title: How is the distance to a $\gamma \mathrm{-ray}$ burst (GRB) measured in just a few days?

text: Recently the Fermi Gamma-ray Space Telescope recorded the most energetic Gamma Ray burst (GRB 130427A) yet observed with a peak $\gamma \mathrm{-ray}$ energy of $94\, \mathrm{GeV}$. Various sources have reported that the burst was determined to be $3.6 \times 10^9\, \mathrm{lightyears}$ away. How can a distance measurement like this be made so quickly? It has only been a few days since the GRB. No articles mention any supernova remnant being seen yet or anything else besides just the GRB. I don't see how the photons in a GRB could have absorption or emission spectra that would help and there isn't any mention of the GRB being localized to a particular galaxy. NASA says: > The burst subsequently was detected in optical, infrared and radio > wavelengths by ground-based observatories, based on the rapid accurate > position from Swift. Astronomers quickly learned that the GRB was located > about 3.6 billion light-years away, which for these events is relatively > close. How are distance measurement like this made so quickly and what sort of accuracy do they have?


title: Possible implications of Quark Quartet

text: Today on Nature's website appeared a news about the discovery of a quark quartet (formed from two quarks and two antiquarks). They say that this particle containing four quarks is confirmed. This is the link to the news Quark Quartet Also, they state that the quarks arrangement in this new particle could have implication for quantum chromodynamics. This is where I get stuck. What implications does a quark quartet have on QCD? The article references:   * Liu, Z. Q. et al. Phys. Rev. Lett. 110, 252002 (2013).   * Ablikim, M. et al. Phys. Rev. Lett. 110, 252001 (2013). for the discovery/confirmation as well as some older papers   * Chen, K.-F. et al. Phys. Rev. Lett. 100, 112001 (2008).   * http://arxiv.org/abs/1105.4583


title: Rotation of Taylor expansion of a scalar

text: I have a scalar magnetic field in a volume expressed by the formula $$B(x,y)=B_0 + \frac{\partial B}{\partial x}(x-x_0) + \frac{\partial B}{\partial y}(y-y_0)$$ which approximates the non-homogeneity of the magnetic field with linear gradients. This is defined in a specific frame of reference in one plane perpendicular to the $z$-axis. Multiple planes will provide the magnetic field in the volume. I need to rotate this formula around the $z$-axis with an angle $\phi$. Can this be done and how will the derivatives transform in this case? How will this be done with higher order derivatives (secondary question)?


title: How does a Trumpet loud speaker work?

text: I pierced a hole in a cone shaped cardboard's tip and attached it to my phone speaker. Surprisingly the sound produced when attached is three times louder than the sound when it is removed. I do know that it is something relevant to trumpet loud speaker.What makes it to produce louder sounds? ![enter image description here](http://i.stack.imgur.com/VWBpM.png)


title: Astronomical Constant in Astronomical units?

text: I'm doing a computer simulation of the solar system and I'm having trouble working with big numbers (implementation specific problem). So what would be the Newtonian gravitational constant $G$ in relation with the Earth mass instead of kilograms and astronomical units instead of meters?


title: Anti-symmetric 2 particle wave function

text: Suppose we want to construct a wave function for 2 free (relativistic) fermions. As we are dealing with fermions the total wave function has to be antisymmetric under interchange of the coordinates, $$ \Psi(x_1,x_2) = - \Psi(x_2,x_1) $$ If we assume that we can factorize the wave function in terms of single particle wave functions we can write $$ \Psi(x_1,x_2) = \psi_{1}(x_1) \psi_{2}(x_2) - \psi_{1}(x_1)\psi_2(x_2) $$ which fulfills the anti-symmetry requirement. The plane wave single particle states are given by, $$ \psi_{\mathbf{k},m_s} (x) = u_{\mathbf{k},m_s}(s) \phi( \mathbf{k} \cdot \mathbf{r}) $$ So I would expect the total wavefunction to be \begin{align} \Psi(x_1,x_2) &= u_{\mathbf{k}_1,m_{s_1}}(s_1) \phi( \mathbf{k}_1 \cdot \mathbf{r}_1) u_{\mathbf{k}_2,m_{s_2}}(s_2) \phi( \mathbf{k}_2 \cdot \mathbf{r}_2) - u_{\mathbf{k}_1,m_{s_1}}(s_2) \phi( \mathbf{k}_1 \cdot \mathbf{r}_2) u_{\mathbf{k}_2,m_{s_2}}(s_1) \phi( \mathbf{k}_2 \cdot \mathbf{r}_1) \\\ &= u_{\mathbf{k}_1,m_{s_1}}(s_1) u_{\mathbf{k}_2,m_{s_2}}(s_2) \phi( \mathbf{k}_1 \cdot \mathbf{r}_1) \phi( \mathbf{k}_2 \cdot \mathbf{r}_2) - u_{\mathbf{k}_1,m_{s_1}}(s_2) u_{\mathbf{k}_2,m_{s_2}}(s_1) \phi( \mathbf{k}_1 \cdot \mathbf{r}_2) \phi( \mathbf{k}_2 \cdot \mathbf{r}_1) \end{align} However I have seen this written as $$ u(\mathbf{k}_1,m_{s_1}) u(\mathbf{k}_2,m_{s_2}) \phi( \mathbf{k}_1 \cdot \mathbf{r}_1) \phi( \mathbf{k}_2 \cdot \mathbf{r}_2) - u(\mathbf{k}_2,m_{s_2}) u(\mathbf{k}_1,m_{s_1}) \phi( \mathbf{k}_1 \cdot \mathbf{r}_2) \phi( \mathbf{k}_2 \cdot \mathbf{r}_1) $$ If I'm not mistaking one cannot freely change the order of the Dirac spinors ($ u(\mathbf{k}_1,m_{s_1}) u(\mathbf{k}_2,m_{s_2}) \neq u(\mathbf{k}_2,m_{s_2}) u(\mathbf{k}_1,m_{s_1}) $) so these expressions seem to be uncompatible. What would the correct expression look like? Maybe related to my question is my confusement about the spin coordinate in the Dirac spinor. It is my understanding that the Dirac spinor only depends on the projection of the spin $m_s$ which denotes a quantum number or a quantum state, and is not a coordinate. So is $m_{s_i}$ invariant under a coordinate switch $s_1 \leftrightarrow s_2$? Why explicitly write the spin coordinate?


title: Relativity of Simultaniety

text: ![enter image description here](http://i.stack.imgur.com/73vNK.jpg) In the first figure, A and B are two equidistant points from the observer O in S. In the second figure (reference frame S') the corresponding points are A'and B' such that A'O'=O'B', where O' is the observer in S'. The first figure represents the state of S and S' at time t=0 when two events occur at A and B in S and the corresponding points In S' are A' and B'. Now S' moves with a velocity v w.rt. S. The second figure represents the state of S and S' at time t=t1 when the rays from A and B reaches O simultaneously (if possible). Clearly, since at that time O and O' don't coincide, to O' the events should not be simultaneous. Conversely, if at time t=t1' the rays from A' and B' reaches O' simultaneously (if possible), for the same reason O will not find the events to be simultaneous. Since the light rays are unique, they cannot meet more than once. So only one observer should find the the events to be simultaneous. In this case which observer will find the events to be simultaneous and why?


title: Rotation of object on another object under rotation

text: First, I would like to know the rotational velocity of disk2 if disk1 turns at $\omega1$. The axis "x" is fixed to the ground and disk1 is allowed to turn around it. Axis "y" is fixed to disk1 and disk2 is allowed to turn around it. For me, disk2 turns around axis "x" and around axis "y" but not in the same manner. I can understand its rotational velocity is $\omega2$ and for me even disk2 turns around axis "x" and because disk1 is turning, this doesn't change its rotational velocity $\omega2$. I'm not sure. Can you explain please ? In fact, what's a rotational velocity in this case for disk2 ? ![enter image description here](http://i.stack.imgur.com/Uo4sT.png) Second, with $\omega1=-\omega2$. A motor is fixed between disk1 and disk2 (in axis "y"), stator on disk1 and rotor on disk2 (idea of Floris, thanks). If a torque from rotor increase $\omega2$ this would say another torque from stator increase $\omega1$. The motor need energy for give a torque to disk2, I'm agree with that. But I don't understand why the motor need energy for apply its torque from stator to disk1. For me, like stator and rotor turn at the same rotational velocity around axis "x" it's not difficult to add torque to disk2 even the stator+rotor turn around "x" in the same time. The motor turn around the axis "x", when stator turn $d\theta$ degree in one direction, rotor turn $d\theta$ degree in the same time. So, it's not "difficult" (need energy) to apply torque on disk1 for me. If rotor moves far away from stator, in this case I'm agree, I will be more difficult to accelerate it, but here stator and rotor never move from each other. If I need to give forces that stator gives to disk1, I'm agree I need energy, but these forces are only a reaction from the stator because rotor apply a torque. I'm not sure I explain very good what I think, I hope someone can clear this idea. I would like to understand why the motor need energy for apply its torque to disk1. \------------------------Added from comment of Floris: I'm agree, if I'm on object that move back and I try to move an object in front of me, I need more energy. I drawn disks and 2 points A and B: ![enter image description here](http://i.stack.imgur.com/OJYLN.png) Imagine, disk2 don't turn around its center of gravity (axis y). Motor and disk2 turn only around axis "x". You could look at distance AB, it is always the same even the stator rotates of 45°, because the rotor rotates of 45° too. It's not like stator move in one direction and rotor in other. Now, the rotor turn around axis "y" but why it's not the same with a linear trajectory ? Now, distance AB change but only because stator "attack" rotor, in the same time stator rotates around axis "x" but rotor rotates around axis "x" too. Maybe my confusion come from I dissociate 2 movements: first the rotation around axis "x" and second the rotation around axis "y". For me, inertia and centrifugal forces rotate motor and disk2 around axis "x" and torque from motor add rotational velocity of disk2 around axis "y", I don't see where the stator move "back" like your example, could you explain more please ? Maybe I don't have the right to think like that. Sorry if my level of physics is low. I added forces, maybe like that it's easier to explain the problem: ## ![enter image description here](http://i.stack.imgur.com/qEhuC.png)


title: Laser excitation of Phonon Modes

text: Can a laser _only_ excite optical modes? The name appears to have historical significance in terms of the sodium ion, but I presume it must be true when looking at the dispersion relationship (the dispersion for light would only cross the optical modes). The overall context of the question is: when exciting with a laser, is energy eventually dumped into all phonon modes?


title: Calculate Avogadro's constant based on grating constant and density of NaCl crystal

text: The tittle says it all. I need to calculate Avogadro's constant based on grating constant of NaCl crystal ( in this case 278 micrometers ) and crystal density ( 2.1 grams per cubic centimeter ).


title: Charge Amplifier response and frequency response

text: I am getting ready for my final and have completed everything on my study guide except for two questions I cannot figure out. Here is the first question: ![enter image description here](http://i.stack.imgur.com/J63N3.png) I have gone through all my lectures and previous HWs and cannot find anything similar to this. Could someone help me walk through this problem? Any help will be appreciated!


title: Why is a gun less accurate when the barrel heats up?

text: I was out target shooting with a friend of mine, and about 2 hours into it I commented how my accuracy seems to be going down the longer we shoot. He (a fire arms instructor in the Navy, so I tend to believe him) said when a barrel heats up, the gun becomes less accurate. On a side note, he said that when snipers are going for long (~1 mile) long shots. they take out the magazine and leave it in the sun allowing the ammo to heat. They will then load a single bullet at a time because, although a heated barrel will cause a decrease in accuracy, a heated bullet will be more accurate. Assuming this is true, why would that happen? Is the heated barrel expanding and causing some of the gas to escape around the bullet? And would a heated bullet expand to cause more pressure (more speed/spin?)


title: Water falling, why does it spin?

text: I have noticed that water, when falling will rotate. Looking closely at a thin stream from a faucet and placing a flat object mid stream you will see the water is rotating. The further down the stream you go you will notice the rotation is much quicker. Am I confused at this occurrence or is there a reason? I can only come up with the rotation of the earth taking into affect.


title: What electromagnetic wave produces the strongest electrical current when making contact with an element?

text: More specifically, what electromagnetic waves can we utilize to generate electrical power and out of those waves, which one would produce the most power? Additionally, which one would be the most reasonably accessible and usable? Note: The reason I ask this question is because I was wondering what kind of wave we could use in order to have, lets say, wireless laptop chargers and what not.


title: Is it possible to calculate the half-life of a nucleus?

text: Is it possible to calculate theoretically the half life of a nucleus (how?) or they are all known through measurements? As an example how do you calculate the half life of Carbon-14?


title: What would happen if the moon was in perpetual opposition of the sun

text: What would happen if an artificial force made the moon to stay at a perpetual opposition from the sun? Assume that the artificial force necessary is possible, and capable of making the moon stay at sun's opposition and keep from being dragged towards the planet by the gravity. this question was inspired by another of my questions: Planet in which satellite(moon) and star(sun) appear together once a year


title: Molecular Hamiltonian

text: I was reading some material on the Molecular Hamiltonian on Wiki. It said that, > _Almost all calculations of molecular wavefunctions are based on the > separation of the Coulomb Hamiltonian first devised by Born and Oppenheimer. > The nuclear kinetic energy terms are omitted from the Coulomb Hamiltonian > and one considers the remaining Hamiltonian as a Hamiltonian of electrons > only._ I am not sure why this is done. This won't be the "full" Hamiltonian if we omit the KE terms of the nuclei. Can somebody please explain to me why the nuclear kinetic energy terms can be ignored from the Coulomb Hamiltonian.


title: If randomness doesn't exist, how come the universe isn't a perfect sphere with predictable distribution of matter?

text: I'm presuming that the scientific community pretty much agrees that randomness doesn't exits, and that everything has a cause. Please correct me if I'm wrong, I've heard of quantum mechanics, but as far as I know, it only says that it is impossible to know the electron's position and speed in the same time, because of the uncertainty principle, but I don't think that this makes the electron move randomly. Now, lets consider big bang. A point starts expanding in size, as the time flows. If there isn't any randomness, it is logical to conclude that matter will position itself in some kind of a predictable pattern, not chaotic shapes as we see today. So, I ask you, how did the universe form as it is today? Is that proof that randomness truly does exits? Does randomness break laws of logic and physics?


title: Relationship between gauss and decibels

text: In my ongoing effort to understand the world around me, I want to wrap my head around the relationships between two units of measure. Specifically gauss and decibels. The quandary comes from my understand of waves. Hertz is the measure between wave peaks and describes the frequency of the wave. And from what I know about sound, decibels is the measure of intensity. I've played around with a spectrum analyser designed for sound and really got an understanding of how it all works. Then I turned my attention to electromagnetic waves. I was looking for a tool that I could use to measure electromagnetism at any given location. The first tool I came across was an electromagnetic field meter (EMF meter) which is measured in gauss. Wouldn't it be equally effective to measure in decibels? I also could not find a conversion from one to another, so I would assume they measure different things. Can you clear this up for me?


title: Do excited electrons drop back to same quantum state?

text: I'm trying to wrap my head around spectroscopy, therefore, I am looking for as complete an answer as possible here, hence why I have broken the question into a different points. Here is what I know so far:   1. If an electron has an energy level `E1` and the next energy level is `E2`, then a photon coming in with energy equivalent to `E2-E1` will kick that electron up to its next available state, `E2`.   2. Eventually that electron will drop back to energy level `E1` as it is more stable.   3. When it does so, the electron emits a photon. Here is what I want to know:   1. What happens to that photon after it is absorbed/used? Does it become a part of the electron or does it continue on?   2. When the electron drops down, does it have to drop back to energy level `E1` or can it drop to some other energy level? Does it have to drop back relative to the energy level of the photon that originally excited it?   3. Where does the emitted photon come from?


title: Thermal Energy from Friction on a Rope

text: Question: A capstan is a rotating drum or cylinder over which a rope or cord slides to provide a great amplification of the rope's tension while keeping both ends free. Since the added tension in the rope is due to friction, the capstan generates thermal energy. If the difference in tension ($T_0-T'$) between the two ends of the rope is $520N$ and the capstan has a diameter of $10.0 cm$ and turns once in $0.90s$, find the rate $P_{thermal}$ at which thermal energy is being generated. My Work: $F = 520N$ $d = 0.1m$ $\Delta T = 0.90s$ $\Delta U = Q - W \implies Q = \Delta U + W$ $W = \tau \Delta \theta = Fd(2\pi) \implies W = 326.7J$ $P = \frac{\Delta W}{\Delta T} = 363W$ However, this is the incorrect answer. (I don't know the correct one.) Can anybody give me any guidance here?


title: Would Quantum entanglement theoretically allow prediction of the future?

text: This article describes how a choice made by the recipient of an entangled photon can affect measurements taken on that photon's "partner" _before_ the decision was made. So let's say there are two recipients ( _A_ and _B_ ) receiving streams of paired photons. Recipient _A_ chooses whether to combine certain photons based on some observation (like the movement of a particular stock ticker).   1. Would this make it possible for recipient _B_ to know how that stock ticker moved before it happened?   2. If so, would it be possible for recipient _B_ to have affected some of the photons they received based on their earlier observations, so that recipient _A_ could know what would happen to the stock ticker before they even observed it?


title: Lorentz Force Law and cycloid motion

text: The question I have is from Intro to Electrodynamics by Griffiths (Page 206, Example 5.2) http://imgur.com/a/sfBlt When using the initial conditions $y(0) = z(0) = 0$, I get: $y(0) = 0$ implies $C_3 = C_1 = 0$ and $z(0) = 0$ implies $C_4 = C_2 = 0$. However, how does this work with every $C_1, C_2, C_3, C_4 = 0$ ? Also, how did the author arrive at the general solution that $y(t) = C_1 \cos (\omega t) + C_2 \sin (\omega t) + (E/B)t + C_3$ \ $z(t) = C_2 \cos (\omega t) - C_1 \sin (\omega t) + C_4$


title: Is this a series or parallel connection?

text: I am confused how the capacitors in this circuit are connected. $C_4$, $C_6$ and $C_5$, $C_3$ appear to be parallel, but both $C_4$ and $C_6$ seem to be in series with $C_1$ as do $C_5$ and $C_3$. Am I missing something? I couldn't find explained examples of a circuit with a capacitor in between two parallels like that. ![example of circuit](http://i.imgur.com/QKE2ndw.jpg)


title: Testing the speed of gravitational waves in superfluids

text: Ok. Light can be slowed down in superfluids. I would like to know whether if a Cavendish like experiment could be possible within inside superfluids i.e, to rotate two balls such that to observe their gravitational attraction just like the big G is determined and test whether gravitational waves(might take debroglie wavelength) are slowed down or not? Or whether it could be tested for celestial bodies' gravitational wavelength (or debroglie wavelength) redshifted well enough to an observable limit. Would deduce something about gravitons?


title: Why Light and Observers have different laws of physics

text: Special relativity states:   * The speed of light in a vacuum is always $c$, regardless of the velocity of the observer.   * The laws of physics are the same for all observers in uniform motion. These two statements that we know as "special relativity" indicate that $c$ (speed of light) does not follow the same laws of physics as the observer.   * The laws of physics are the same for all observers in uniform motion.   * The observer is (anything that never travels at the velocity $c$).   * The laws of physics are the same for (anything that never travels at the velocity $c$).   * The laws of physics are not the same for anything that does travel at the velocity $c$. This suggests that when we use our physics to measure and predict light, what we are predicting and measuring is only the disturbance in our physical laws, caused by the passing of something that does not exist within our physical laws. As an analogy, the electromagnetic wave is to the photon as thunder is to lightning. Our physical laws enable us to measure and predict the disturbance in our reality that we know as electromagnetic wave light, but the cause of this electromagnetic wave exists under entirely different laws of physics and therefore a different reality.


title: Quantum tunneling effect in a potential of the kind $V(x)=A\frac{x^2}{1+x^4}$

text: Given a potential: $$V(x)=A\frac{x^2}{1+x^4}$$ with $A\gt 1$ and a quantum particle inside the well around the point $x=0$. I'm stuck on the calculation of the transmission and reflection coefficients for this particle vs. its energy.


title: What are the implications of the Holographic principle?

text: What are the implications for the Holographic principle? I understand the basics of the principle, the relationship with black holes and string theory but what this is going to tell us? Does it help to explain quantum gravity? Is the model compatible with any multiverse theory? The Holographic principle seems to be proposed as a new theory but where does it fit with the fine- tuning problem?


title: Complex Versus Real Wave Velocities in Quantum Mechanics

text: There's a fantastic quote in Schrodinger's second 1926 paper1 that apparently provides some motivation for the discrete energy levels (I think) that I'm having trouble interpreting: > I would not like to suppress the remark here (and it is valid quite > generally, not merely for the oscillator), that nevertheless this vanishing > and becoming imaginary of the velocity of propagation is something which is > very characteristic. It is the analytical reason for the selection of > definite proper values, merely through the condition that the function > should remain finite. I would like to illustrate this further. A wave > equation with a real velocity of propagation means just this : there is an > accelerated increase in the value of the function at all those points where > its value is lower than the average of the values at neighbouring points, > and vice versa. Such an equation, if not immediately and lastingly as in > case of the equation for the conduction of heat, yet in the course of time, > causes a levelling of extreme values and does not permit at any point an > excessive growth of the function. A wave equation with an imaginary velocity > of propagation means the exact opposite: values of the function above the > average of surrounding values experience an accelerated increase (or > retarded decrease), and vice versa. We see, therefore, that a function > represented by such an equation is in the greatest danger of growing beyond > all bounds, and we must order matters skilfully to preserve it from this > danger. The sharply defined proper values are just what makes this possible. > Indeed, we can see in the example treated in Part I (Hydrogen atom). that > the demand for sharply defined proper values immediately ceases as soon as > we choose the quantity E to be positive, as this makes the wave velocity > real throughout all space. I'm in danger of misinterpreting this claim due to my lack of knowledge of quantum mechanics, so could anyone elaborate on the implications of a wave solution of the Schrodinger equation having a complex velocity implying discrete eigenvalue energy levels, & a positive velocity removing this requirement (if that's what he means)? Thanks * * * 1 Quantization as a Problem of Proper Values, Part II. _Annalen der Physik_ (4), vol. 79, 1926. Available as part of _Dreams That Stuff Is Made Of: The Most Astounding Papers of Quantum Physics_ here, or in _Collected Papers on Wave Mechanics_ from here.


title: Global phase symmetry for complex scalar field theory

text: I have started to study QFT. And I have some difficulties in such classical situation. Suppose i want to calculate $\frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\phi$ for lagrangian density $\mathcal{L}=\partial_\mu \phi^*\partial_\mu \phi-m^2\phi^*\phi$ ($\phi$-complex scalar field). I know I should obtain something like $\left[(\partial_\mu \phi)^*\phi-(\partial_\mu \phi)\phi^*)\right]$ $(1)$ but I don't understand how to get this. It's very new subject for me, so I'll be glad to see any answers. **EDIT** I'm reading Gross D. Lectures on QFT. There are a paragraph called "LOCAL SYMMETRIES". There was proved the following fact: Consider an internal symmetry transformation $\phi_{i} \rightarrow \phi_{i}^{'}(x)=\phi_{i}+\Psi_{i\alpha}(x)\omega_{\alpha}(x)$ For this transformation the current is $J^{\alpha\mu}(x)=\frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi_{i})}\Psi_{i\alpha}(x)$ $(2)$ For described situation the current was written above. So, this equations ($(1)$ and $(2)$) should be equal. But I cant get equation $(1)$ by direct differentiation in $(2)$.


title: Is inertia present in a body while in state of motion?

text: According to Newton's law of inertia (written in book: **The Mathematical Principles of Natural Philosophy**** ) it is said that in all objects having mass, have always inertia included in their property but if a body is in motion well then, would there be inertia in that body. For instance: A ball is hit by a bat and is in state of motion in air so would there be inertia present in that current state of ball or not? According to friction law of physics friction is any thing which exists when two or more bodies come in contact with one-another and it is against the direction of force (pushing a body) which is against inertia so would friction be helpful too in supporting inertia of a body consequently? If yes then could it be said that, inertia is directly proportional to the friction?


title: How does a car's low gear increase power while going slower?

text: People have always told me that when a car goes into low gear, it goes slower but puts "more power" or "more torque" on the wheels, which allows it to descend slippery slopes or get out of mud traps more easily. I've never had a satisfactory answer as to what that actually means. Doesn't more power on the wheels mean they'll go faster?


title: Auxiliary field and loop expansion

text: Something bugs me with the use of auxiliary fields in QFT. On one side I understand that they are nothing more than Lagrange multipliers and should be replaced by their equation of motions in the action, and this works perfectly on-shell (by definition) but what about this replacement at the quantum level, where the equations of motions may not be satisfied? Let's say I have an action with one physical and one auxiliary field, I do two hbar expansion (loop expansion if you prefer): the first after getting rid of my auxiliary field, the second keeping track of it, will I, for sure, find the same calculable quantities in those loops?


title: Emf Of a Cell in a common circuit

text: ![enter image description here](http://i.stack.imgur.com/TZeXG.png) My questions will be based on the above figure.   * The Emf Source V1 and R1 Together form a cell(R1 is internal resistance)   * R2 Represents the entire load on the source ## VoltMeter * * * My teacher told us that Emf was the terminal potential between the electrodes of the source when the ciruit is open and the current drawn is zero. Earlier in the class he told us that a volt meter is considered to have $\infty$ Resistance so as to draw nearly zero amperes from the loop. Next He told us that the current through the Resistor R1 is zero as the circuit is open do the reading on the volt meter will only be the potential of the Source V1 i.e. Emf My question is   * If the circuit is open and the current through R1 is zero and also the voltmeter is drawing zero current then how could the voltmeter possibly show any reading at all?    * How can one measure the voltage if the circuit is open .


title: Hydrostatic pressure on a teapot spout

text: The phenomenon where water flows on the outside side of a teapot spout is named "The teapot effect", and occurs due to a difference in pressure between water and the atmosphere. Consider the image of a teapot spout below, and consider the pressures at points A, B, C and D. ![Teapot](http://i.stack.imgur.com/NMRU9.png) ( _Quick translation:_ "Bico" means "Spout", and "Água" means "Water") I've been kind of lost in this question due to different theories, so I'm going to arrange them into statements to make it more organized:   1. (This doesn't alter the answer, but I wanted to know if it's correct.) The whole stream of water has a lower pressure (if compared to atmospheric) **because** it has a certain velocity, and fluids with velocity have lower pressure;   2. A and D must be atmospheric pressure, since they're both in direct contact with air;   3. B must be higher than both because of Pascal's Law;   4. C must be lower than D, but I don't have a clue why this is true. I'm assuming that because it **must** be the pressure difference that supports water against gravity (considering that I'm right about D being atm pressure), but that is kind of "doing the problem in reverse", what would the real reason be?


title: Why are Markov chains better than naive algorithm for Random picking?

text: I have a question about the problem of coming up with a random distribution of non-overlapping coins in a given two dimensional space. I don't understand why using the random sequential adsorption technique (picking an initial random position for one coin, then do the same for the next; if it overlaps, keep trying until you find a non-overlapping position for it and so on) is not equivalent to using Markov chains to solve the same problem. Thanks!


title: What are the practical limits on the pecular motion of stars?

text: What are the practical limits on the pecular motion of stars and planets?


title: Does the mass of a battery's change when charged/discharged?

text: ... and if so, how much? Is it possible to detect it, or is it beyond any measurement? I'd say there are two possible scenarios (depending on the battery type) and both seem interesting:   1. The battery reacts chemically with its environment.   2. The battery doesn't exchange any matter with its environment except electrons. I suppose there should be some difference at least due to the principle of energy-matter equivalence, but the difference is most likely immeasurable.


title: What are some significant contributions of string theory to other fields of physics?

text: What are some contributions that string theory has made to other branches of physics/science (other than research in string theory)? I'm looking for specifics, for example mentioning what string theory has contributed to superconductivity rather than saying merely that it has applications in superconductivity. If there is a reference in which such collection of applications of string theory is listed it would be great. Update (thanks to drake): If it is possible, it would be also helpful to mention which contribution have led to new predictions and which have led to reproducing a well-known result through a stringy argument.


title: I've been reading that it's possible to create a "mostly magnetic" wave, and I have a few questions

text: Would it be possible with the "mostly magnetic wave" to have it behave in such a way that it would be undetectable by radio triangulation? I read about the monument at the CIA headquarters that was designed by an artist. Supposedly it's cryptography is very difficult to decipher, but some of it has been deciphered. One of the lines reads "It was transmitted magnetically undergrund". That's the actual spelling of the translation by the way - "Undergrund". I've also read that waves that are mostly magnetic penetrate the ground far more deeply than a simple radio wave. So my question is multi-faceted. Could waves that are mostly magnetic carry a signal of any kind better than a radio frequency generator, and if they're mostly magnetic would it follow that they'd be mostly undetectable to people trying to find the source of a radio transmission?


title: Adiabatic quantum Hamiltonian of variable dimension

text: Is adiabatic quantum Hamiltonian of variable dimension possible? This is very hypothetical and I am afraid may not have enough merit to belong to this forum. I would still like to elaborate. Here is an example. Is adiabatic quantum evolution possible on a system which contains four spins when the evolution starts, throws away (remove) two spins during the process and finally is left with two spins by the time the evolution finishes?


title: Why does a car go down the hill backwards even though the engine keeps running?

text: I dont get why a forward gear allows sliding a car backwards. Any ideas? So this is a car with an automatic transmission. The transmission is in the drive mode (move forward). Car is at the slope facing the hill up. I am in the car pushing the gas pedal very gently. The car is supposed to move forward going up the hill. Instead it moves backwards down the hill, because I am not pushing the gas pedal hard enough. I haven't switched it to reverse. This is where I don't get it, because it turns out that the wheels are spinning in the opposite direction of what the transmission gears tell them to spin. How can this be possible? Or, to put it in a different way, how can a car move backwards when it is in "drive" mode (supposed to go forward)?


title: Thermography time evolution

text: I have an imaging problem. I essentially have a metallic plate with a number of holes through it. I am looking at the number of holes with a thermal camera. While looking at the plate I have two phases of this analysis, 1.a source of hot fluid is flowing through the holes and behind the plate 2.a source of cold fluid flowing behind the plate and through the holes. During each phase I take a number of images N. So in effect I have a set of random variables for each pixel in the image. $H[x,y] = (x_1, x_2 .... x_n)$ and similarly $C[x,y]=(x_1, x_2 .... x_n)$ where H is the hot frames, C is the cold frames , x-y are the focal plane position of that particular pixel and 1,2,3 are the discrete time of the reading x. As it stands I'm just taking the mean value for H and C then subtracting them to generate an image ($I=\bar{H} - \bar{C}$ where the bar denotes the expected value) to gain an image that has significantly decreased noise and removes much of the background effects. **This is really just to decrease the noise but I think there is more information there that I'm not utilizing considering this is not a wide sense stationary process, but is evolving with time as the temperatures reach equilibrium for each phase.** I'm looking for a way to utilize this data and for any recommendations on processing this time evolution to form an image. Any suggestions? I have tried Finite Difference Operator to approximate first and second derivatives, but this and various other algorithms have failed me.


title: Simple question about circular motion

text: The picture below shows a page of my mechanics (M2) textbook. At the top of this page, you'll see that it says that "a=-ω^2r". Why is it then that all the answers to the question in exercise 6B (also on the page in the picture attached) are positive? Surely the minus sign in the equation for 'a' should man that all the answers should be negative? ![Page from M2 textbook](http://i.stack.imgur.com/UsRpX.jpg) Unfortunately, I am the only person in my Further Maths class who doesn't do physics, so this mechanics module has been quite difficult for me. This is probably therefore a really stupid question... but oh well; better to ask than to not know.


title: Can path integral paths go backwards in time?

text: The paths can cross any coordinate at any time in the whole space (e.g. Universe space). Integration goes over all could-you-imagine paths. But time goes strictly forward. Can time variable resemble coordinate variable and path be able to expect backward turn? Upd 2014-01-04: yes, it's called spacetime, but the time coordinate is still very special.


title: Finding the drag force (Air resistance force) for accelerated ball?

text: As you know if I want to find the force for an accelerated object I will use the law $F_o=ma$ so I can get the affecting force of it. But there is another force affecting against the object. It's the air resistance force, So I will have to calculate the drag force (Air resistance force) and the subtract it from the accelerated object force to get the exact affecting force $F_{net}=F_o-F_d$ while $F_o$ is accelerated object force and $F_d$ is drag force (Air resistance force). Now, how can I calculate the drag force (Air resistance force)? OK, Actually I know the formula below: $F_d=\dfrac{\rho\,\nu^2AC_d}{2}$ While: $\rho$ is the air density, $\nu$ is the speed of the object relative to the air, $A$ is the cross sectional area of the object and $C_d$ is the drag coefficient. So my problem is: I don't know what is the $A$ cross sectional area of the sphere (in my state I used a ball) and I don't know what is the $C_d$ drag coefficient of a sphere (ball)?


title: Is it possible to reach the edge of a room if there isn't any gravitational acceleration?

text: Consider that a large room(an indoor badminton court) is orbiting the earth with a person floating exactly at its center without any relative initial velocity. Consider that the person has no spacesuit(so he can freely breathe, see below.) and the room is pressurized. **Can the person reach the edge of the room?** I'm thinking if he can breathe in from on side, turn his head, and blow out to another side, the conservation of momentum of the airparticles can impart a very small motion, enabling him to reach the edge. Also, **can the same blown air reflected from the other edge help this process?** **What (regular geometrical)shape of the room(keeping the total volume of the room same) would be best to enhance this process?** **Is there an other efficient method?**


I do not know much about tensors. So I wonder: Is it possible to explain general relativity without tensors? I have some understanding of special relativity. I also have some understanding about differential equations and matrices.


title: Are principle of Conservation of energy and principle of conservation of momentum consequences of Newton's laws?

text: It is known that principle of Conservation of momentum and principle of conservation of energy are two fundamental principles of physics.But in RP Feynman's _Lectures of physics,_ in the chapter of conservation of momentum, it is said that conservation of energy and conservation of momentum are consequences of Newtons laws of dynamics.Is it correct?


title: Photon temperature above Electroweak Symmetry Breaking (EWSB) transition

text: In discussions of the history of our Universe, photon temperature is substituted for time. As the Universe cools, phase transitions break symmetries, including electroweak symmetry. Why does it make sense to speak of photon temperature prior to Electroweak Symmetry Breaking (EWSB)? Is this a misnomer? Is it shorthand for "boson for unbroken $U(1)$" temperature? Or did I misunderstand something.


title: What are physical effects that could be employed to emulate this system?

text: This is a simple system consisting of a tree of numbers such as `((1 2 (3 4)) (2 6) 1 6)` and a rule of application, that states that a tree A applied to B is a copy of A, where every number matching its own deepness on that tree is replaced by a copy of B. For example, that sequence applied to "9" is `(1 9 (3 4)) (10 6) 10 6`. The numbers replaced by 9 were those matching how deeply nested they were - for example, "2" in (2 6) because it has 2 enclosing parenthesis. This can be obviously done with computers, but this would involve lots of redundant electron mashing in a physical level. I'm looking for a physical system that implements this operation as effectively as possible. Do you guys have an idea where I can start looking for it? Note: I'm not sure if this question fits here but I don't know where else to ask.


title: Vertex operator for closed string tachyon

text: The problem related to this post, but my question is even more elementary. In p 101 of Polchinski's string theory vol I, it is stated > Using the state-operator mapping, the vertex operator for the closed-string > tachyon is $$V_0 = 2g_c \int d^2 \sigma g^{1/2} e^{ik \cdot X} \rightarrow > g_c \int d^2 z : e^{i k \cdot X}: \tag{3.6.1}$$ I miserably and completely don't get it. How to derive Eq. (3.6.1)?


title: What will be the effect of placing a light source very close to a photodiode?

text: What will be the effect of placing a photodiode really close to a laser source and what should be the appropriate distance between a light source and photodiode to get maximum output current?


title: Plotting Dividing Streamline

text: I'm trying to plot just the dividing streamline of a flow on Maple. I have the complex potential $$\Omega(z)=Uz+\frac{m}{2\pi}ln(z)$$ with Stream function $$\psi(r,\theta)=Ur\sin\theta + \frac{m\theta}{2\pi}$$ I calculated the stagnation points to occur at $$\Omega'(z)=U+\frac{m}{2\pi z}=0$$ Hence occur at $$z=-\frac{m}{2\pi U}$$ I thought to find the dividing streamline, I would set the stream function equal to the stagnation point as this would show the streamline passing through i.e. $$\psi(r,\theta)=Ur\sin\theta + \frac{m\theta}{2\pi} + \frac{m}{2\pi U}=0$$ but I can't seem to get the curve I expect from Maple. Any help greatly appreciated!


title: Uncertainty principle

text: Think of a particle known to be trapped in a box of size $\Delta x$ and cooled down to near absolute zero. I know that attempting to measure the momentum of this particle repeatedly will give a random range of answers. So if I had to write down a formula that gives an estimate of the spread in the possible results of the measurement of momentum of the particle, would it just be the uncertainty principle? $\Delta x \Delta p \geq \frac{\hbar}{2}$? Then considering an electron, what size $\Delta x$ would result in this spread of results being so large that a positron-electron pair could be formed out of the kinetic energy of the original electron?


title: How do we show that no hidden variable theories can replace QM?

text: I've always hit two big stumbling blocks in conceiving of the proof or disproof of hidden variable theories as being even valid idea, let alone an answerable question... I feel I must be misunderstanding some very fundamental things.   1. Quantum mechanics is deterministic, ignoring the bit where we take our complex number and fudge it into a probability.   2. We use computers to make calculations to provide the predictions of quantum mechanics - how is this not itself a hidden variable theory? From what I understand the famous Bell theorem and work around it doesn't disprove hidden variable theories, just one specific flavour of them, and even then I am not convinced. I feel like I must be missing something again, because this result seems to me in no way profound... although it certainly fits into the picture of the EPR 'paradox' and is a good demonstration of the validity of QM. I guess the crux of my problem is that this 'area' really addresses wave function collapse and the problems it causes, but I don't see the need for some collapse mechanism to begin with... again I feel like I am missing something really fundamental. Apologies if this is a bad question. I have had a look around and there are similar questions, but I don't feel that either of my points are addressed...


title: Optical theorem and conservation of particle current

text: The optical theorem $$ \sigma_{tot} = \frac{4\pi}{k} \text{Im}(f(0)) $$ links the total cross section with the imaginary part of the scattering amplitude. My lecture notes say that this is a consequence of the conservation of the particle current. How do I get to this consequence?


title: Group of symmetries of Lagrange's equations

text: Consider the following statements, for a classical system whose configuration space has dimension $d$:   1. Lagrange equations admit a smaller group of "symmetries" (coordinate change under which equations are formally unchanged) than Hamilton's;   2. The 'symplectic diffeomorfism' (=coordinate changes whose jacobian is a symplectic $d$-parametric matrix) Lie group has dimension greater than $\dim G$, $G$ being the (Lie?) group of symmetries of point one. The first is well known to be true. What about the second? There exists such a $G$ (at a first sight it seemed to me to be the whole $Diff(M)$; but if it is so, then 2 is false)? If it is true, can point 2 explain point 1?


title: In the big crunch theory, when the big crunch singularity forms, can the resulting black hole decay through hawking's radiation?

text: I've been pondering about this and I couldn't really find the answer for this. The big crunch theory postulates that the universe will eventually stop expanding and reverse back in on its self into a hot-dense singularity. Now I would assume that when that happens, all known matter would be clumped into that. Now what happens after that? I know that one possibility is that another big bang could occur, giving birth to a new universe. But what if it doesn't? What if it remains a blackhole? Can hawking radiation eventually pull it apart?


title: Is the stress finite at the centre of a spherical continuous charge distribution?

text: At the centre of a spherical continuous charge distribution with no external electric fields, the electric field is zero from symmetry arguments. But does the stress at the centre remain finite?


title: Is antigravity the source of accelerating expansion (dark energy)?

text: Is antigravity the source of accelerating expansion(dark energy)? From the observation of 1998, we found that our universe has been continuing accelerating expansion, and the unknown cause for this accelerating expansion was named dark energy. However, nobody is sure whether dark energy truly originates from antigravity, for other several reasons as follows.   1. No antigravity has been observed in laboratories or around the earth, thus far.   2. Contrary to that the force coming from dark energy is $F = + kr$ shaped as a ${\vec F_\Lambda } =\frac{1}{3}\Lambda m{c^2}r\hat r$ shape, antigravity is $F = + \frac{k}{{{r^2}}}$ shaped.   3. As dark energy is an unknown effect itself, there is a possibility that other unknown force different from existing ones exists. Since we still have no idea about the source of dark energy, it's been hard to call dark energy "antigravity", even though it was possible to call it "anti- gravitational effect", in the way that its effect is repulsive. **A. Gravitational potential energy, when antigravity exists.** We are aware of what gravitational self-energy (gravitational binding energy) as the sum of gravitational potential energy is displayed as follows, when matters show a three-dimensional spherical distribution. ${U_S} = - \frac{3}{5}\frac{{G{M^2}}}{r}$ ( r:radius, M: the mass of the sphere ) http://en.wikipedia.org/wiki/Gravitational_binding_energy Because we are planning to apply this to cosmology, **Assumption** : For simple modeling, we will suppose that antigravity source has a uniform distribution on a cosmological scale of a level of cluster of galaxies. When gravitational self-energy by ordinary matters is as below in our universe, ${U_M} = - \frac{3}{5}\frac{{G{M^2}}}{r}$ Because we don't know how big gravitational potential energy by antigravity is, let's introduce and indicate a constant ${k_h}$ which is easy for comparison as below, for a simple comparison. ${U_{DE}} = {k_h}\frac{{G{M^2}}}{r}$ **B. Force generated by positive gravitational potential energy.** $\vec F = - \nabla {U_{DE}} = -\frac{{\partial {U_{DE}}}}{{\partial r}}\hat r = - \mathop {\lim}\limits_{\Delta r \to 0} \frac{{{U_{DE}}(r + \Delta r) - {U_{DE}}(r)}}{{\Delta r}}\hat r$ ${U_{DE}(r)} = {k_h}\frac{{G{M^2}}}{r} = {k_h}\frac{{G{{(\frac{{4\pi }}{3}{r^3}{\rho _r})}^2}}}{r} ={k_h}G{(\frac{{4\pi }}{3})^2}{\rho _r}^2{r^5}$ ${U_{DE}}(r + \Delta r) = {k_h}G{(\frac{{4\pi }}{3})^2}{\rho _{r + \Delta r}}^2{(r + \Delta r)^5}$ When considering the law of conservation of mass-energy, ${\rho _r}{r^3} = {\rho _{r + \Delta r}}{(r + \Delta r)^3}$ ${\rho _{r + \Delta r}} = {\rho_r}{(\frac{r}{{r + \Delta r}})^3} = {\rho _r}(1 - 3\frac{{\Delta r}}{r} + 6{(\frac{{\Delta r}}{r})^2}...)$ ${\rho _{r + \Delta r}}^2 = {\rho_r}^2(1 - 6\frac{{\Delta r}}{r} + 21{(\frac{{\Delta r}}{r})^2}...)$ ${(r + \Delta r)^5} = {r^5}{(1 + \frac{{\Delta r}}{r})^5} = {r^5}(1 + 5\frac{{\Delta r}}{r} + 10{(\frac{{\Delta r}}{r})^2} + \cdots )$ $F = - \mathop {\lim }\limits_{\Delta r \to 0} \frac{{{k_h}G{{(\frac{{4\pi }}{3})}^2}[{\rho _{r + \Delta r}}{}^2{{(r + \Delta r)}^5} - \rho _r^2{r^5}]}}{{\Delta r}}$ $F \approx - \mathop {\lim }\limits_{\Delta r \to 0} \frac{{{k_h}G{{(\frac{{4\pi }}{3})}^2}{\rho _r}^2{r^5}[(1 - 6\frac{{\Delta r}}{r} + 21{{(\frac{{\Delta r}}{r})}^2})(1 + 5\frac{{\Delta r}}{r} + 10{{(\frac{{\Delta r}}{r})}^2}) - 1]}}{{\Delta r}}$ $F \approx - \mathop {\lim }\limits_{\Delta r \to 0} \frac{{{k_h}G{{(\frac{{4\pi }}{3})}^2}{\rho _r}^2{r^5}[(1 + (5 -6)\frac{{\Delta r}}{r} + (10 - 30 + 21){{(\frac{{\Delta r}}{r})}^2}) - 1]}}{{\Delta r}}$ $F \approx - \mathop {\lim}\limits_{\Delta r \to 0} {k_h}G{(\frac{{4\pi }}{3})^2}{\rho _r}^2{r^5}[ -\frac{1}{r} + (\frac{{\Delta r}}{{{r^2}}})]$ $F \approx + {k_h}G{(\frac{{4\pi}}{3})^2}{\rho _r}^2{r^5}(\frac{1}{r})$ use to $\frac{{4\pi }}{3}{r^3}{\rho _r} = M$ Therefore, the force by antigravity source which uniformly distributes $\vec F = + (\frac{{4\pi G}}{3}){k_h(t)}M{\rho _r}r\hat r$ As a $\vec F = + k\hat r$ shape, this force is repulsive force, and is proportional to r like dark energy. If we assume that this force is the same as the existing force related to dark energy, $(\frac{{4\pi G}}{3}){k_h (t)}M{\rho _r}r = \frac{1}{3}\Lambda M{c^2}r$ $\Lambda = \frac{{4\pi G{k_h (t)}{\rho_r}}}{{{c^2}}}$ Here, the total mass, M was used, as the force by gravitational potential energy affects all particles in the three-dimensional sphere. Then, let's figure out constant $k_h$ from the current observation results, and verify whether $\Lambda $ calculated by us is a right value. Not mass-energy, we are measuring a gravitational effect from the observation of the universe, and supposing the existence of mass-energy corresponding to the gravitational effect. The ratio of magnitude of gravitational effects of the present dark energy and matters can be yielded as below. $\frac{{DarkEnergy}}{{Matter}} \approx \frac{{72.1}}{{4.6}} = 15.67$ ${k_h} = 15.67 \times \frac{3}{5} = 9.40$ $\Lambda = \frac{{4\pi G{k_h}{\rho _r}}}{{{c^2}}} =\frac{{4 \times 3.14 \times (6.67 \times {{10}^{ - 10}}{m^3}k{g^{ - 1}}{s^{ -2}}) \times {k_h} \times (4.17 \times {{10}^{ - 28}}kg{m^{ - 3}})}}{{9 \times{{10}^{16}}{m^2}{s^{ - 2}}}}$ $\Lambda = \frac{{4\pi G{k_h}{\rho_r}}}{{{c^2}}} = 3.64 \times {10^{ - 52}}[\frac{1}{{{m^2}}}]$ This value is in accord with the dimension of cosmological constant that is being inferred from the existing observation results, and is similar with the prediction, too wiki/Cosmological_constant > Thus, the current standard model of cosmology, the Lambda-CDM model, > includes the cosmological constant, which is measured to be on **the order > of 10^−52 m^−2** , in metric units. **Anyways, we can see that the force generated from gravitational potential energy by antigravity has the same shape as the force by dark energy, and that it is possible to accurately explain its magnitude and repulsive effect.** Moreover, we figured out the secondary term to verify whether this model would be right, The force generated from gravitational potential energy by antigravity can be indicated like $F = (\frac{{4\pi G}}{3}){k_h(t)}M{\rho_r}r = \frac{1}{3}\Lambda(t) M{c^2}r$ Since the previous analysis of dark energy was proportional to radial distance r * * * 1) We can consider a general shape, $U = k{r^n}$ (n is real number) as a cause for dark energy, and thus there is a high possibility that it is no accident that the above evidence is valid. 2) We can answer the CCC (Cosmological Constant Coincidence) problem of "Why does dark energy have the similar scale with matters?". It is because it has the same gravitational effect as them. 3) While the existing cosmological constant or vacuum energy is a concept not to conserve energy, gravitational potential energy is conserved. **Is antigravity the source of accelerating expansion(dark energy)? What do you think of that?**


title: Hypersingular Boundary Operator in Physics

text: This has been a question I've been asking myself for quite some time now. _Is there a physical Interpretation of the Hypersingular Boundary Operator?_ First, let me give some motivation why I think there could be one. There is a rather nice physicial interpretation of the Single and Double Layer potential (found here: Physical Interpretation of Single and Double Layer Potentials). To give a short summary of the Article:   * We can think of the Single Layer Potential as a potential induced by a distribution of charges on the Boundary.    * And the Double Layer Potential of two parallel distributions (as in the single layer case) of opposite sign. As the Hypersingular Operator arises from the Double Layer, I would think that it would have an analog interpretation. The Hypersingular Operator $W$ is (most commonly) defined as: $W \varphi (x) := -\partial_{n_x} K \varphi(x)$ for some $x\in\Gamma$, where $\partial_{n_x}$ is the normal derivative at $x$ and $K$ denotes the double layer boundary integral operator: $K\varphi(x) := -\frac{1}{4\pi} \int_\Gamma \varphi(y)\partial_{n_y} \frac{1}{\vert x-y\vert} ds_y$ I was wondering, is there some physical, intuitiv or geometric way of thinking about this (or perhaps a paper that could help me gain some intuition)? Or is it merely an Operator meant to "tidy" things up a bit?


title: Latent heat vs temperature of phase transitions?

text: Is the latent heat associated with phase transitions correlated with the temperature at which they occur? The latent heat is related to the difference in energy between the two phases, and the temperature of the phase transition occurs at the point where the difference in energy between the two phases is comparable to thermal fluctuations. What factors would lead to departures from a linear relationship between the two, e.g. in different materials or different phase transitions in the same material? Or is there an error in my assumptions?


title: Energy required to remove both electrons

text: The question is: **Q.** An energy of $24.6$eV is required to remove one of the electrons from a neutral Helium atom. The energy(in eV) required to remove both the electrons from a neutral Helium atom is: $a.$ 38.2 $b.$ 49.2 $c.$ 51.8 $d.$ 79.0 **My try:** Since after removing an electron the Helium atom becomes a single electron atom, Bohr's Model can be applied. The energy of the single electron is hence given by $-13.6\frac {z^{2}}{n^{2}}$ (where z is atomic no. and n is the no. of the shell in which the electron resides). Thus the energy comes out to be $-13.6\frac {4}{1}$, which is $-54.4$. Thus the total energy required to remove both the electrons is $24.6+54.4=79.0eV$, which should be option $d.$. But the answer is $a.$. Did I go wrong somewhere? Please correct..


title: QED coupling constant at one loop

text: On page 257 in Peskin's QFT book a qualitative sketch of the QED coupling is given (see the picture below). Why should I expect such a behavior from QED? The QED beta function is $$\beta_{qed}=\mu\frac{dg}{d\mu}=\frac{g^{3}}{12\pi^{2}}$$ So why the fixed point is not zero? Is there a need to go beyond one loop here? Is this figure enough to determine that QED has a bound state of electrons or photons in high enough energies? ![](http://i.stack.imgur.com/0XsF6.png)


title: How to find SUSY with near-degenerate masses?

text: In SUSY models, you can have the case that sparticles and their decay products have near-degenerate masses. For example $$ m(\tilde \chi^\pm_1) - m(\tilde \chi^0_1) < 1\,\mathrm{GeV}$$ Then in the leptonic decay mode $$ \tilde \chi^\pm_1 \rightarrow \tilde \chi^0_1 + \bar\nu + e^-$$ you'd have the electrons basically produced at rest, or their momentum will be at least well below what you can comfortably detect at a hadron collider. How would you detect SUSY in such a scenario? (Assume that you can't just search for other SUSY particles or decay chains, since you are either doing a model-independent search and don't know how heavy gluinos etc. are, or your other particles are out of range, or also degenerate in masses. Nature can be nasty.)   * You certainly can't just look for a drop in total cross section (disappearing events), since the SUSY cross sections are way too low.   * I was wondering if you could use associated production to find these kind of decays, for example if you produce a Z along with your SUSY particles, you'd see a boosted Z decay balanced by nothing to the other side. Would that work?   * I heard these scenarios would be easier to study with the ILC. Is that just because of the cleaner events, and that you'd be able to see those displaced decays easier?


title: Crash course how cosmologists develop mathematical model for the Big Bang theory

text: First of all, probably it might be useful to introduce me. I have sufficiently good enough mathematics and physics knowledge but only in bachelor level in engineering course. I am extremely interested in cosmology and right now I cannot wait to know how the cosmologists develop mathematical model to formulate the Big Bang theory chronologically from the earliest stage up to the conclusion that the space- time is expanding. The explanation should not be too detailed but please keep the mathematical aspects intact by providing me with the main, basic formulae. Ten paragraphs with 5 sentences each might be more than enough. Hopefuly I can have a good guidance to start learning cosmology from the given answer.


title: Why mountain roads are winded up rather than keeping them straight?

text: In my opinion, to prevent the line passing from the center of gravity of a body (e.g bike or car) trying to climb the mountain or hill to fall outside the base of support so to maintain stable equilibrium and balance. This prevents them from falling down the hill. Is my answer right?


title: Given partial derivatives find the state function

text: I have to find the state function of a gas (which under very low pressures behaves as an ideal gas). So, first I tried writing it as part of an equation $ dV = \dfrac{\partial V}{\partial T}\ dT + \dfrac{\partial V}{\partial p}\ dp $ and then checking if the "switched" derivatives will be equal. And then I tried to find an integrating factor as a function of $p$ and then $T$. The result in both cases was overly complicated which suggests that it is not the correct answer. Could you please explain to me how to solve it? And when is it alright to change $V, p, T$ using the ideal gas equation to make calculations easier? Moreover, I have a conceptual difficulty - what would the integrating factor times $dV$ represent? I only used integrating factor to prove that $1/T$ was the integrating factor of heat (which gives entropy). ![the partial derivatives](http://i.stack.imgur.com/YWeR4.jpg)


title: Can we have a physical interpretation for a time independent Schrodinger equation of this form?

text: I am interested in a time independent Schrodinger equation of this form. $$F*\psi - \frac{\hbar^2}{2m} \frac{\partial^2{\psi}}{\partial{x^2}} = E\psi$$ Here the product $V\psi$ is replaced by the convolution $F*\psi$. What I want to know is that is there any such $F$ where we can assign some kind of an intuitive physical meaning to it? It may be field or quantum field or whatever exotic thing. The product replaced by convolution enables a lot of mathematically beautiful things to happen, but to begin with I strongly need a physical interpretation. PS : My approach is to take a mathematically beautiful/appealing objects/equations and try to make sense of them in physical applications.


title: Does gravity exert more "power" when an object is traveling faster?

text: So, this question arose when I was pondering the meaning of horsepower and torque in cars. I thought of the following question: There is a 1 kilogram weight on planet M. Planet M has no atmosphere and has a gravitational constant of 1 meter per second per second. The weight is raised to a height of 2 meters and dropped. The weight will fall through the first meter in 1 second and the second meter in 0.4 seconds (rounding a bit). So, in terms of work, gravity does 1 Joule of work on the weight over each 1 meter interval. However, in terms of power, gravity exerts 1 watt of power over the first interval and 2.5 watts over the second interval. Why does it seem that gravity is magically more powerful when the object is travelling faster? The same question applies to a rocket ship in space. Assuming infinite fuel, the rocket will exert a constant force no matter the speed and burn fuel at the same rate, but from a constant reference frame, from where the rocket launched, it will appear that the faster the rocket travels the more energy it expends per second. I think these questions accurately portray the confusion I've had with the concept of power ever since physics 2 in college so many years ago. Thanks for reading.


title: What is Anderson localization? Could someone give an example worked out in detail?

text: What is Anderson localization, for someone with no previous knowledge on the subject? I tried to read Anderson's original paper, but it was too terse for me. I have seen a couple of intuitive explanations, e.g. _50 years of Anderson localization_ on Physics Today. I also read _"Localization of waves"_ by van Tiggelen, but it is more of a review with a lot of formulas and no deductions. What I need is an introduction to the subject through **one** example of Anderson localization, worked out in detail. You can skim over the tedious math. If you point out what needs to be done, I'll work it out (and if I get stuck I'll ask!). (Related Phys.SE question: Introduction to Anderson localization)


title: Rotational velocity of face-on spiral galaxies using spectroscopy

text: I am doing my first steps in spectroscopy (IFS actually) and how we can learn more about galaxies by using it. I came up with a simple question which, unfortunately, I can not answer: How can we measure the rotational velocity of a spiral galaxy given that the galaxy is perfectly face-on? I understand how to do so if the galaxy was tilted or edge-on: By measuring the Doppler shift of the spectral lines for each spatial position. One side will be red, the other blue, and the rest somewhere in between. But what about if the galaxy is perfectly face-on? The Doppler shift will be zero right? Most of the resources, papers etc I find online are about tilted galaxies.


title: Magnetic Field in the presence of a conductor

text: I am studying for my quals and came across an old question that reads like the following: > There are two regions in space separated by an infinite conducting plane. > Region 1 has a magnetic dipole of moment $\vec{\mu}$ located a distance $d$ > from the plane. What is the magnetic field $\vec{B}$ everywhere in region 1? I know that for a perfect conductor (superconductor), the normal component of $\vec{B}$ is zero–although I don't exactly know why–but I don't know if that is the case when the problem involves a "conductor" (not explicitly a perfect conductor). TL;DR: Can anybody give me some insight about the magnetic boundary conditions of a stationary magnetic field in the presence of a conductor? Thanks!


title: Friction fire lighting

text: Having watched a few youtube guides on making a fire by friction, namely the spindle and fireboard method, I've heard many of the instructors talk about how the shape of the spindle at its ends should be point-like at the top and blunt/round at the bottom. They then go attribute this to the idea that one would want as little friction at the top and most friction at the bottom. Whilst this seems to be intuitively correct, my very basic knowledge of physics tells me that idealised friction is independent of apparent surface area and just proportional to the normal force (also proportional to actual contact area?). I tried thinking about this in terms of energy but still couldn't get my head around it. I also find it difficult to believe that the consensus of many, especially those with years of experience find this to be the case. It seems unlikely,though not impossible, that they have all come to wrong conclusion. So, my question is this: Is a blunt end for a spindle better than a sharp point, or is the shape irrelevant and if so how might you reconcile these 2 ideas (are they all wrong?)? Also if you have any empirical evidence to back this, or links to, that would be greatly appreciated.


title: What happens to the index of refraction of a lens if placed in water?

text: What happens to the index of refraction and focal length of a lens that is initially in air that is then placed in water?


title: Two springs and a mass between length L

text: I am trying to solve the problem that is depicted below; ![two springs and a mass](http://i.stack.imgur.com/IFHpe.png) I am writing the equations with state variables as $x_2$ and $v_2$within the matrix form as; $$\begin{align*}\dot{x_2} &= v_2\\\ \Sigma F_2 &= m_2a_2 \\\ \dot{v_2} &= -\frac{k_1}{m_2}x_1-\frac{k_3}{m_2}x_3\end{align*}$$ from this point how can I construct my transition matrix for; $$\begin{bmatrix} \dot{x_2}\\\ \dot{v_2}\end{bmatrix} = A\cdot\begin{bmatrix} x_2\\\ v_2\end{bmatrix}$$ edit: Only the block between the springs has mass. $x$ is denoted as displacement, so $x_1$ denotes the displacement of spring 1 by $x$.


title: Why do electrons in an atom 'fall' back to the ground state?

text: Why, after absorbing a photon does an atom's electron 'fall' back to its ground state (what causes it to immediately lose its absorbed energy)?


title: The curvature of the space of commuting hermitian matrices

text: This is a question that I asked in the mathematics section, but I believe it may get more attention here. I am working on a project dedicated to the quantisation of commuting matrix models. In the appropriate formalism this problem is reduced to a quantisation in a curved space -- the space of commuting matrices. The general prescription for quantisation in curved space involves ambiguity of the Hamiltonian operator proportional to the scalar curvature of the curved space - hence my question. A set of $p$ commuting $n\times n$ hermitian matrices $X^{\mu}$ for $\mu=1,\dots p$, is parametrised in terms of a set of $p$ diagonal matrices $\Lambda^{\mu}$ and an unitary matrix $U$ via: $X^{\mu}=U\,\Lambda^{\mu}\,U^{\dagger}~~$ for $~\mu=1\dots p$, clearly not all degrees of U contribute to this parametrisation, for example a reparametrisation $U'= D\,U$, where $D$ is a diagonal unitary matrix would result in the same set of commuting matrices. In other words only the elements of the quotient space $U(n)\,/\,U(1)^n$, which is the maximal flag manifold $F_n$, contribute to the parametrisation. The metric on the resulting curved manifold can be calculated as a pull-back of the metric on the space of hermitian matrices defined as: $ds_{X}^2=Tr\,\left( dX^{\mu}dX^{\mu}\right) $ , Using that $U^{\dagger}d X^{\mu} U=d\Lambda^{\mu}+[\theta,\Lambda^{\mu}]~~$, where $\theta$ is the Maurer-Cartan form $\theta=U^{\dagger}dU$, one can write the induced metric as: $ds^2=\sum\limits_{i=1}^n(d\vec\lambda_i)^2+2\sum\limits_{i<j}(\vec\lambda_i-\vec\lambda_j)^2\theta_{ij}\bar{\theta}_{ij}~~$, where $~~\vec \lambda_i =(\Lambda^1_{ii},\dots,\Lambda^p_{ii})$ . Now I need the Riemann curvature of the above metric. It seems that it is convenient to work in tetrad formalism, using tetrads $E_{ij}=|\vec\lambda_i-\vec\lambda_j|\,\theta_{ij}$, for $i<j$. The problem is that $d E_{ij}$ will now contain a term proportional to $(\theta_{ii}-\theta_{jj})\wedge\theta_{ij}$ and since $\theta_{ii}$ are not part of the basis the spin curvature cannot be written easily without using the explicit parametrisation of $U(n)$. Intuitively, I know that the scalar curvature should depend only on the lambdas ($\vec\lambda_i$), and I have verified that explicitly for $SU(2)$ and $SU(3)$, however a general result seems to require some invariant way to express the pullback of the term $(\theta_{ii}-\theta_{jj})\wedge\theta_{ij}$ on the submanifold spanned by the off diagonal $\theta$'s. I was wondering if mathematicians have explored the manifold of commuting hermitian matrices. In fact even a reference to a convenient parametrisation of the maximal flag manifold $F_n$ would greatly help me in deriving a general expression for the scalar curvature. Any comments/suggestions are welcomed.


title: Find the tension and angle from a vertical of a rope hooked up to an object

text: Below is the homework problem I am working on: > A 18.3-kg object hangs in equilibrium at the end of a rope (taken as > massless) while a wind pushes the object with a 63.9-N horizontal force. > Find the tension in the rope and the rope's angle from the vertical. The > acceleration due to gravity is $9.81 \space m/s^2$. I am having a hard time correctly defining the system of two equations to solve for tension and angle. I came up with $$T\cos{(\theta)} -F_H=0 \\\T\sin{(\theta)}-(-F_g)=0$$ where $F_g$ is the force due to gravity and $F_H$ is the horizontal force. I use a free body diagram where $F_H$ is on the x-axis and $F_g$ is on the y-axis. Apparently, my setup is incorrect. Could you put me on the right track. Let me know if more clarification is needed.


title: Macroscopic chromodynamics

text: Lately I've been reading about gamma ray lasing phenomena, and I've been wondering about the applications of this. More concretely, the above fantastic question led me to wonder if we could somehow collimate the polarization of coherent gamma rays, and radiate hadrons with some resonant chromodynamic frequency (probably very high, but possibly attainable?) that would stimulate excited hadronic states with non-zero color fields of high multipolar rank (quadrupolar or octopular non-zero moments), that at low-energy would thermalize to a high-order aligned macroscopic field?


title: Stress-energy-momentum tensor

text: In Wald's General Relativity, he writes on pg 61 > _For an observer with 4-velocity $v^a$, the component $T_{ab}v^a v^b$ is > interpreted as the energy density, i.e. the mass-energy per unit volume, as > measured by the observer._ However, if we use this with the stress tensor for dust $$T_{ab}=\rho_0 u_a u_b,$$ we get $$T_{ab}v^a v^b= \rho_0 u_a u_b v^a v^b = (\rho_0 u_a v^a) (\rho_0 u_b v^b)/\rho_0 = U^2/ \rho_0$$ where I assumed $U=- \rho_0 u_b v^b$ is the energy density (since $E= - m_0 u_a v^a $). What am I missing here?


title: Is there a thought experiment which brings to light the contradiction between General Relativity and Quantum Mechanics?

text: I've been told that GR and QM are not compatible, is there an intuitive reason/thought experiment which demonstrates the issue? (Or one of the issues?)


title: Measuring the solid air surface tension

text: For hydrophilic and hydrophobic materials, ![enter image description here](http://i.stack.imgur.com/Y883N.png) $Y_{SG}$= Interfacial tension between the solid and gas $Y_{SL}$ = Interfacial tension between the solid and liquid $Y_{LG}$ = Interfacial tension between the liquid and gas If you wanted to measure the effects of putting a layer of hydrophobic material on a glass sheet, how would you do it? I know you could first put a drop of water on the sheet and check the angle and then compare it to when you added the hydrophobic material on the surface. But how would you find the surface tension the water droplet has on the hydrophobic material? (By that I am asking what effect does the hydrophobic material have on the surface tension.) I know $Y_{LG}$ would be the same as before, and it would be interfacial tension between water and air. But what would $Y_{SL}$ and $Y_{SG}$ be? If I knew one of those I could find $Y_{SL}$ which would be the interfacial tension between the hydrophobic material and the water droplet. I'm basically trying to find a value that quantifies the huge difference in surface tension between the surrounding water in a hydrophilic material and then putting a hydrophobic material around it which keeps the water inside.


title: Trace of Spin Products Using Rotation operators

text: So I am working on this problem involving the trace of spin matrices. I am trying to solve for $Tr(S_iS_j S_kS_l)$ using rotation operators. I know how to go about solving for $Tr(S_iS_jS_k)$. It is as follows: $$Tr(S_iS_jS_k)=Tr(US_iU^\dagger US_jU^\dagger US_kU^\dagger)$$ This is performed using the fact that the rotation operator is unitary, and the cyclic property of trace. If I choose a rotation around k, such that $i\rightarrow j$ and $j\rightarrow -i$ $$Tr(S_iS_jS_k)=-Tr(S_jS_iS_k)$$ If I take rotation around i such that $k\rightarrow-k$ $$Tr(S_iS_iS_k)=-Tr(S_iS_iS_k)$$ I can then conclude that $$Tr(S_iS_jS_k)=b\epsilon_{ijk}$$ Which, when plugging in the fact that $S^2=\hbar^2s(s+1)$ I get $$Tr(S_iS_jS_k)=\frac16i\hbar^3s(s+1)(2s+1)\epsilon_{ijk}$$ Based on this, I figure that $$Tr(S_iS_jS_kS_l)=A\epsilon_{ijkl}$$ But I am not sure how I could do this out. I am having a hard time visualizing rotations in 4 dimensions. Additionally, I am told that to solve it, I should have three constants, deltas, and levi-civitas. I can then contract it with $\delta_{ij}$ and $\epsilon_{ijk}$ to solve for the constant. Any help would be greatly appreciated!


title: Is there a strong force analog to magnetic fields?

text: In special relativity, magnetism can be re-interpreted as an aspect of how electric charges interact when viewed from different inertial frames. Color charge is more complex than electric charge, but also has deep similarities to it. This leads to three questions:   1. _Is it mathematically possible to re-interpret standard chromodynamics in terms of frame-dependent combinations of “chromostatic” and “chromomagnetic” interactions?_ The obvious analogy would be that moving color charges would create chromomagnetic fields that could in turn alter the paths of other nearby moving color charges. (Note: My just-created word “chromomagnetic” is analogical only, since the component of chromodynamics that it describes would be no more related to ordinary magnetism than color charge is to electric charge.)   2. _If such re-interpretation is possible, has there been prior work on this idea?_ That is, has the idea of a chromomagnetic analog to the magnetic fields proposed or assessed? If so, does anyone know the correct keywords for searching for such works, or have any specific references?   3. _If such a re-interpretation is possible, is there any real advantage to it?_ That is, even if chromodynamics _can_ be split into two frame-dependent components, that does mean it should be. It could be an idea that is plausible in terms of the some mathematical framework, but has no real conceptual or modeling merit. Conversely, if meaningful cases exist in which a sustained chromomagnetic field could be generated, the concept of chromomagnetics might prove useful for the same reason that we still have a concept of independent magnetic fields, more than a century after such fields were shown fundamentally to be only another aspect of moving electrical charges. **2012-09-09 Comments on Answer by David Bar Moshe** I am awarding the answer to David Bar Moshe specifically for the excellent reference he provided to a popular-style 1997 Edward Witten paper on the issue of quark confinement. In particular, on page 3 of that paper in the bottom left corner Witten says this: > "As a non-Abelian gauge theory, QCD has fields rather similar to ordinary > electric and magnetic fields but obeying a nonlinear version of Maxwell’s > equations. Quarks are particles that carry the QCD analog of electric > charge, and are confined in vacuum just as ordinary magnetic charges would > be in a superconductor. This analogy led in the 1970s to the idea that the > QCD vacuum is to a superconductor as electricity is to magnetism. This is an > important idea, but developing it concretely was out of reach in that > period." This answers all three of my questions: 1. = Yes, QCD analogies to EM were explored decades ago (!), back in the 1970s, albeit incompletely due to lack of sufficient mathematical support at that time (and possibly still today, according to David Bar Moshe's comments); 2. = Yes, there was prior work and continuing work, to which David Bar Moshe has provided some references; and 3. = Yes, the interpretation does appear to have have value, since it enables a useful analogy between monopole magnetic fields in a superconductor and QCD "magnetic-like" color force components that in a vacuum produce a similar effect. So, David, thanks! For anyone else reading this, I would note that I'm pretty sure we are still talking here about an _analogy_ of magnetic-like components within the color forces and the separate but mathematically similar description of true magnetic fields between (hypothetical) monopoles. Dave, if I am mistaken about that -- if you are suggesting that there is more than just an analogy going on between the component of QCD that produces confinement and the monopoles with conventional magnetic fields -- then you may want to add a note to that effect, since I'm still assuming (as Witten seemed to do) that this is an analogy or mathematical similarity only, versus an actual link between QCD and magnetic fields. I may add more comments after reading more from your other references. I appreciate your observations about unknown areas, also. So again: Interesting answer, and one that for me had a very unexpected outcome. Since I was only basing my question on an analogy to relativistic electromagnetics, I never would have guessed that it was used decades ago for something as important as quark confinement.


title: Electromagnetic fields and human behaviour

text: To what extent does electromagnetic fields and/or radiation from space have influence on human behaviour and/or physiology?


title: Lorentz force equation from relativistic Lagrangian

text: The relativistic Lagrangian is given by $$L = - m_0 c^2 \sqrt{1 - \frac{u^2}{c^2}} + \frac{q}{c} (\vec u \cdot \vec A) - q \Phi $$ I need to derive, $\displaystyle \frac{d\vec p}{dt} = q \left( \vec E + \frac 1 c (\vec u \times \vec B)\right)$. Everything (in my note) is fine until there is one expression which I don't understand. It writes, $$ \frac 1 c \nabla (\vec u \cdot \vec A ) = \nabla \Phi $$ to make $\displaystyle \vec E = - \nabla \Phi - \frac 1 c \frac{\partial \vec A}{\partial t}$. Why would dot product of $\vec u$ and $\vec A$ be $c$ times the scalar potential? Here is the derivation as requested: > The equation of motion is given by $$\frac{d}{dt} \left( \frac{\partial > L}{\partial u_i} \right ) - \frac{\partial L}{\partial x_i} = 0$$ Since the > relativistic Lagrangian is transitionally invariant, there is no dependence > on coordinates so the last term is zero. taking derivative w.r.t $u_i$ > $$\frac{d}{dt} \left( \frac{m_0 u_i}{\sqrt{1 - \frac{u^2}{c^2}}} + > \frac{q}{c} A_i \right ) = 0 $$ Adding $i$'s, we get $$ \frac{d}{dt} \left( > \gamma m_0 \vec u + \frac{q}{c} \vec A \right ) = 0$$ $$\implies \frac{d > \vec p}{dt} + \frac{q}{c} \frac{d\vec A }{dt} = 0$$ \begin{align*} \implies > \frac{d \vec p}{dt} &= - \frac{q}{c} \left( \frac{\partial \vec A }{\partial > t} + (\vec u \cdot \nabla)\vec A\right )\\\ &= - \frac{q}{c} \left( > \frac{\partial \vec A }{\partial t} + \nabla (\color{Red}{\vec u \cdot \vec > A})- \vec u \times \left( \nabla \times \vec A \right )\right )\\\ &= - > \frac{q}{c} \left( \frac{\partial \vec A }{\partial t}+ \nabla > \color{Red}{(c\Phi)} - \vec u \times \vec B \right )\\\ &= q \left( -\nabla > \Phi - \frac 1 c \frac{\partial \vec A }{\partial t} + \frac 1 c \vec (u > \times \vec B) \right)\\\ &= q\left ( \vec E + \frac 1 c \vec (u \times \vec > B) \right ) \end{align*}


title: Do we still need Newtonian G in General Relativity?

text: I believe we can use Newtonian Physics to make incredibly good predictions about the movement of celestial bodies as long as they are not too fast/massive and there are only two of them (well, we can make predictions for more bodies, but not the general case, right?) And I think the only number we need in order to make predictions, besides the positions/speeds/masses of the bodies, is $G$ (i.e. Newton's gravitational constant), and all the math we need is what we call calculus. But we can make even better predictions if we use General Relativity, and some mathematical objects called tensors, and the speed of light $c$, right? Or do we still need $G$ in GR?


title: Introduction to spinors in physics, and their relation to representations

text: First, I shall say that I am familiar with the intuitive idea that a spinor is like a vector (or tensor) that only transforms "up to a sign" when acted on by the rotation group. I have even rotated a plate on my palm to explain this to my fiancee! I have also looked at spinors as mathematical objects, such as the 2d subspace of complex 3-space such that $X·X = 0$, and feel that I understand this well also. I am confused by spinors in physics. Are they still vectors that are isotropic (inner product with themselves is 0)? In what vector space? Normally states are vectors in infinite dimensional spaces! Every attempt to find literature which pins down specifically what a spinor is (in physical terms) seems to assume that one is already well acquainted with the idea. Take, for example, the Dirac equation. I can see that the solutions are four- component wavefunctions, which then splits into two parts. Is this a spinor? Why? What vector space do these solutions live in? I believe I've heard that the answer has something to do with representation theory, perhaps of the Poincare group? I am also familiar with the basics there, so don't hesitate to explain in terms of representations.


title: Red Giant branch and Asymptotic Giant branch

text: What's the difference between the RGB and the AGB? I can't seem to find an clear distinction anywhere. Thanks.


title: Why is there a difference between additive and subtractive trichromatic color theories?

text: Helmholtz distinguished between additive and subtractive trichromatic color theories. Additive theories concern optical combinations of colored light sources and are usually modelled on RGB while subtractive theories model pigment mixing and are usually modelled on RYB or CMY. What is the physical basis of this distinction?


title: Is there a term for the argument of the sine function outside of geometry?

text: Are there similar terms in other areas for the idea the "angle" conveys in geometry? I find that functions for abstract things such as pressure, electrical currents (nothing geometric there) on AC circuits and are described by the sine function (argument is an angle, therefore a geometric entity). Do we really have that abstract things are necessarily described by geometric entities? Maybe the concept of angle we know is a simply an example of a greater idea (like a a measure of difference between instances of the same thing) applied to geometry or am I tripping?


title: Why are the magnetic moment and the angular moment related?

text: I've always read everywhere that they are related but found nowhere a satisfactory explanation of the cause


title: How far to the 'edge' of the galaxy?

text: Wikipedia lists the average thickness of the milky-way to be about 1,000 LY - but where (roughly) within that is the sun currently? In asking this, I'm fully aware that there's no well-defined edge - a rough number is just fine for my purposes. Also - what direction is the closest edge (i.e. the 'top' or 'bottom' of the disk, not the outer-edge)? E.g. in the direction of Procyon, Tau Ceti, etc.? (I'm asking because I'm working on a bit of science-fiction, with a couple of scientists looking to directly view the other side of the galaxy in a time where FTL propulsion is available)


title: Does a lightning rod prevent lightning strikes?

text: I was always under the impression that a Lightning rod worked to protect a building by being the tallest part of the building and having a low path of resistance to the ground, thus being a good target for lightning to hit, reducing the chances of lightning strikes elsewhere on the building. However when reading an Ars technica article, one comment (from user "malor") said that theory is incorrect, and explained that a lightning rod actually _prevents_ lightning strikes in the first place: > Lightning happens when a really huge negative charge builds up in the > ground, corresponding to a positive charge overhead, and the differential > becomes sufficient to jump the gap. (and, as others are pointing out > repeatedly, air is an excellent insulator, so it takes a whacking huge > voltage differential to make the arc.) > > A lightning rod doesn't exist to provide a spot for the lightning to strike. > Rather, it exists to dissipate the charge so that the strike never happens > at all. This comes from early experiments with the Leyden jar; if a pointed > metal rod was attached to the jar, it wouldn't charge. The electrons are > able to leap off a pointed tip, and into the air, dissipating charge as fast > as it accumulates. The lightning rod does the same thing, on a larger scale; > it spits out electrons into the air like crazy, so that the charge won't > build up sufficiently, and the lightning never hits at all. > > Now, if the charge accumulates faster than the rod can dissipate it, there > can still be a lightning strike, and the rod typically IS the best route to > ground. But everything around the rod is going to take a hell of a jolt > anyway, including, most likely, your electronics. A lightning rod getting > hit means it failed to work adequately; ideally, it should never be hit at > all. How does a lightning rod actually work? Does a lightning rod actually prevent lightning strikes?


title: What are the statistics of three to five bosons?

text: This should be a very easy question. If you look at the bottom of "Identical Particles" in Wikipedia, you see Table 1, which gives you the two particle statistics for bosons, fermions and distinguishable particles. The problem is to extend this table for three, four and five particles, or give an equivalent formula. I think I know what the answer is for fermions and distinguishable particles, but what about bosons? My first guess is it would always be evenly distributed, but the many body limit does not equal the classical result, so that can't be right. Or can it? What is the formula, and the first few rows of the "Pascals triangle for bosons"?


title: Causality and Quantum Field Theory

text: I have a problem with proof of causality in Peskin & Schroeder, _An Introduction to QFT,_ page 28. To avoid confusion I use three vectors notation, rewriting the Eq. (2.53) for $y=0$ as follows: $[\phi(x,t),\phi(0,0)]=\int \frac{d^3p}{(2\pi)^3}\frac{1}{2\sqrt{p^2+m^2}}\left(e^{-i\mathrm{p}.\mathrm{x}-it\sqrt{p^2+m^2}}-e^{i\mathrm{p}.\mathrm{x}+it\sqrt{p^2+m^2}}\right)$ The book goes on about how the integrand being Lorentz invariant makes this integral zero for the x out of the light cone. But I (not being a special relativity expert) want to see it more rigorously: after changing variables $p\to-p$ in the first term, the equation simplifies to: $[\phi(x,t),\phi(0,0)]=\int \frac{d^3p}{(2\pi)^3}\frac{-2i}{2\sqrt{p^2+m^2}}e^{i\mathrm{p}.\mathrm{x}}\sin\left(t\sqrt{p^2+m^2}\right)$ using spherical coordinates: $[\phi(x,t),\phi(0,0)]=\int \frac{dpd\phi d\theta p^2\sin\theta}{(2\pi)^3}\frac{-i}{\sqrt{p^2+m^2}}e^{ipx\cos\theta}\sin\left(t\sqrt{p^2+m^2}\right)\\\ [\phi(x,t),\phi(0,0)]=\int_0^{\infty}\frac{dpp}{(2\pi)^2}\frac{-2i}{x\sqrt{p^2+m^2}}\sin (px)\sin\left(t\sqrt{p^2+m^2}\right)$ again after another change of variables $u=\sqrt{p^2+m^2}$, $[\phi(x,t),\phi(0,0)]=\frac{-2i}{x}\int_m^{\infty}\frac{du}{(2\pi)^2}\sin (x\sqrt{u^2-m^2})\sin\left(tu\right)$ I cannot see how this integral should be zero for $x>t$ !!! Can somebody please explain this to me?


title: Gravitational Redshift around a Schwarzschild Black Hole

text: Let's say that I'm hovering in a rocket at constant spatial coordinates outside a Schwarzschild black hole. I drop a bulb into the black hole, and it emits some light at a distance of $r_e$ from the center, with a wavelength of $\lambda_{e}$ in the rest frame of the bulb. What would the wavelength of the light be when it reaches me, at $r_{obs}$ in terms of the radius at which it is emitted, $r_e$? This is a subquestion from Sean Carroll's _Spacetime and Geomtery_. Earlier in the chapter, Carroll asserts that any stationary observer $(U^i= 0)$ measures the frequency of a photon following a null geodesic $x^{\mu}(\lambda)$ to be $$\omega= -g_{\mu\nu}U^\mu\frac{dx^\nu}{d\lambda}$$ I don't understand where this expression comes from. How does one even conceptualize things like wavelength and frequency of light in terms of general relativistic quantities like $U, g_{\mu\nu}, ds^2$, etc?


title: What does it mean for something to be a ket?

text: Ok so I will provide the following example, which I am choosing at random from Sabio et al(2010): $$\psi(r,\phi)~=~\left[ \begin{array}{c} A_1r\sin(\theta-\phi)\\\ A_2\frac{K}{2}r^3\sin^3(\theta-\phi)\\\ A_2r^2\sin^2(\theta-\phi)\\\ -A_1r\sin(\theta-\phi)\\\ \end{array} \right].$$ Obviously, this is a 4-component vector, but the author calls it a wavefunction. In fact, calling such things wavefunctions is fairly common in my little corner of condensed matter theory, and I'm still unsure whether this is sloppy language, or I am missing something. Perhaps the thing on the LHS should in fact be the ket $|\psi\rangle$ because my understanding of a wavefunction is that it can not be a vector. I.e., it is defined: $$\psi(x)~=~\langle x|\psi\rangle.$$ This should just be a number correct? I.e. at any point (let's say $x=1$ for a 1-dimensional system) that wavefunction should just be a number, not a vector?


title: How strong must a signal be at the edge of the Solar System to penetrate into the Sytem?

text: A sort-of follow-up to Are the Voyager probes still sending us a signal ? Still following on the news report referenced in the above question, this report indicates further magnetic surprises at, or near to, the interface of Sol's family with the rest of the universe. I recall reading there are such things as constructive/destructive interference which serve to amplify/attenuate an EM wave respectively. By this I assume there is a limit on the minimum amount of power required to penetrate a given magnetic field (I know it's possible to operate QRP 1W CW across antipodes!) What is the minimum strength a signal must be at the edge of the Solar System to penetrate the magnetic field/s and be audible on Earth? EDIT: Assuming   1. The discovered magnetic region is of uniform strength, spherical in nature (centred around Sol), and    2. The source magnetic field is in the planetary plane END EDIT


title: Violation of Lorentz invariance (Lagrangian for particle)

text: I'm trying to get the relativistic action (or Lagrangian) for a free particle in the case of violation of Lorenz invariance. Suppose we have the modified dispersion relation: $$ E^{2}=\Omega^{2}(p^{2}) $$ Here $E$ and $p$- energy and momentum of the particle, $\Omega^{2}$ is a function that takes the form $\Omega^{2}(p^{2})=m^{2}c^{4}+p^{2}c^{2}$ if we have Lorentz invariance. In the other word, we have equation $$ \left(v\frac{\partial L}{\partial v}-L\right)^{2}=\Omega^{2}\left(\left[\frac{\partial L}{\partial v}\right]^{2}\right) $$ **We want to define the Lagrangian**. For example, if $E^{2}=m^{2}+(1+\xi)p^2$, we can obtain(overriding $\tilde{v}=v(1+\xi)^{-1/2}$, we present the equation written above to the standard relativistic form, above which we know everything): $$ L=-m\sqrt{1-\frac{v^{2}}{1+\xi}} $$ **I want to find lagrangian and action for the following case** : $$ E^{2}=p^{2}c^{2}+m^{2}c^{4}+\frac{p^{4}}{M^{2}} $$ Here $M\gg m$. _So, we have equation_ : $$ \left(v\frac{\partial L}{\partial v}-L\right)^{2}=\left(\frac{\partial L}{\partial v}\right)^{2}c^{2}+\frac{1}{M^{2}}\left(\frac{\partial L}{\partial v}\right)^{4}+m^{2}c^{4} $$ -I tried to find the solution in the following way: $L(v)=L_{0}+L_{1}v$, where ${{ L_0}}^{2}={{ L_1}}^{2}{c}^{2}+{\dfrac {{{ L_1}}^{4}}{{M} ^{2}}}+{m}^{2}{c}^{4}$, and $|L_0| \ge mc^2$. I set it in the original equation, but it didn't give significant results.   * _Then I've found the following article_ : http://arxiv.org/abs/1209.0464 (arxiv: 1209.0464) Here (pages $6$-$7$) they obtaining the Lagrangian for the case I described above, and they say that in the general case Lagrangian can be defined as (equation $18$) $$ L=-m\sqrt{1-v^{2}}F\left(\frac{1}{\sqrt{1-v^{2}}}\right) $$ I tried to find a solution in this form (by substituting in the equation) but I didn't succeed. **Can you help me to obtain Lagrangian (action) for the relation I wrote? Also it would be great if you gave the usefull references devoted to the topic** (for example, where they obtain Lagrangians, etc)


title: How is it the Voyagers are a few seconds closer to Earth than earlier?

text: The Voyager 2 tweet of March 01, 2013 put it's distance at 14 hrs 04 mins 23 secs of light-travel time from Earth. A more recent (earlier today) tweet says it is 14 hrs 04 mins 22 secs of light-travel time from Earth. An older tweet put it still further out at 14 hrs 04 mins 25 secs of light-travel time. The Voyager 2 tweets on Voyager 1's proximity to Earth too has reduced similarly to 17 hrs 07 mins 07 secs of light-travel time earlier today from 17 hrs 07 mins 11 secs of light-travel time reported on Feb 28 2013 It could quite simply be a typo ... If not a typo then my curiosity is piqued; I was under the impression the Voyagers are outbound from the Solar System now without any major in-system activities now. How is it the Voyagers are closer to Earth than before?


title: Stokes' theorem and alike for fractal surfaces

text: Has anyone ever read an article dealing with the extension of integral theorems to fractal surfaces ?


title: What is the proper time used in relativistic non equilibrium statistical physics?

text: In the literature one often finds covariant relativistic generalizations of classical non equilibrium statistical equations (Boltzmann, Vlasov, Landau, fokker-planck, etc...) but I wonder what is the meaning of the time which is used. As far as I know, one can only write interaction between two relativistic charged particles by doing the computation in the proper space- time frame of one of the particle. With three relativistic charged particles I am already wondering about how to tackle le problem of the proper time, so for N close to a mole...I am lost. Since non equilibrium statistical mechanics is derived from Hamiltonian mechanics, I ca reformulate my question as follow. What is the Hamiltonian of N relativistic interacting charged particles ?


title: Reflectivity of mirror?

text: Is mirror displaying the original image. Is there a constraint for the reflective property of mirror. Does mirror reflect with 100% perfection?


title: Conditions permitting rotation to imaginary time

text: I often see that action is written with a Euclidean metric instead of the original Minkowski metric. My question is basically this : Under what conditions is okay to make a wick rotation? I am thinking of the Wick-rotation in a manner analagous to a change of contour in a contour integral. In the case of contour integral, before making a similar change in contour, I would consider issues like location of poles of the integrand, behavior of the integrand at infinity of the complex plane etc. But in case of Wick rotation, I don't see such things discussed. I would appreciate if some of you could answer or give some inputs to answer the following questions I have: Is the rotation just as trivial as a change of variable : $\tau=\imath t$ ? How do I know that the rotation should be $\tau=\imath t$ and not $\tau=-\imath t$ Can I always make a wick rotation for any Lagrangian? Thanks. EDIT/PARTIAL-ANSWER/GENERAL-UPDATE: http://arxiv.org/pdf/hep-th/9403084v2.pdf sheds some light on the issue. The short section on lack of an analytic continuation tells me that in a general case wick rotation needs to be justified.


title: Difference between pressure and stress tensor

text: What is the difference between hydrostatic pressure and stress tensor?