step? I know string theorists have shown extremal and near-extremal BPS black holes have stringey entropies which match the holographic bound, but not only does this not apply to black holes in general, there are no signs of complementarity in the derivation. The AdS/CFT correspondence is also conjectural and based upon nontrivial consistency checks, but no derivation? Thanks a lot.


title: Why are some surfaces slippery?

text: Why are ice and oil slippery? In general, why do certain substances make a surface difficult to walk on?


title: on what fundamental force is a black hole based on?

text: what fundalmentel force does a black hole based on? It seems people is very unfamilar with black holes. I will take a guess, is it electromantic force? please explain.


title: How big is a nuclear reactor pressure vessel?

text: With all the sudden discussion related to Nuclear power, safety, fuel, waste, etc, there's one question whose answer has so far eluded me. How big (height and diameter) is the actual pressure vessel of a conventional BWR or PWR? I've seen, now, about a thousand images depicting the structures of Fukushima, Chernobyl, and TMI, but none of them include units of measurement for the size of what I'm looking at. Thanks! Eric B


title: How can you tell between gas, liquid and crystal in a microscopic way?

text: I know that molecules in ideal gas can move freely, and molecules in crystal are bonded to some specific location. But can I describe this in a more quantitative way? Do gas molecules have more degrees of freedom?


title: Force exerted by fluid in circular pipe

text: Imagine a pipe which is bent to form a circular arc and a liquid is force through this pipe. How will you find the net force exerted by the fluid on pipe? Is the only force acting on fluid centripetal force or is there a tangential force too? No drag forces or viscous forces


title: Calculating $dB/dt$ from velocity

text: I have recently carried out an experiment to verify Faradays law for a falling magnet. My starting point was to keep both the area of the coil and the number of turns constant whilst changing the velocity (the different velocities were obtained by dropping from different heights).What would be good is if a graph of emf induced vs. $dB/dt$ could be plotted so that the gradient of the graph will be equal to the product of the area and number of turns. From $e = -nA(dB/dt)$ In short, is there an equation to change velocity to $dB/dt$?


title: Showing specififc internal energy $e$ is a perfect differential

text: I am reading a book on Gas dynamics and there is a small section on thermodynamics before the conservation laws of mass momentum and energy are introduced. The book says $$ p = R \rho T$$ where $R$ is a constant. When that is the case we can write $$TdS = de + p d (\frac{1}{\rho}) \\\ dS = \frac{de}{T} - d(R \log \rho)$$ It follows that $de/T$ must be a perfect differential and therefore a function of $T$ alone. How does this last statement follow?


title: Interpretation of Free Damped Vibrations

text: I'm studying vibrations; so I'm using Beer-Johnston-Cornwell Dynamics book. I am worry about the equation for Underdamped Vibration, which in the book it is: $$x_{(t)}=x_0e^{-\lambda t}\sin(\omega_d+\phi)$$; where $$\omega_d=\sqrt{\omega_n^2+c^2/4m^2}$$. I think that $x_0$ would be replaced by the result vector of constants $c_1$ and $c_2$ affected by the factor $e^{-\lambda t}$. It means, an $x_m$ or an amplitud, but not the initial position, because it could be 0, with an inicial velocity. Also the graphic, it depicts the boundary equation with $x_0$. I attached a picture. Can you help me and comment? How I should interpret $x_0$? Maybe I misunderstood this topic. ![damp](http://i.stack.imgur.com/obyol.jpg)


title: Electron scattering

text: I'm trying to figure out the missing step here, in a problem about X-ray crystallography. I am referring to the attached image: ![](http://i.stack.imgur.com/EkwDw.png) In the image, $A =$ electron density, $Z =$ distance traveled, $\lambda =$ X-ray wavelength, $p$ = electron position. It shows two electrons hit by an X-ray, and then excited in all directions. In this case, only one of those directions, S', is considered. rj= pj - p1. Working off the basics of the image, suppose now there are $n$ electrons, $e_1,\dots, e_n$ at positions, $p_1, \dots, p_n$. And the X-ray scattering from $e_j$ is: $$X_j = A_j*\exp\left(\frac{2\pi i p_j S}{\lambda}\right)$$ I have understood that equation, but I do not understand how to use that to derive that the total scattering from all n electrons is: $$X = F*exp\left(\frac{2\pi i p_1 S}{\lambda}\right)$$, where $F = \sum_{1<=j<=n} A_j*\exp*\left(\frac{2\pi i r_j S}{\lambda}\right)$


title: Universe being flat and why we can't see or access the space "behind" our universe plane?

text: I'm a layman, but i watched some intereting videos about big bang on youtube[michio kaku, hawking this kind of things, not some crackpots :)] I described everything on my picture: ![enter image description here](http://i.stack.imgur.com/fqZAC.png) So is there any possibility to see that inner side, for example, by creating wormhole, or entering new dimension? Or i get something wrong, on the way, and my model is totally wrong? And another question. I heard that even if you would fly a ship across the universe you would eventually end in the place where you started, because we live in a 3d space that is defined on a surface of big sphere. But why a big sphere? Universe might be a big mobius strip, and the same principle of ending at start will apply. Is it possible? Thanks in advance, and please don't bash me for silly questions. Im just curious, but i don't have any degree in physics. Im also not an english native speaker.


title: Scattering amplitude and LSZ formula

text: I'm arriving at a contradiction. To calculate the scattering amplitude, one usually follows the prescription given by the Feynman rules that you only consider **fully connected** diagrams with the required number of incoming and outgoing external legs (See Peskin & Schroeder pg 111 where they say: Only fully connected diagrams contribute to the $T$ matrix). By **fully connected** , one means that you consider only graphs from which you can get from one line to any other line (See page 3 of this document). On the other hand, we have the LSZ formula, which says that the scattering amplitude is given by the residue (as the momenta go on-shell) of the corresponding correlation function. For example, in $\phi^4$ theory, \begin{align} &\mathcal{M}(p_a,p_b \to k_1, k_2) \delta^{(4)}(p_a + p_b-k_1 -k_2) \sim \nonumber\\\ &\lim_{p_a^2,p_b^2,k_1^2,k_2^2 \to m^2} (p_a^2 - m^2)(p_b^2 - m^2)(k_1^2 - m^2)(k_2^2 - m^2)G(p_a,p_b,-k_1,-k_2). \end{align} But these two prescriptions seems to give a contradiction. Consider in $\phi^4$ theory, the $\mathcal{M}(4 \to 4)$ scattering. We have this diagram (ok if someone could draw the diagram that'll be great), \begin{align} \text{X} \text{X} \end{align} which consists of two separate $2 \to 2$ scattering processes. This diagram is not fully connected, so we should ignore it by the first prescription, yet, it does not evaluate to $0$ under the LSZ formula, so we should include it. Physically it makes sense that the leading order contribution to a $4 \to 4$ process is given by two separate $2 \to 2$ ones, but the fully connected prescription misses that out. So, is there a caveat to the fully connected rule of drawing Feynman diagrams, since I believe the LSZ formula is mathematically true and physically reasonable?