Sum total distance of electrons on a spherical surface

What is the sum total distance between every possible pair of point charges when there are n point charges on a spherical surface? All point charges can only and are located on the infinitesimal spherical surface. Basically, we're going to have a bunch of points staying as far apart as possible on the surface of a sphere. Is there a general equation for this? And whats the sum total distance between every pair of points? (Both the distances by travelling the shortest distance on the spherical surface and the shortest distance travelling through the interior volume of the sphere. I'm confident that the relationship between those two values require a relatively simple equation. Is there a similar mathematical model/problem which can be used to solve this problem?


Explaining to a five year old - why don't bubbles run like water

My five-year old daughter was asking about astronauts the other day and why they float in space. After me showing her a few bits on the kids section on the NASA web site I started explaining about the planets and how the sun was a ball of gas and you couldn't stand on it. I then had to explain to her what a gas was, using ice, water and steam as examples for the three main states. A few hours later she asked me if the bubbles from the bubble-bath in the bath water were a liquid and if they were why didn't the gravity make them run off her hands like water. That had me stumped. I'm not a scientist but I've been doing my best to try and figure this out and explain it to her but I'm not fully sure, either. Firstly, are bubbles from bubble-bath a liquid or have I made a bad assumption? I thought it might be down to friction but I assume bubble-bath is a detergent and shouldn't encounter much friction. I then thought it might be because the bubbles had a large surface area relative to their weight and would suffer wind resistance as a result. My best guess now is that it's because the bubbles were more viscous than the water. Are any of these right, if not can someone explain it to me in simple terms so I can tell her, please? **UPDATE** Wow, thanks for all the responses! I'm usually on Stackoverflow and I don't think that in two and half years on there I've asked anything that's generated this level of response. Thank you to everyone who took the time to answer or comment - I've read all that's been written here. I explained this to my daughter last night saying that the bubble bath liquid was sticky and as a result would stick to things and slow down gravity's pull. I drew a bubble and explained about the liquid stopping the air in the middle getting out and by standing opposite and holding hands both I explained how we were like the liquid of the bubble squeezing the air in the middle which she understood. I expect that if she's asking questions like this now I'll be on here again soon asking something else. I've certainly learnt a lot! Thanks again.


What is the meaning of $G/cm^2$?

I'll prefix this question by stating that I am not a physicist, I am a programmer. I am working on updating a (very old) program that calculates the performance of a magnet. This whole program is in CGS units and it is required of me to change it to SI units. A particular equation in this program gives the Gauss/square centimeter. I understand this as the gauss going through a 1 square centimeter area. Is there a proper name for the unit of $\frac{G}{cm^2}$?, the closest I can find in CGS terms in a Maxwell unit which is $G \cdot cm^2$ It's less about the name of the unit and more about being able to check whether this empirically derived equation is correct. Unfortunately I cannot post this equation as I do not have the necessary permissons. * * * In the comments it has now been shown that $$\frac{G}{cm^2} = \frac{T}{m^2}$$ So the question now becomes, what does this mean? The field strength in an area?


What are "finely subdivided" substances?

As in the title, what does it mean for a substance to be _finely subdivided_ , or _finely grained_? For example: > It is only in the cases for which the ratio area/volume is very large (for > example, a _finely grained_ substance) that the surface must also be > considered. or: > In the case of a system composed by two homogeneous substances, it will be > possible to express the internal energy of the system as the sum of the > energies of the two substances only if we can neglect the surface energy of > the two substances where they are in contact. The surface energy can > generally be neglected only if the two substances are not very _finely > subdivided_ ; otherwise, it can play an important role.


Modular invariance of CFT

I am looking at the Cardy formula for entropy in CFT, and in the article 'Kerr/CFT correspondence and its Extensions' there is a sentence: > In any unitary and modular invariant CFT, the asymptotic growth of states... I've looked a bit, but couldn't find any simple explanation of the term modular invariant CFT. All I find is that modular invariance is the invariance under the group $SL(2,\mathbb{Z})$. But what does that mean, what's the physical explanation of it and what's it's effect?


Is there an upper frequency limit to ultrasound?

Wikipedia has this diagram of the acoustic frequency spectrum: ![enter image description here](http://i.stack.imgur.com/N8klp.png) Is there an upper limit to the frequencies you can transmit through the air? Are they absorbed more and more at higher frequencies, resulting in shorter travel distances? Are there "windows" of absorption and transmission like there are for radio waves? ![enter image description here](http://i.stack.imgur.com/9x3VJ.jpg) **Update:** This says > An additional problem is created by the strong absorption of ultrasound in > air, at least for frequencies higher than 250 kHz. As a consequence, > ultrasound of e.g. 1 or 2 MHz can propagate in air over a distance of not > more than a few centimeter Also found some references, but I can't access them: http://scholar.google.com/scholar?q=Atmospheric+absorption+of+sound


Compatibility between solutions of explicit Maxwell equations vs. wave equation?

When trying to solve for the allowed propagation frequencies in a cylindrical waveguide, I approached the problem by solving the wave equation for all three components of $\bar{E}$, and subsequently apply boundary conditions - $E_z(R) = E_\phi(R) = 0$ and $\nabla\cdot\bar{E}=0$. This yields the modes: $$E_i=A_ij_m(k'\rho)e^{\pm im\phi}e^{i(k_zz-\omega t)},\ k'^2\equiv\frac{\omega^2n^2}{c^2}-k_z^2, \ i=x,y,z$$ Where the boundary conditions set the degrees of freedom (the discrete values for $k'$, setting the $A_i$'s, etc.) On the other hand, reading through Jackson (3rd ed. chap. 8), solving directly Maxwell's equations, he states that only $E_z$ should satisfy a wave equation, and the other (traverse) components are given by $E_z$'s derivatives. This obviously leads to Bessel derivatives $j'_m(k'\rho)$, as he demonstrates later in that chapter, which are absent from the modes I found above, if we ignore the relation between $j'_m$ and $j_{m\pm1}$. Where does this discrepancy come from? I would imagine that the transverse elements can easily be found by   $$E_\rho=\cos(\phi)E_x + \sin(\phi)E_y, \ E_\phi = -\sin(\phi)E_x+\cos(\phi)E_y$$ If one wishes to avoid solving the wave equation directly in polar coordinates, as then the components are mixed together.


Double rainbows

In my garden, when I'm watering the plants I sometimes see a rainbow or two. How did two rainbows appear? Why can't I see three rainbows then, or how can I see three rainbows?


Using $A = {\lambda}N$ to find when a the amount of a radioactive source becomes constant

The question and mark scheme I will write in bold and my own thoughts in normal sized text. I'm told that: **When a $\bf{_{92}^{235}U} $ nucleus is exposed to free neutrons it can absorb a neutron. The resulting nucleus decays, first to $\bf{_{93}^{239}Np}$ and then to $\bf{_{94}^{239}Pu}$.** I'm then asked a few questions this, one of which I don't understand the answer to. They say that: **The number of $\bf{_{93}^{239}Np}$ nuclei present eventually becomes constant, calculate this constant number of $\bf{_{93}^{239}Np}$ nuclei, given that the half life of $\bf{_{93}^{239}Np} = 2.04 \times 10^{5} s$ and that the number of $\bf{_{93}^{239}Np}$ nuclei produced is at a constant rate of $ \bf{1.80 \times 10^{7} s^{-1}} $** The mark scheme uses the equation: $ \bf{A = \lambda N}$ and rearranges this to say that: $\bf{N=\dfrac{A}{\lambda}}$ **and we also know that** $\bf{\lambda = \dfrac{0.693}{t_\frac{1}{2}}}$ $\bf{\therefore \lambda \approx 3.397 \times 10^{-6}}$ I understand all of this and I understand the maths of the next step, I just don't understand why it gives you they value of the number of nuclei of $_{93}^{239}Np$ when the rate of decay of $_{93}^{239}Np$ equals the rate of formation of $_{93}^{239}Np$. **Substituting this value of lambda into our equation for $\bf{N}$ gives us:** $\bf{N = \dfrac{1.8 \times 10^{7}}{3.397 \times 10^{-6}} \approx 5.3 \times 10^{12}}$ **$\bf{{\therefore}}$ the number of $\bf{_{93}^{239}Np}$ nuclei when this number becomes constant is $5.3 \times 10^{12}$**


Is Joule heating only between charged particles?

The Wikipedia page for Joule heating explains _"It is now known that **Joule heating is caused by** interactions between the moving particles that form the current (usually, but not always, electrons) and the atomic ions that make up the body of the conductor. **Charged particles** in an electric circuit are accelerated by an electric field but give up some of their kinetic energy **each time they collide with an ion**. The increase in the kinetic or vibrational energy of the ions manifests itself as heat and a rise in the temperature of the conductor. Hence energy is transferred from the electrical power supply to the conductor and any materials with which it is in thermal contact."_ However, I wonder why they only talk about ions. Of course, electrons can easier interact with particles, which also have a long range field, but what about the non-charged particles which are also all around? > Is Joule heating only between electrons and ions?


Computer simulation of Schrödinger equation

I am looking for a computer program which simulates the Schrödinger equation (say for a single particle) in two dimensions and for potentials and initial states specified by the user. Typical situations I have in mind are the double slit experiment, harmonic oscillator, Aharonov–Bohm, tunneling effect etc. Unfortunately I was only able to find the one dimensional case on the web. So are there some 2d programs available? PS: I don't think my question is a duplicate of this one. I only ask about a single particle, not about thousands. On the other hand I want freedom in my choice of potential. Also I want a numeric solution of a PDE, while the other question is about (as far as I understand, which is not ver far) a Monte Carlo simulation. Anyway these are completely different requirements.


Bragg diffraction and lattice planes

Crystalline substances show, for certain sharply defined wavelength and incident directions, very sharp peaks of scattered X-ray radiation. From the illustration below we see that we get constructive interference when the path-length difference is a multiple of the wavelength $\lambda$. ![Bragg diffraction](http://i.stack.imgur.com/mxwmj.png) In real crystalline materials we have a large amount of closely packed lattice planes. This large amount accounts for the sharp peaks for certain $\theta$. I do not understand how this follows from the Bragg reflection formula $$ n\lambda = 2d \sin \theta , $$ since $d$ is not constant anymore. I understand the model for two lattice planes as in the illustration. Is it true that $d$ can only take on values of the seperation of lattice planes, so $d$ is defined to be the seperation of points in the reciprocal lattice, or in others words, is $d$ constrained to be the absolute values of some reciprocal lattice vector? How does the Bragg condition account for very sharp peaks when we let $d$ run through all such absolute values?


Weighted average whenever a variance is 0?

So I have data for the number of times a certain event happens. Each column is a different event and each row is one trial. A sample of data would look like \begin{bmatrix} 1& 4& 7& 6& 5\\\ 1& 3& 9& 4& 5\\\ 1& 3& 7& 8& 8\\\ \end{bmatrix} I then collapse this data down into one row, and each number is just the average of the column and has its own variance. I want to take a weighted average of this row and obtain the associated variance as well, but in this example the first number has a variance of 0, and thus the weight would be 1/0. What does one do in a situation like this?


Gamma Ray Bubble at the center of our galaxy seen by Fermi Telescope

How could we measure high energy photons, whithout measuring them ? I can't understand how we can "see" those Gamma Ray Bubbles if they are not reaching here In this graph from Nasa you can see those "bubbles" are not reaching solar system: ![Art about bubles](http://i.stack.imgur.com/PEM2t.jpg) Then how could be measure that Gamma Ray without the Gamma Rays Thanks for any answer!


Why does lambertian surface reflection result in uniform radiance measured from every direction?

I'm reading through the light measurement handbook and page 28 is confusing me. I knew previously that lambertian diffuse reflections distribute the reflection of incoming intensity such that the surface looks equally bright from every direction from which it is measured (only dependent on incoming light direction and surface normal). Specifically, the measured radiance stays constant. However, the page shows that the actual reflected energy (the text says energy, I'm assuming it's talking either about radiant flux or intensity) isn't actually uniformly distributed, but forms essentially a cosine lobe centered about the surface normal: ![figure from page 28](http://i.stack.imgur.com/AaJ0u.png) I'm assuming that the "uniform radiance" results somehow from the measured area in relation to Lambert's cosine law cancelling out this cosine distribution to somehow result in a uniform distribution. How can this be shown mathematically? Also, how does this influence the light received by surfaces receiving this reflected energy? Are they lit such that every surface placed at equal distances to the surface receives the same amount of light, regardless of its orientation w.r.t. the surface normal, or do they essentially receive this cosine distribution?


Tried to do the double slit experiment, failed. Why?

I tried, and failed, to do the double-slit experiment. I thought I had a good experiment setup, but obviously I was wrong. Can anyone offer some insight in what I might have done wrong? Most of this was done using some vague memory of experiments way back in High School, so there might be a better approach. I did search through past questions. This question was the closest to what I am shooting for, but there are significant differences and did not enlighten my particular situation. **Setup:** I used a variety of laser pointers as the light source, both red and green. One laser pointer was home built using a red laser diode (200-250 mW) from a DVD burner going through an adjustable lens. The slits were made by depositing soot from a candle onto a microscope slide, then "cutting" slits in the soot using razor blades. Two blades were held together and the slits "cut" at the same time with a single swipe of the razor blades. Initially I used old fashioned double-edged razor blades but the blades were too thin and only a single slit was made in the soot. I switched to X-Acto blades, which made two slits approximately 0.5 to 0.8 mm apart. I didn't measure this, I just eyeballed it. I did both a single slit and a double slit. I varied the distance from the laser to the slit, from inches to 20 feet. The distance from the slide to the wall was varied, inches to 8 feet. **Results:** I never clearly saw an interference pattern. I saw things that were probably some kind of interference pattern, but there was no consistency. One experiment showed a pattern of lines that was about 2 cm apart, while just changing the "quality" of the slit changed the pattern to about 0.25 cm apart (not changing the laser/slit/wall distances)-- this just seemed wrong to me and implied some fundamental experiment setup problem. I also expected a difference between the single and double slit, but that was not the case. The variation of patterns seen for a single slit was similar to what I saw with the double slit. When the laser-slit distance was 20 feet, and the slit-wall distance was inches then I could clearly see an impression of the slits on the wall with no hint of an interference pattern. **Other experiment notes:** The soot was surprisingly difficult to put slit into. If the soot was made thick enough to block all light then the edges of the slit were ragged and the width of each slit was not consistent. If the soot was thinner then the slit was smoother and consistent, but there was some light leakage in the areas that should have been solid black. **Questions:** Is the "soot on a microscope slide" a valid method for making the slits? Is the laser pointer with adjustable lens an appropriate light source? Should I expect to see a diffraction pattern with only the double slit, and not with a single slit? Did you see any other improvements I could make to this experiment?


$N=4$ supersymmetric yang-mills theory and S-duality

[Question suggested by @Lawrence B. Crowell's answer to the question on T-duality] There are three parts to my question: A. What is the action for $N=4$ SUSY Yang-Mills and what is the physics of the various terms in the action? B. Give a simple explanation for the origin of Montonen-Olive duality in this theory. This duality maps the physics at gauge coupling $g$ to the physics at $1/g$, i.e. this is a duality between the strong and weak coupling regimes of the theory. C. **Auxiliary Question** : Explain how one can decompose a SUSY gauge field into its bosonic and fermionic parts. [ **Background** : I am familiar with non-abelian gauge theory and have had a class on SUSY some years back. So I pick up on the jargon but am missing a fuller picture.]


Green functions in Quantum Mechanics

How the Green's functions and the Quantum Mechanics are related? Do they can be used to solve the Schrödinger equation of an particle subjet to some potential that is not a Dirac's delta? And the proprieties of some Green's functions that are symmetrical, i.e. $ G(x|\xi) = G(\xi|x)^{\ast} $, has some relation with the propriety of the inner product $ \langle \alpha \vert \beta \rangle = \langle \beta \vert \alpha \rangle^{\ast} $?


Weight held by jet stream of water

> _Consider a bucket of weight $W$, held in air by a jet stream of water from > the ground (moving vertically upwards) at height $h$. The water is fired > from the ground at the rate of $\mu$ (units kg/s) with an initial velocity > of $v_0$. Find the maximum possible value of $h$. Find conditions to achieve > the same._ (To observers, this is a problem from Kleppner & Kollenkow: _An Introduction to Mechanics_ ). **What I did:** Consider a differential mass element $dm$ near the bucket before hitting it. Its velocity is $v_f = \sqrt{v_0^2 - 2gh}$, so its momentum is $v_f dm$. Suppose after hitting the bucket it had a velocity of $v'$, and the time of contact was $\Delta t$. Since we must exert a force of $W$ upwards on the bucket, the rate-of-change of momentum of $dm$ is $W$. Clearly $dm(v' + v_f) = W\Delta t$, which in the limit $\Delta t \to 0$, becomes $W = \mu (v' + v_f)$. Thus $2gh = v_0^2 - \left(\frac{W}{\mu} - v'\right)^2 $. This raises a question. Setting $v' = \frac{W}{\mu}$, we can attain $h = v_0^2 / 2g$, but at that height, the water would have no velocity, so no momentum change. What are my errors, and how to attack such problems (with continuous masses)? ( Please excuse me for any silly mistakes. I'm only a beginner :( ). A detailed solution which I can study would be extremely helpful.


How uncertainties affect values

If I calculate the equivalent resistance of a circuit, for example: $$1/R_{eq} = 1/R_1 + 1/R_2 + 1/R_3 = 1/1472 + 1/3260 + 1/5580 \Rightarrow R_{eq} = 858.22\,\Omega$$ And then calculate its uncertainty: $$\Delta R_{eq} = |\delta 1/\delta R_1| \times \Delta R_1 + |\delta 1/\delta R_2| \times \Delta R_2 + |\delta 1/\delta R_3| \times \Delta R_3 = 0.001\,\Omega$$ Will the uncertainty affect the value $(858.22)$, given that it only has 2 decimal numbers?


Can we make a camera that fits in one of the bands of the double slit experiment?

So, in Young's double slit experiment, we see where the particle lands on the back wall. What if we were standing at the back wall, looking toward the slits? Could we gain more information not by simply observing the light bouncing at the back wall, but looking at it our selves? Of course, for electrons or lasers, that ain't a great idea. And the slits are too small for our eyes to really make out, I'd gather. Frogs can possibly detect a single photon. What if we trained a frog to lick its left eye if it detects a photon from the left slit, and its right eye if it detects a photon from the right slit. Or better yet, build a tiny robot with a camera. Would that robot see both slits illuminate as it detects the photon? Seems testable in theory.


Tool for Born-level Cross Section Generation with Color Decomposition

I'm looking to find a tool, like CalcHEP, that calculates basic cross sections and allows for symbolic output which is decomposed by color. I understand that MADGRAPH 5 will decompose amplitudes by color in the calculation, but I'm not sure if I can extract those individual amplitudes in a reasonably easy way. Being unfamiliar with MADGRAPH, I'm also not sure how that output would look...or if it's symbolic in nature. I am also beginning to look at Comix* but I have not made much progress through the manual yet. I would like to be able to specify my basis, but I suppose that's a luxury. Any recommendations?


Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in a uniform gravitational field, or in an equivalent accelerating frame. My question is about light: Special relativity doesn't say anything about how light falls in a gravitational field, so if you are in a rocket ship accelerating at $g$ why should it be true that when you shine a light in the rocket ship, you see the same thing happening as if you shined a light on earth? (to clarify, if you shot a bullet in the rocket ship, I understand why the trajectory of the bullet would look the same as if the bullet were shot on Earth, but this is because special relativity (or classical mechanics) tells us what the trajectory of a bullet looks like on Earth).


Is it really to solve problem below by using, in the main, Gauss law?

There is an infinite cylinder surface which uniformly charged along and has a surface charge density, which can be represented as $$ \sigma = \sigma_{0}cos(\varphi ), $$ where $\varphi$ - polar angle in a cylindrical coordinate system (it means that z-axis is matches with cylinder axis). There need to find z-component $|\mathbf E|$. I tried to learn use Gauss law, but tasks, where density isn't constant on the surface, are still hard for me. Can you help?


Why Do Hurricane Balls Spin So Fast?

I was wondering if anyone could offer an explanation as to why the balls described in this video spin so fast. Here's the setup: Two metal balls are wielded together. When spun with air, they acquire a massive amount of rpm.


Plausible explanations for 3 local space dimensions

Every now and then I see accounts of models that claim to explain why we experience only 3 space dimensions (locally, i.e. within cosmic horizons and outside black hole horizons). One such of course is string theory; but I wondered if there might be others, and perhaps even a survey of this topic along the lines of those expository articles one often sees in the ArXiV.


Motion of a plank hinged about a point

There is a plank hinged about a point O. At the free end of the plank a small impulse is given. Will the plank perform pure rotation or both rotation and translation?


Measurement of event time by different observers

Follow up question to Doppler redshift in special relativity A source of light pulses moves with speed v directly away from an observer at rest in an inertial frame. How will the time of the emission of a light pulse as measured by the emitter be different to the time as measured by the observer (how will it be different than the time of the pulse reaching the observer)? edit: to elaborate slightly, let us say $ t_{E_1} $ is the time of emission as measured by the emitter, $ t_{E_2} $ is the time of emission as measured by the observer, and $ t_O $ is the time of observation of the pulse by the observer. How are these three times different, how would they be measured in practice?


Action for a point particle in a curved spacetime

Is this action for a point particle in a curved spacetime correct? $$\mathcal S =-Mc \int ds = -Mc \int_{\xi_0}^{\xi_1}\sqrt{g_{\mu\nu}(x)\frac{dx^\mu(\xi)}{d\xi} \frac{dx^\nu(\xi)}{d\xi}} \ \ d\xi$$


How Scientist Came to Know the Shape of our own galaxy without going out of it?

As far as I know, scientists have been able to see a lot of differently shaped galaxies in our visible universe through modern age telescopes. But I was wondering how it was possible to know how our own galaxy looked like without going out of it to see it's shape?


Getting a given wavelength radio signal given an antenna with real-world constraints

Supposing you are given a transmitting antenna of whatever type of metal is most commonly used these days, and supposing that you are applying an AC current with the intent of transmitting a 1 m wavelength radio signal, about how far is one electron likely to make it in one direction along the antenna conductor in one half cycle from a negative peak to a positive peak, factoring in the likelihood of the presence of antenna material atoms affecting the electron's path? Can individual charge carriers actually make it very far (on the order of meters) through metal? But if the answer is that individual charge carriers actually only make a microscopic or very small displacement in space, how could a 1 m electromagnetic wave be produced? I don't see how a large number of charge carriers each only making a very small displacement in space can add up to a 1 m wave. This site, especially Fig. 2 there, is where I'm getting my basic understanding of how alternating current gets an EM wave transmitted. From that is where I got the feeling that charge carriers would actually need to make a displacement in space on the same order as the intended EM wave.


Conservation of energy and momentum via the continuity equation in asymmetric time and space translation

I am confused about energy and momentum conservation, time and space translation symmetry, and the continuity equation. Suppose we have a mass $m$ in inertial space far from any gravitational fields. Suppose the mass has an initial velocity $v$; thus, it has an initial momentum $p=mv$ and an initial kinetic energy of $T=\frac12mv^2$. My understanding of the continuity equation is we imagine a closed surface this mass passes through and we say momentum is conserved if the momentum of $m$ exiting the imaginary surface is the same as the momentum of m entering the surface. This comes about by space translation symmetry. Now, suppose during the time $m$ is within the closed surface, an impulse is applied to the mass, so that when it exits the surface, it has a greater momentum. Do we say the momentum is still conserved because we include the impulse that acted on the mass during its transit within the closed surface? Also, the same question applies to the kinetic energy the mass gains by work being done on it by a force $f$ and displacement $d$ within the closed surface. We still say energy is conserved because work was done on the mass while it was in transit within the closed surface. Correct? Now, suppose the mass $m$ starts out in a gravitational field and free falls to the earth. During its fall, it also passes through an imaginary closed surface. The momentum and the kinetic energy of the mass will have increased from its initial values prior to entering the closed surface. But, relativity states gravity is not a force, but a curving of space-time. While the mass accelerates through the imaginary closed surface, it gains energy and momentum even though there is no force or "weight" acting on it. Is it correct to say that because there was no time or space translation symmetry within this closed surface-- spacetime is curved-- that energy and momentum is not conserved? Or, do we think of a real force acting on the mass due to the gravitational field so that we can assert energy and momentum is conserved locally?


Entropy of a two-level system

Consider a two-level system with energies and degeneracies $\epsilon_0 = 0, g_0=1$ and $\epsilon_1 = \epsilon, g_1=4$. I can show that the temperature at which both levels are equally populated is given by $\exp\left(\frac{\epsilon}{kT_0}\right) = 4$, at which the partition function, $q=2$ and the molar internal energy $U(T_0) = \frac{1}{2}N_A\epsilon$. This means that the entropy at $T_0$ is $S(T_0) = R\ln 2 + \frac{N_A\epsilon}{2T_0}$, right? Is there any special interpretation of this value of the entropy? Can the two terms here be described separately by something physically meaningful?


The Double Slit Experiment - delayed measurement

I'm not a physicist; I'm just curious about what would happen. According to this video "Explained ! The Double Slit Experiment" (at 2:50): > "Somebody decided to leave the detectors on but just not take any data. > [...] So if it was also going to a magnetic tape - there was no magnetic > tape loaded. [...] And what do you think happed? They got this. They got the > diffraction pattern." So the act of measuring (beeing concious of the data) destroys wave-form pattern? If so lets consider these cases:   1. What if I'd throw a dice after the experiment to decide if I should look at the data or to destroy it? (e.g. look at the data if the number on dice is even)   2. What if the information about measurement would need to travel longer period of time than the particle would need to hit the wall?  To above cases: Would it mean that information travelled instantly - faster than light or that "the particle can look into the future"?


Amount/flow rate of N2 needed to cool substrate

I'm trying to cool a substrate inside a vacuum chamber with liquid nitrogen. The substrate holder is a block of copper suspended from the top of the chamber via nylon screws (for thermal insulation). A copper tube runs from the LN2 tank through the flange, through one of the substrate holder's through- hole, bend back through the other substrate holder through-hole, and exits the chamber. Upon exit, the LN2 is simply dumped into the atmosphere. The substrate holder starts at 288.2K, LN2 ~77K. The LN2 tank's line pressure is around 5 psi, and ends in standard pressure upon exit. I'm trying to calculate whether with my current setup I just described, I can actually cool the substrate (ITO coated with aluminum, with a foil of indium between it and the substrate holder surface) down to 77-90K. My problems right now are setting up the diff eqs describing the heat exchange inside the substrate holder. The flow rate of N2 inside the pipes depend on whether it would be heated to gas...I'm not exactly sure how to incorporate this into the diff eqs. I would really appreciate it if someone can walk me through how to approach this or point me to a sample calculation. Also, what would be the best way to achieve this kind of cooling? We've used a reservoir approach (having a vat of LN2 on top of the substrate holder) before with success, but it takes up a lot of space. If my current setup turns out not sufficient, can I just keep increasing the initial line pressure (to >5psi) to achieve the desired cooling? Thanks, Al


Uses of the 'Golden Ratio' in Physics

What are some physics applications of the golden ratio? $$\varphi~=~ \frac{1+\sqrt{5}}{2}~\approx~ 1.6180339887\ldots$$ Does it ever function specifically as a constant in any formulas or theorems? EDIT: Original title said _Golden Radio... facepalm._ I originally asked this question at math.stackexchange but the answers there were all too abstract or useless for me.


Is the charge of a current carrying wire real or hypothetical?

Realist753 Theory Relativistic Electrodynamics assert that a current carrying wire being neutral in a laboratory frame of reference appears electrostatically charged to an observer in relative motion to that wire (“Relativistic Wire”), like an ordinary pre-charged wire would appear at rest. The theory of this apparent charge of a Relativistic Wire is covered by most textbooks dealing with Relativistic Electrodynamics.Look here: {http://chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf} by Hans de Vries. Experimental evidence Experimentally such charge has indirectly been inferred from the electrostatic potential around a Relativistic Wire. My opinion however is that for a doubtless proof of such fundamental theory it would be justified to require more credible and immediate experimental evidence of the postulated nonzero charge of a “Relativistic Wire”. Proposed Experiment Missing evidence could preferentially be obtained by means of a sliding “galvanic” contact acting as a probe* to directly pick up the electrostatic potential of a “Relativistic Wire” and adequately store the collected charge as a measure of its potential. Subsequently, the sliding contact and the probe would have to be disconnected in motion, stopped and the conserved charge be measured. A nonzero collected charge could already be regarded as indisputable proof of a nonzero charge of the wire. Question: Does anybody know if the proposed experiment has ever been done? Your comments will be welcomed.   * To avoid disturbing homopolar induction in the vacuum field around the wire the probe should be magnetically isolated.


How does the curve ball drag air around it?

In cricket or baseball there is a type of ball called the curve ball. ![enter image description here](http://i.stack.imgur.com/HRcNA.jpg) This is the top spin of the ball.I read that due to spin the ball drags the air around it due to friction in the way shown above.Can you please explain why??


who will win a race between man, horse and car of same power

Other day I got into a chat with my friend on work power and energy where he asked an intelligence related question the question was like this > if a race was conducted between a man a horse and a car of SAME POWER then > who will most probably win the race and to his question i answered that obviously man could win it because the definition of power states that > power is the fraction of work done in a given time and as per the definition of work it is described as the dot product of force and displacement and from newton's second law we get F=ma the displacement of all the three is same as their end point. so the product of mass and acceleration must be same for all and in this situation a normal man will have less weight than horse and car so it clearly states that acceleration must be of more magnitude for man. but to my surprise he said my answer is wrong and he did'nt explained how it was wrong am i really wrong? please guide me if i am wrong in which aspect.


When to use which representation for an electric field

In class we covered three types of possibilities to evaluate the electric field for static problems. Unfortunately, most physics textbooks cover these ways without addressing the question of applicability when they introduce these equations due to historical motivation. One possibility is Gauß's law: $$\int_{\partial V} \langle E, n \rangle dS = \int_V \frac{\rho}{\varepsilon_0} dx$$ This can only be used, when $E$ does by geometrical consideration not depend on the variables that the surface integral depends on(like in spherical symmetry, when it is not a function of the angles, but just of the radius), then it can be used to determine the electric field by a charged sphere. What we can get then, is an electric field on the surface of some volume that contains a particular charge. Then we have: $$ E(x) = \frac{1}{4 \pi \varepsilon_0} \int_{\mathbb{R}^3} \frac{\rho(x')(x-x')}{||x-x'||^3} dx'.$$ This is more general in the sense that it does not require any symmetry or reduction to charges inside some volume. And finally we have $$\Delta \phi(x) = -\frac{\rho(x)}{\varepsilon_0},$$ which is the most general way to think about electrostatic problems and contains (assuming that the solution fulfills all boundary conditions) all information. I hope my understanding was correct so far. In that case, my question is: How do I distinguish boundary value problems from problems where the first two equation apply? Many problems are like: Given a sphere with a particular charge distribution, calculate the field everywhere around! What does this mean, does this mean that I should think of this as a ball of charges assembling in vacuum and the material around being vacuum too? Cause if I assume that this is a metallic sphere or a sphere made out of some material which is different from the material (probably varcuum) around, then this would give me an interface which means that my first two equations don't apply anymore, as I would get boundary conditions. ( I am talking now about this in a strict theoretical sense, maybe they would give me the right result, but for the wrong reasons). Or do these two equations also apply, if the ball is an insulator?


Gears and efficiency/speed

For Christmas me and my brother got an AR Drone, the propellers are on a large gear, which is rotated by a small gear that is connected to the motor. This means the small gear (and therefore the motor) must rotate many times in order to rotate the propeller just once. Surely swapping the gears, so that the propellers are on a small gear, which is rotated by the large gear that is connected to the motor, would mean the propeller would spin faster (given that the motor is operating at the same speed as before), or that the motor could operate at a slower speed (and therefore use less energy) and maintain the same speed of the propeller as before? Also what is the advantage of using any gears at all? Why not lose the gears, and get rid of the friction between the gears and between the gear and what holding them, and the added weight?


How Relative Is Relativity With Respect To Visual Effects?

This might seem naive, but here goes. Imagine Albert and Rick, of equal mass, accelerate together to a significant fraction of light-speed (call it v) relative to Earth, enough to clearly see the effects of light aberration when looking at the stars. They expend 2 units of energy to do this. The two are now in an inertial frame of reference. Can Albert now accelerate further so that his speed relative to Rick is v, expending 1 unit of energy? How can you be in an inertial frame of reference, and still witness light- aberration effects?


Why do heavier objects fall faster in air?

We all know that in an idealised world all objects accelerate at the same rate when dropped regardless of their mass. We also know that in reality (or more accurately, in air) a lead feather falls much faster than a duck's feather with exactly the same dimensions/structure etc. A loose explanation is that the increased mass of the lead feather somehow defeats the air resistance more effectively than the duck's feather. Is there a more formal mathematical explanation for why one falls faster than the other?


Mathematica package for supergravity and string theory

I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra computations. Also, I would like this package to be able to do wedge and hodge dual, and other computation relating to forms. Can anyone suggest a specific one? I looked for atlas2, but it seems I have to pay to use it without a trial version.


Magnitude of a photon?

I encountered the following sentence in my textbook, which I don't quite understand, and after an unfruitful google search, I still can't figure out what they mean by **magnitude** in this context: > ..."split a photon into N components with magnitude ϵ"?


Can a link between photons that don't exist at the same time provide communication with the past?

They have published something about a link between photons that don't exist at the same time. Does this means that it is possible to build a device that will receive messages from itself but these messages will be received earlier than they will be sent? Can someone operating this device can win the lottery? How would you describe in numbers the bandwidth of such device? Larger than infinite? Negative?


Will current pass without any resistance?

I've learned that a resistor converts some electrical energy into heat energy while the current flows through it and thus causes a power loss, but what if there's not any resistor in a circuit. Will current still flow?


Which is more characteristic of an element absorption or emission spectrum?

Absorption and emission spectrum are used to reveal the identity of an element and even to find new elements. But, which of them is more characteristic? The mission spectrum would have more lines than the no. of lines missing in the absorption spectra simply because de-excitation can occur from any higher energy level but excitation always starts from the first energy level. So is absorption spectrum more characteristic than emission spectrum?


Is projectile trajectory on Earth affected by the fact that it isn't a singular point?

So in high school physics, we were told that projectiles traveled in a parabola, but Google searches have said that it's more like an ellipse, since the Earth isn't flat. However, I was thinking that since most projectiles stay so close to Earth, you can't really assume that gravity acts only towards the center, since gravity dictates that all particles are attracted to each other, so the core isn't the only thing on earth pulling the object "down". Is this logic valid? High School: $$d = v_{0}t + \frac{1}{2}at^2$$


Why are the Higgs phase and the confinement phase identical in Yang-Mills-Higgs systems?

If we couple a Yang-Mills theory with a Higgs field and some quarks in the fundamental representation, we can have a Higgs phase and a confining phase. However, they are indistinguishable. The Wilson loops scale according to the perimeter law, not the area law in the confining phase because of hadronization. In the Higgs phase, there is no cluster decomposition for the Higgs field because distant points have to be connected by a Wilson line with exponential falloff as the length of the Wilson line. Why are both phases indistinguishable?


Runge-Lenz vector and Keplerian Orbits

Is the loss of _closed_ Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?


Does "Crack The Whip" actually speed you up?

"Crack The Whip" is a game played on ice skating rinks where several individuals line up all facing the opposite end of the rink, and skate forward. When the group reaches the opposite end of the rink, the "point man" or the person on one end of the line stops, and everyone else pivots around him. Supposedly, the person on the opposite end swings around, and rockets forward at much greater speeds. However, I don't believe this is possible. Because the question remains, where would the extra speed come from? I was told that the momentum of all the people is transferred into the one person on the end. While there is a ponderous amount of outward force on the chain of people, I don't think it's possible to actually gain speed. And after watching my friends do it several times, I concluded the person on the end didn't seem to go any faster. Was it simply that the process was inefficient? Or is the theory even possible?


Is it possible to create a hologram using X-Rays?

Is it possible to create a hologram using X-Rays (or other penetrating EM- waves)?


reflection, refraction and diffraction occur in radio waves, which one occurs the most?

One of the things about Radio waves is that they undergo different behaviors such as reflection, refraction and diffraction when in contact with obstacles such as walls, buildings etc. what i want to understand is that, which of the behaviors would occur the most in let's say an environment filled with trees and the slope is rough?


Finding Directions using moon

Is it possible to find directions just by looking at moon(not full bright)? I was curious to use the clue that if moon is half lit then the direction in which it is lit will it be east?


The acceleration of a particle in uniform electro-magnetic field

A particle of charge $q$ and mass $m_0$ is subject to the action of a uniform electro-magnetic field $\vec{E}=(0,E,0), \vec{B}=(0,0,B)$ and at $t = 0$ moves with velocity $\vec{v}=(v_1,v_2,v_3)$. What is the acceleration at $t = 0$ if $v_1 = v_3 = 0$?


Does a Weak Energy Condition Violation Typically Lead to Causality Violation?

In the answer to this question: ergosphere treadmills Lubos Motl suggested a straightforward argument, based on the special theory of relativity, to argue that light passing through a strong gravitational region which reaches infinity cannot reach infinity faster than a parallel light ray which does not pass through the strong gravitational region. The argument is just the standard special relativistic one, that if you can go faster than light, you can build a time-machine. To do this, you just have to boost the configuration that allows you to go faster than light, and traverse it in one direction, then boost it in the other direction, and go back, and you have a closed timelike curve. In the condition of the question, where the strong gravitational region is localized, you can do this using pre-boosted versions of the solution. Preboost two far away copies of the solution in opposite direction, one boosted to go very fast from point B to point A (at infinity) and the other boosted to go from point A to point B. Then if you traverse a path from A to B, crossing through the first boosted solution, then cross the second on the way back, you can make a CTC. I was skeptical of this argument, because the argument I gave required the Weak energy condition, not a no CTC condition. The argument from null energy just says that a lightfront focuses only, it doesn't defocus, the area doesn't ever spread out. Any violation of weak energy can be used to spread out a light front a little bit, and this corresponds to the geodesics passing through the violating point going a little bit faster than light, relative to the parallel geodesics nearby. So if both arguments are correct (and although I was skeptical of Lubos's argument at first, I now believe it is correct), this means that a generic violation of the weak energy condition which is not hidden behind a horizon could be turned into a time machine. Is this true? Question: Can you generically turn a naked violation of weak energy condition into a closed timelike curve? A perhaps more easily answerable version: If you have an asymptotically flat solution of GR where there is a special light ray going from point A to point B which altogether outruns the asymptotic neighbors, can you use this to build a time machine, using boosted versions of the solution?


Finding out the minimum deviation angle

![enter image description here](http://i.stack.imgur.com/nsFgB.png) Let a light incident on a prisom at right angle. I want to determine the minimum deviation angle. I know a relation $$ \frac{\cos i_1}{\cos r_1} = \frac{\sin i_1}{\sin r_1}$$ and minimum angle of deviation $$\delta_m = i_1 +i_2 -A$$ It can be seen that, $i_1$ is given but how to get $i_2$ and A. A is the prism angle. and $i_1 =90 $ and $i_2 $ is the angle of the outgoing ray.


Could the speed of light change outside our solar system

Theory: The speed of light changes when it enters or exits the solar system due to a difference in medium (dark matter possibly). Potential problem 1: refraction If there was a speed change at the edge of the solar system, refraction would occur. This would manifest in ways similar to the sunset effect. Solution: the sunset refraction occurs because the angle against the edge of the atmosphere is extreme. No effect is noticed at high noon. Earth's proximity to the edge of the solar system, in contrast, makes it's angle nearly perpendicular in all directions. Wouldn't this negate any sunset effect? Sub-solution: My research on refraction seems to indicate that what I'll call the "distinction level" of the edge of the mediums has an effect on the level of refraction. So that, if the edge were not solid, but rather tapered, the refraction is reduced. SO, what would be effect on light entering our solar system if the light were severely slowed--let's say by a factor of 1,000,000 times, to what it is now. What, if any, refractive effects would be observed? How much would these effects change if the tapering of the edge were severe?--Could any refractive effect be overcome by tapering? Another question, what would be the effect of the light coming from Alpha Centauri if it's system had a similar medium transition at it's edge? How would it be noticable? This picture illustrates my thoughts: ![refraction](http://i.stack.imgur.com/FSZzo.jpg)


Understanding Normal Force Change

_I know this has been asked around, my question is a bit more specialized towards my personal problem._ If I have an object the magnitude of the weight is usually equal to the normal force, right? I could be mistaken but from what I have read the normal force is the force the object is feeling opposite to the $(mass*gravity)$. If that is the case, and I put my hand on the object does my Force get added to the object's weight and thus the normal force of that object increases? Therefore if I keep adding hands to the object will the normal force keep compensating? Also is the normal force the negative charged electrons repelling each other (electromagnetism)? ![enter image description here](http://i.stack.imgur.com/sPXjk.jpg)


How far into space does one have to travel to see the entire face of earth?

Virgin Galactic will take passengers aboard SpaceShipTwo as high as 65 miles above the surface of the earth. But from this altitude, passengers will only be able to see a certain segment of the curvature of the earth through windows as large as 17 inches in diameter. How much further into space would SpaceShipTwo have to travel to give passengers a view of the entire sphere of earth through one of these windows?


Why is $r'/r^2 = -1/r$?

If $r=r(t)$, why is $\frac{r'(t)}{(r(t))^2}$ = $\frac{1}{r(t)}$ where $'$ denotes the derivative? I saw it in a lecture. Can you please explain?


Will the black hole evaporate in finite time from external observer's perspective?

There is the problem that is bothering me with the black hole evaporation because of Hawking radiation. According to Hawking theory the black hole will evaporate in finite time because of quantum effects randomly producing particle-antiparticle pairs on the opposite sites of horizon. However, the gravity causes the time dilatation, which goes to infinity on the horizon itself, so the arbitrarily small amount of time from horizon's perspective is going to be infinitely long from external observer's perspective? So, from which perspective is the time the black hole will evaporate calculated? If it is calculated from horizon's perspective, it would mean, the black hole will never evaporate from the external observer's perspective?


Is the equivalence principle strictly fulfilled by general relativity?

The equivalence principle states _The outcome of any local experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime._ Any real local experiment needs some finite space, since nobody is a point particle himself. In principle I will always feel some deviation. Since in (pseudo-)Riemannian geometry I can only change to flat coordnates in a single point $p$ of the spacetime manifold (and not in a finite neighborhood), is the deduction right, that the equivalence princpil is only fulfilled by general relativity in an approximative sense?


In layman's terms, what is a quantum fluctuation?

What causes it and how does it occur? If you do post some mathematics, please explain what each term means too please.


Is 4-velocity normalized to -1 even for non-geodesic timelike curves?

In Hartle's General Relativity book ("Gravity"), one of the problems (chapter 8 problem 6) is to prove that $g_{\mu\nu}u^\mu u^\nu$ is conserved along geodesics (really not hard to show), where $u^\mu$ is the 4-velocity. My question is: Isn't it true that $g_{\mu\nu}u^\mu u^\nu$ is equal to $-1$ for _any_ timelike curve whether it is a geodesic or not? This follows (I think) from $$ g_{\mu\nu}u^\mu u^\nu = g_{\mu\nu}\frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\tau} = \frac{g_{\mu\nu}dx^\mu dx^\nu}{d\tau^2}=\frac{ds^2}{d\tau^2} = \frac{-d\tau^2}{d\tau^2} = -1. $$ Am I wrong about this? Why should we need the geodesic equation to prove this if it's true for any timelike curve?


Where are the ice rings in X-ray crystallography located?

I threw this image of one of my protein crystal's diffraction pattern (not the greatest) on a poster, and was wondering where (what reciprocal dimension) the ice rings are located as it might be a useful reference (or talking point). While I can find information about water ice's unit cell parameters (4.5 Å, 7.3 Å), I'm not sure if these are where the reflections would be located (the inner two rings seem far too close for that disparity, and I believe the outer two rings are at a much higher resolution (< 3 Å) ![enter image description here](http://i.stack.imgur.com/FTPb4.png)


Non-separable solution for the Schrödinger equation

Schrödinger solutions are usually if not always of the type: $\psi=\operatorname{T}(t)*\operatorname{X}(x)$ (we use the separation of variables method to arrive at the time independent Schroedinger equation). I was trying to find a non-separable solution. To this purpose I tried the following method: compose the product T(t)*X(x) into another function. For example: $\sinh(\operatorname{T}(t) \cdot \operatorname{X}(x))$ or $\ln(\operatorname{T}(t) \cdot \operatorname{X}(x))$ or $(\operatorname{T}(t) \cdot \operatorname{X}(x))^2$ and so on. Then I try first time derivative of $\psi = \mathrm{second}$ position derivative of $\psi$ (trying to find a solution for the null potential. In addition I know I need a constant but it's for simplification). I arrive at a differential equation. I try simple solutions for one of the functions like $\operatorname{T}(t)=t$. I get to a very difficult differential equation that can't be solved even with a look at: http://www.amazon.com/Handbook-Solutions-Ordinary-Differential- Equations/dp/1584882972 If there any obvious non separable solution that I am missing?


paper about black branes and implications to 4d black holes

This paper makes a case for piezoelectric response (electric dipole moment under mechanical oscillations) of black branes. This paper does not make an implication of their results for 4D black holes (do their results apply or not apply to them?). Can someone explain if this implies something for usual 4D black holes in De Sitter space? Do "standard" black holes have such a response as well?


Any example of lower symmetry in high temperature phase than the low temperature phase?

All the phase transition cases I came across so far have this property: the lower temperature phase has lower symmetry than the higher temperature one. But it is nowhere explicitly said that, lower temperature phase always has lower symmetry than the higher temperature phase. So, I was thinking, is there any counter-example to show that higher temperature phase in a phase transition can have lower symmetry too?


Is a macroscopic pair where I observe one of them quantum entanglement?

Of what little I know/understand about quantum entanglement can somebody confirm if the following experiment is a good analogy to quantum entanglement of pair of particles? PS: please don't laugh as this could be very very lame! I take an orange and an apple (of similar shape & weight). I put each of them in a non transparent bag separately and seal it off. I put both the bags in a box. I close my eyes and shake it thoroughly such that I no longer know which bag contains what fruit. Then I randomly pick one bag and take a flight to other part of the country. Now given the above setup, I will not know what fruit is in my bag. In other words the fruit in my bag could be both apple/orange at the same time until I open the bag and see what is inside. As soon as I open it it is determined (similar to wave function collapsing) that I have an orange (for example) and there by making the fruit in the bag that was left in the box an apple (or vice versa). Does this in anyway come close to what they are doing with quantum entanglement?


What is the difference between Newtonian and Lagrangian mechanics in a nutshell?

What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something like the explanation of the Lagrangian formulation of mechanics you'd give to someone who just finished a semester of college physics. Things I'm hoping to have explained to me:   * What's the overall difference in layman's terms? From what I've read so far, it sounds like Newtonian mechanics takes a more local "cause-and-effect"/"apply a force, get a reaction" view, while Lagrangian mechanics takes a more global "minimize this quantity" view. Or, to put it more axiomatically, Newtonian mechanics starts with Newton's three laws of motion, while Lagrangian mechanics starts with the Principle of Least Action.   * How do the approaches differ mathematically/when you're trying to solve a problem? Kind of similar to above, I'm guessing that Newtonian solutions start with drawing a bunch of force vectors, while Lagrangian solutions start with defining some function (calculating the Lagrangian...?) you want to minimize, but I really have no idea.   * What are the pros/cons of each approach? What questions are more naturally solved in each? For example, I believe Fermat's Principle of Least Time is something that's very naturally explained in Lagrangian mechanics ("minimize the time it takes to get between these two points"), but more difficult to explain in Newtonian mechanics since it requires knowing your endpoint.


Models of higher Chern-Simons type

It has long been clear that (the action functional of) Chern-Simons theory has various higher analogs and variations of interest. This includes of course traditional higher dimensional Chern-Simons theory (abelian and non-abelian) as well as the algebroid-version: the Courant-sigma model, but also seemingly more remote systems such as string field theory (and hence essentialy also its effective truncations), a fact that is already somewhat remarkable. In a recent article we claimed that there is a systematic sense in which also all AKSZ sigma-models are special cases of a general abstract notion of "infinity-Chern-Simons theory". These AKSZ models include, in turn, also the Poisson sigma-model (hence also the A-model and the B-model). Also BF-theory coupled to topological Yang-Mills theory fits in. Therefore in a precise sense all these systems are examples of a single underlying basic mechanism. My **question** is: can you point out other models of interest in the literature (or in your drawer) that look like they might be "of generalized Chern-Simons type", along these lines? (I am not just looking, say, for "Chern-Simons term"-summands in higher supergravity actions, even though these are related, but for example new variants of full higher dimensional Chern-Simons (super)gravity.) For instance: has there been a proposal for a nonabelian 7-dimensional Chern- Simons-type model that might be the holographic partner to the self-dual nonabelian 6d (2,0)-superconformal QFT (so that the state spaces of the former are the conformal blocks of the latter)? While we did come across a natural non-abelian 7-dimensional Chern-Simons type TQFT whose fields are string-2-connections (here), I am not sure how to see if this might be the relevant one. Do you?


What causes an aircraft to roll when rudder is applied

When continuous rudder is applied in a typical light aircraft during straight and level flight at "normal" flying speeds and altitudes, the primary effect is that the aircraft will yaw to the left - so it's flying "sideways" to some extent. It is commonly understood amongst pilots that the secondary effect in most aircraft, is that the aircraft will also start rolling in the direction of yaw (i.e. applying left rudder causes left yaw, and left roll). What causes this roll? And does the Dihedral angle have anything to do with it?


Calculating rotor torque out of mass center

Suppose I have an engine with propeller. I know there is aerodynamic force pushing the propeller opposite direction the engine is turning it. One component of this force is creating lift, but second is braking the prop. Now these forces are applied at some distance from engine shaft, thus they're creating torque, which is turning the whole engine if it wasn't fit somewhere. And now my problem: how to describe what happens, after fitting this engine out of mass center. For example take a ruler, that has pivot somewhere and at the end of it, there is this engine with propeller. How do I describe momentum at the center of mass - the pivot, instead at the engine (engine has no weight in this example)?


String theory landscape and false vacua

What is the multiverse of string theory? I always thought it would be from brane cosmology where there's chances for multiple collisions of the branes that can make a universe. So this "multiverse" would be in the "bulk". But when I read up on the string theory landscape it implies a relation to bubble cosmology and false vacua? How does that work? What's the connection? There's no need for strings in bubble cosmology and no need for bubble nucleation in brane cosmology so... what's going on?


Electrons skip randomly around their orbits

I read where the electron (as well as a few other particles) skips around in its orbit randomly rather than move around the orbit smoothly. This effect has been repeatedly observed in the laboratory over the years. I know if we treat this using quantum physics the electron exist in a fuzzy cloud of probability but in the old days before quantum physics what were they seeing in the laboratories when they found this effect?


Electric field a distance $z$ above the center of a circular loop. The Hard way

> _Problem 2.5: Find the electric field a distance $z$ above the center of a > circular loop of radius $r$ which carries a uniform line charge $\lambda$._ This problem is in refereced here (with solution): http://teacher.pas.rochester.edu/PHY217/LectureNotes/Chapter2/LectureNotesChapter2.html But it is solved using a trick. The trick is: okay we know there is symmetry so let us just take the magnitude and not use the vectors. The problem I have is I am unable to solve it without using the trick and I would appreciate someones help in doing the problem without the shortcut, using the vectors. When I do it the r compontent doesn't cancel. Using polar coordinates here is the setup: $$dE = \frac{1}{4 \pi \epsilon_0} \frac{\lambda}{\rho^2} ~ \hat{\rho} ~ r d \theta$$ $$\hat{\rho} = \frac{z \hat{k} + r \hat{r}}{\sqrt{z^2 + r^2}} $$ $$ E = \frac{\lambda}{4 \pi \epsilon_0} \int_0^{2 \pi} \frac{r z \hat{z} + r^2 \hat{r} }{(z^2 + r^2)^{3/2}} ~ d \theta$$ $$ E = \frac{\lambda}{4 \pi \epsilon_0} \int_0^{2 \pi} \frac{r z \hat{z} }{(z^2 + r^2)^{3/2}} ~ d \theta + \frac{\lambda}{4 \pi \epsilon_0} \int_0^{2 \pi} \frac{r^2 \hat{r} }{(z^2 + r^2)^{3/2}} ~ d \theta $$ If I now evaluate the $z$ component I get the correct answer. When I evaluate the $r$ component, shown below the $r$ doesn't not cancel the way it should. why not? $$\frac{\lambda}{4 \pi \epsilon_0} \frac{r^2 2 \pi }{(z^2 + r^2)^{3/2}} - \frac{\lambda}{4 \pi \epsilon_0} \frac{r^2 0 }{(z^2 + r^2)^{3/2}} $$ $$ = \frac{\lambda}{4 \pi \epsilon_0} \frac{r^2 2 \pi }{(z^2 + r^2)^{3/2}} \hat{r}$$


Cross Section Peskin vs Srednicki

in Peskin Schroeder after the derivation of the differential cross section there is a comment for the central mass system (CMS), which says: In the special case, where all four particles have identical masses (...), this [the general formula] reduces to the formula[...] (p.107): $$ \left(\frac{d\sigma}{d\Omega}\right)_{CM}=\frac{\left|\mathcal{M}\right|^2}{64\pi^2E_{CM}^2}$$ However in Srednicki the general formula for the differential cross section in the CMS is (p.97): $$\left(\frac{d\sigma}{d\Omega}\right)_{CM}=\frac{\left|\mathcal{M}\right|^2}{64\pi^2E_{CM}^2}\frac{\left|\textbf{k}^\prime\right|}{\left|\textbf{k}\right|} $$ where $\left|\textbf{k}^\prime\right|$ is the outgoing three-momentum in the CMS and $\left|\textbf{k}\right|$ the incoming. Now to get from the formula from Srednicki to Peskin's formula I don't need the masses to be all the same but merely the incoming masses equal to the outgoing masses, so to say elastic scattering. I didn't see a further restriction in Srednicki's formula apart from being in the CMS. If I take e.g. Compton scattering I get with Srednicki's formula: $$\left(\frac{d\sigma}{d\Omega}\right)_{CM}=\frac{\left|\mathcal{M}\right|^2}{64\pi^2E_{CM}^2} $$ but Peskin gets on page 164 with his formula for the differential cross section: $$\left(\frac{d\sigma}{d\Omega}\right)_{CM}=\frac{1}{32} \frac{1}{E_1E_2}\frac{\left|\textbf{k}^\prime\right|}{E_{CM}}$$ where $E_1+E_2=E_{CM}$. I don't see, that this is equal? Is it actually equal? Where did I miss something?


What is the relation between the representation the Higgs field transforms under, the types of couplings in the theory and Higgs/Coulomb branches?

When reading about Higgs and Coulomb 'phases' I came across two separate definitions: The first tells us that the Higgs/Coulomb phases are determined by the representation that the Higgs field transforms under, as explained on Wikipedia. The Higgs field breaks the gauge symmetry; If the Higgs is in the adjoint then we're left with U(1)s and we have a Coulomb phase, if the Higgs transforms in any other representation then (typically) no U(1)s are left and we have a Higgs phase. However, the second definition tells us that the these phases are determined by the potential between two electric test charges (as read in Sannino's book). A potential proportional to 1/r is the Coulomb phase and a constant potential gives the Higgs phase. Also, there are other phases: Confining, free-electric, free-magnetic and perhaps others. Question 1) Is there a link between these two definitions? I can see why the Coulomb phase as described in the Wikipedia article might lead to a 1/r potential (due to the surviving U(1) groups). But why would the Wikipedia definition of a Higgs phase lead to a constant potential? Furthermore, if there is a link, what sort of phase (As in the Wikipedia article) would give us confining, free-electric and free-magnetic potentials? Then there are Higgs and Coulomb 'branches'. These are the moduli (scalar fields) of the N=2 hyermultiplet and vector multiplet respectively. Question 2) Do these link in with the phases described above or are the concepts of branches and phases very much distinct? Christian Samann's notes tell us (on page 13) that the Coulomb _branch_ is what we get when the gauge group breaks to U(1)'s. I think this is just an inconsistency in what different authors mean when they talk about branches and phases.


Is it possible to separate the poles of a magnet?

It might seem common sense that when we split a magnet we get 2 magnets with their own N-S poles. But somehow, I find it hard to accept this fact.(Which I now know is stated by Gauss's Law) I have had this doubt ever since reading about the quantum-field-theory and I know I might sound crazy but is it really impossible to separate the poles of a magnet? **What about black holes**? They attract matter and everything else only inwards into them, right? So then, are they the only such case/exception? Am I being naive? Is there some proof/explanation that can give closure to this question of an independently existing pole?


Current Carrying Wire Loop near Current Carrying Long Wire

A rectangular wire loop of (width $a$ and height $b$) carrying clockwise current $I_1$ is a distance $d$ below a horizontal infinitely long wire carrying a current $I_2$ to the right. What is the force on the wire loop? I am not sure what equations I have to use here, it's been quite awhile. I know the magnetic field infinite wire is something like $\frac{\mu_0}{2\pi} \frac{I_2}{r}$ And F=v x B. For the horizontal segment of the loop nearest the wire, does $v=\frac{I_1 a}{e}$? Is that right? does F = $\frac{\mu_0}{2\pi} \frac{I_2 I_1 a}{d e} - \frac{\mu_0}{2\pi} \frac{I_2 I_1 a}{(d+b)e} = \frac{\mu_0}{2\pi e}I_2 I_1 a (\frac{b}{d(d+b)})$ towards the wire. Is that the right answer?


Wave or particle in the end

In Young's double slit experiment I put a convex lens after double slit and direct interference pattern on to a fibre. Then I expose the other end of fibre to a screen. What will I observe - the interference pattern (slightly jumbled) or a dot? Will photons behave as wave or particle?


Anti-symmetric forms on Dirac spinors

In order to describe invariant forms on Dirac spinors $S$ one can find trivial subrepresentations in $S \otimes S$. If we use $S \cong (1/2, 0) \oplus (0, 1/2)$ then \begin{multline} [(1/2, 0) \oplus (0, 1/2)] \otimes [(1/2, 0) \oplus (0, 1/2)] =\\\ (0, 0) \oplus (1, 0) \oplus (1/2, 1/2) \oplus (1/2, 1/2) \oplus (0, 1) \oplus (0, 0) \end{multline} Therefore representation theory predicts existence of two invariant forms. It is usually claimed that this two forms are $$ D_1(\chi, \psi)=\bar{\chi}\psi=\chi^T\gamma_0\psi=\chi_R^T\psi_L+\chi_L^T\psi_R $$ and $$ D_2(\chi, \psi)=\bar{\chi}\gamma_5\psi=\chi^T\gamma_0 \gamma_5\psi=\chi_R^T\psi_L-\chi_L^T\psi_R $$ The form $D_1$ is symmetric and it's quadratic form (with complex conjugation on the first argument) is usually used to construct Dirac's Lagrangian. From the other hand, it is known that on Weyl spinors one can also find an antisymmetric invariant forms given as $$ \chi^T_L\sigma_2\psi_L . $$ Let me use this to construct one more anti-symmetric invariant form on Dirac spinors as a sum of two forms on Weyl spinors $$ D_3(\chi, \psi)=\chi^T_L\sigma_2\psi_L+\chi^T_R\sigma_2\psi_R $$ Form $D_3$ is not a linear combination of $D_1$ and $D_2$ and thus I get a contradiction with representation theory prediction. Where I made a mistake?


Ricci scalar higher dimensions

I was wondering if there is a straightforward way to compute the Ricci curvature of a metric that has the form (à la Kaluza-Klein): $g_{MM}\equiv\begin{pmatrix}g_{\mu\nu}&g_{\mu i}\\\g_{i\nu}&g_{ij}\end{pmatrix}$ Ie, finding an expression of the form: $\mathcal{R}(G_{MN})=R(g_{\mu\nu})+R(g_{ij})+(\text{scalar depending on both metrics})$ I tried using the usual formula $R^M_{NPQ}=2\partial_{[Q}\Gamma^M_{P]N}+2\Gamma^S_{M[P}\Gamma^M_{Q]S}$ where $A_{[MN]}=\frac{1}{2}(A_{MN}-A_{NM})$. But this becomes really quickly a mess due to the different indices. Does anyone has an idea how to find the result quickly? For a kaluza klein metric where $g_{ij}$ is a scalar and $g_{\mu j}$ is a vector this is straightforward, but I can't find a nice solution.


What is going on with star's energy?

The sun radiates $3.8 × 10^{26} J$ energy each second, this energy is absorbed by various celestial objects but most of it is reflected or emitted back in the space, similarly there must be energy pouring into empty space from various star systems, what is happening to all this energy ? In what form is it thriving if it is thriving ? Does it ultimately get absorbed by various objects ? Is it bringing some kind of change to the motion of galaxies etc ? Is there some sort of energy sink somewhere ( maybe getting sucked in by Black holes) ? Does it somehow combine and form new bodies via energy mass equivalence ? **what is happening ?** Addendum : This maybe a on the edge of site's mainstream physics discussion policy, but till now all I understood was that no definitive proof of where the energy is going is available, @ John rennie says that due to red shift the wave's are losing energy, he says that energy density is tending to zero, but there is no account for this energy. At the same time, @Thriveth mathematically asserts that the universe is losing energy, I find it a bit of a controversial topic regarding energy conservation and can't shake off the idea that maybe this energy could account for dark energy/matter. I add, millions of stars have died/ emptied their energy into the space since the beginning of time, by the logic of either answer, red shift or violation of energy conservation we can say that this energy is somewhere we can not account for, similarly we till now can't account reasons for dark matter/energy can't we explain both of these with each other ?


Black body balloon in vacuum

**The problem statement, all variables and given/known data** There is a perfectly spherical balloon with surface painted black. It is placed in a perfect vacuum. It is gently inflated with an ideal mono-atomic gas at Kelvin temperature $T_i$, slowly enough so that it reaches thermal equilibrium with the gas, and then it is sealed off. It has radius $r_i$ at this time and contains N atoms. The vacuum is large, so radiation from its walls can be ignored. a) Show that $\frac{T}{T_i}= \left(\frac{r}{r_i}\right)^3$ if the pressure inside the balloon is independent of its radius. b) How much energy does the balloon radiate per second when it is at radius $r$? Express your answer in terms of $r$ and constants. c) What is the rate of change of the internal energy of the gas? Express you answer in terms of $r$, $r˙$, and constants. **Relevant equations:** $$PV = nRT$$ $$J * A = σT^4 (4\pi r^2)$$ **The attempt at a solution:** I already showed a), so I don't need help with that. In part b), I wrote pretty much $J * A = σT^4 (4\pi r^2)$ but I am unsure how to get a speed of radiation. I also have no idea how to do part c), so any help on parts b) or c) is welcome. Thanks!


Problem in geometrical optics

I was trying to solve a problem taken from an Physics Olympiad when I came across a curious and complex mathematical expression. I can not prove with what I know so far about mathematics, does could anyone tell me if the answer is correct? My answer: $d\tan(\arcsin ((\sin(180-t)*H)/ \sqrt(H² + 4d^2 - 4dH\cos(180-t))))$ The correct answer:$(dH\sin(t))/(2d+H\cos(t))$ The mathematical problem: $d\tan(\arcsin ((\sin(180-t)*H)/ \sqrt(H² + 4d^2 - 4dH\cos(180-t)))) = (dH\sin(t))/(2d+H\cos(t))$ Is it true? My solution: Image 1: http://img825.imageshack.us/img825/4248/46611781.png               Â = 180° - ϴ          (A’B)² = (AB)² + (AA’)² - 2. (AB). (AA’).cos(180° - ϴ)     A’B = v(H² + 4d² - 4.H.d.cos(180° - ϴ))          sen(Â’)/AB = sen(Â)/A’B     sen(Â’) = sen(180° - ϴ).H/ v(H² + 4d² - 4.H.d.cos(180° - ϴ))     Â’ = arc sen (sen(180° - ϴ).H/ v(H² + 4d² - 4.H.d.cos(180° - ϴ)))      Image 2: http://img23.imageshack.us/img23/7937/466117811.png               tg(Â’) = CE/A’C     tg(Â’) = L/d     L = d.tg(Â’)     L = d.tg(arc sen (sen(180° - ϴ).H/ v(H² + 4d² - 4.H.d.cos(180° - ϴ))))


Why is the universe map shaped like an oval?

![enter image description here](http://i.stack.imgur.com/W9EiD.jpg) I understand that the Mollweide projection is used to show the map of the universe. Although I understand how this projection can be interesting for Earth where most populated (and of interest) areas are not at polar latitudes, I imagine that in the sky the distribution of interesting places does not follow the same pattern of accentuating the equatorial plane. Do you think this the best projection to represent the Universe? Possible tags: map cosmos universe projection


sun-moon-earth anomaly

When one looks at the sun and the moon in the sky together, why is it that the illuminated crescent of the moon does NOT "point" at the sun? (More correctly the perpendicular bisector of the straight line joining the end points of the moon's terminator does not point at the sun. Intuitively one feels it should - as that is where the light is coming from. It is always around 20 - 30 degrees "off target".)


What does "quantum theory forbids promiscuous entanglements" mean?

The context is this article about black hole firewalls. The phrase appears on page 3. It appears to be saying that only pairs of particles can be entangled, never multiple particles, and that this is essential to the firewall paradox. Of course any number of particles can be entangled, at least in the usual sense of the word. Is Dr. Polchinski using the word in a specialized manner, or has the reporter just misunderstood or over-simplified? If the issue isn't about entanglement, what is it about - something to do with the no-cloning theorem, perhaps?


Would an octahedral magnet work as a magnetic bottle?

First, let me see if I understand all this: Charged particles are curved by magnetic fields, so if the magnetic field is strong enough, the particles "follow" the magnetic field lines, in N or S direction, by spiraling around them: ![particles spiraling around magnetic field lines to the left and to the right](http://i.stack.imgur.com/vSXMg.jpg) (source) ![enter image description here](http://i.stack.imgur.com/IDCml.gif) (source) If the magnetic field lines get closer together, it can create a magnetic mirror, which affects the rotation of the particles such that they turn back and go the opposite way: ![magnetic mirror](http://i.stack.imgur.com/ODBgA.jpg) (source) If you combine 2 magnetic mirrors, you get a magnetic bottle, which can confine charged particles by both spiraling and reflection off the mirrors: ![magnetic mirror and magnetic bottle](http://i.stack.imgur.com/XkOZ9.gif) (source) ![magnetic bottle](http://i.stack.imgur.com/GlzGZ.jpg) (source) So my question is whether it's possible to combine _multiple_ magnetic bottles/mirrors into other, more "spherical" configurations, and still have it confine particles in the center, such as an octahedral magnet (brown arrows are current, magnets show field direction): ![Octahedral magnet](http://i.stack.imgur.com/lp4bE.gif) (source) or a cuboctahedral magnet, or other shapes that can be painted with 2 colors, so the field direction alternates from one face to the next (to avoid trying to create a magnetic monopole field, which obviously wouldn't work).


Expectation value of total energy for the quantum harmonic oscillator

A particles unnormalized wavefunction is given as $$\psi(x)=2\psi_1+\psi_2+2\psi_3.$$ How can I find $\langle E\rangle $ without calculating $\langle T\rangle$ or $\langle V\rangle $ first? I'm pretty sure I have $\langle T\rangle $ and $\langle V \rangle$ though, so is the only way to find $\langle E\rangle $ is to add these two values together? Any help would be appreciated.


Is there a known generalization of the Schmidt decomposition based on a maximal set of "locally recorded branches"?

I came across an unusual multi-partite generalization of the Schmidt decomposition in my work, which I describe below. Usually, when people say "a multi-partite Schmidt decomposition", they mean a sum of product states which is in some sense _minimal_ , and there are different decomposition depending on what metric is used to measure minimality. In contrast, I'm looking at a decomposition of a state into a _maximal_ sum of locally-orthogonal (but not necessarily product) states. I would like to know if this structure has been studied before so I can read more about it. Suppose we are given a normalized quantum state $\vert \psi \rangle$ from a Hilbert space $\mathcal{H}$ composed of $N$ smaller subsystems $\mathcal{H}^{(n)}$ that are tensored together: $\vert \psi \rangle \in \mathcal{H} = \mathcal{H}^{(1)} \otimes \cdots \otimes \mathcal{H}^{(N)}$. Now I am looking for a preferred decomposition $\vert \psi \rangle = \sum_i \sqrt{p_i} \vert \psi_i \rangle$ of $\vert \psi \rangle$ expressed as a sum (weighted by the positive values $\sqrt{p_i}$) of orthonormal vectors $\vert \psi_i \rangle$ such that the $\vert \psi_i \rangle$ live on orthogonal subspaces of _each_ subsystem. More precisely, we require $\vert \psi_i \rangle \in \bigotimes_n \mathcal{H}^{(n)}_i$ where $\mathcal{H}^{(n)} = \bigoplus_i \mathcal{H}^{(n)}_i$ is a decomposition of $\mathcal{H}^{(n)}$ into orthogonal subspaces. This is interesting because it means that the $i$-conditional reduced density matrices of any subsystem $\mathcal{H}^{(n)}$, $\rho^{(n)}_i = \mathrm{Tr}_{\overline{\mathcal{H}^{(n)}}} \left[ \vert \psi_i \rangle \langle \psi_i \vert \right]$ are restricted to the same orthogonal subspaces. (Here, the trace is over all spaces except $\mathcal{H}^{(n)}$.) Therefore, observers can make local measurements on _any_ of the systems $\mathcal{H}^{(n)}$ and determine which "branch" $\vert \psi_i \rangle$ they are on. This structure is special for the following reason. (a) There exists a unique decomposition which maximizes the number of vectors in the sum while still satisfying the requirement of orthogonal records in each of the subsystems. (b) This maximal decomposition can be obtained through a mechanical (i.e. algorithmic) fine-graining procedure; the same decomposition is obtained regardless of the order in which the fine-graining is done. (c) The quantity $E = - \sum_i p_i \ln p_i$ is maximized for the maximal decomposition and defines a measure of the _global_ entanglement (with respect to the particular choice of subsystems); if $v$ is such that any of the subsystems are unentangled with the rest, this quantity vanishes. (d) This structure reduces to the Schmidt decomposition (and $E$ reduces to the traditional entropy of entanglement) when $N=2$. (e) This structure, and the corresponding value of $E$, is insensitive to pairwise entangling interactions between subsystems (so long as they do not destroy the orthogonality of the conditional local states $\rho_i^{(n)}$) even when the strength/type of these entangling interactions are _conditional_ on the branch $i$. So: has this been explored before? * * * (I also submitted essentially the same question in math notation here.)


About an electrostatics integral and a delta-function kernel

I'm having trouble with an integral and I would like some pointers on how to "take" it: $$ \int \limits_{-\infty}^{\infty}\frac{3\gamma a^{2}d^{3}\mathbf r}{4 \pi \left( r^{2} + \frac{\gamma^{2}}{c^{2}}(\mathbf r \cdot \mathbf u)^{2} + a^{2}\right)^{\frac{5}{2}}} $$ Here $\mathbf u$, $a$ and $\gamma$ are constants, and the integrand converges to a Dirac delta $\delta(\mathbf r)$ as $a\rightarrow 0$. The integral must be equal to 1.


Harmonic frequencies of electric guitar are detuned. What could be the cause?

I have tried to record some music with my electric guitar and while playing around and looking the frequencies of single strings I noticed something strange. I took the spectra of the A string and I expected multiples of 440 Hz, but the Results were of by 6 Hz. I recorded again with a tuning fork and I got the 440 Hz as expected.   I used an electric tuning device to tune my guitar and it should have been perfectly tuned. What does this result mean? Is my tuning device broken or is there something I am missing? ![A String](http://i.imgur.com/pAwAsxU.png) ![Tuning Fork](http://i.imgur.com/cESDWvA.png) Here is the raw data from the 434 Hz peak:   Frequency[Hz] Dezibel[db]   ...   430,664063 -80,541397   431,336975 -77,470108   432,009888 -70,965828   432,682800 -62,022697   433,355713 -51,955708   434,028625 -38,634003   434,701538 -32,274822   435,374451 -34,905651   436,047363 -48,552521   436,720276 -55,133629   437,393188 -59,501816   438,066101 -72,979942   438,739014 -74,478226   439,411926 -83,606758   440,084839 -86,944931   440,757751 -85,912453   441,430664 -81,394493   442,103577 -93,493988   442,776489 -81,689384   443,449402 -83,698189   444,122314 -95,337143   444,795227 -106,526367   ...


If matter and light have dual-nature, shouldn't we able to explain the observed phenomenons using either wave or particle?

Historically wave and particle has been perceived as totally different phenomenons (before 20th century). Now is it widely accepted and there are experimental results to show that in fact both matter and light have a dual nature. Let's take light for example. Depending on the experiment it could behave as a wave(as in interference and diffraction) and it could be taken as a particle (as in explanation of photoelectric effect). If it has properties of both wave and particle at the same time, shouldn't we be able to explain the experiments with both wave and particle nature and not selecting either wave or particle? **Why particle or wave, why not particle and wave?** Please help me understand it and this question has been bugging me for quite some time now. I understand the standard explanation of both but I am having trouble putting them together. If there is anything I am missing please provide some link or reference to read.


Where to find Lunar Eclipse data

I am wondering whether there's a good resource to find data about upcoming Lunar Eclipses. For example, showing the percentage of the eclipse over time. Such as: 17:23 GMT - 0%, 17:40 GMT - 10%, etc.


Frequency of cosmic microwave background

Some people refer to cosmic microwave background's (CMB) frame of reference as an absolute one. If I understand correctly, we can measure 'absolute' velocity in this frame by using the Doppler effect. However, I don't know how we can know what the 'basis' frequency of CMB is (in its own frame)? Can it be obtained by some quantum-cosmological consideration?


How to interpret the constraints on Poisson's ratio values, physically?

If I'm not mistaken, a Young's modulus $E$ can theoretically take on any positive value without bound. Physically, I interpret this as though a solid can have any arbitrary "stiffness" (within the limits of its linear stress- strain region, of course). On the other hand, the range of possible Poisson's ratios is constrained to $[-1,0.5]$ for stable, isotropic, linearly elastic materials. I'm not quite sure how to interpret this physically. Why must the Poisson's ratio necessarily be constrained?


Would this pump water up? and if so, how far?

I had this idea of an osmotic pump way back in high school and I never got a satisfactory answer if it would work. If I had this configuration: ![osmotic pump](http://i.imgur.com/xWsW29w.png) Would it continually pump water up given ambient heat so long as the bottom reservoir is full? **EDIT** To explain what is happening, there is pure water in each of the dark blue reservoirs, saline in the cyan containers (same concentration of saline in each container) and a semipermeable membrane at the bottom and near the top of each container. The pure water in each reservoir would be sucked up into each container directly above it due to osmotic pressure (high water concentration flows to lower water concentration), and then dumped out at the top also due to osmotic pressure (saline to air which is almost 0% water concentration). Since the membrane is not permeable to salt, only the water is released from the container into the next higher reservoir. _**NOTE_** that the membrane at the top of each saline container doesn't touch the pure water in the reservoir it empties into. I'm also thinking that the saline containers may have to be completely filled with extra osmotic pressure to spare to counteract the pure water that sticks to the outside of the upper membrane and cause a reverse osmosis effect. Other possible tricks relying on surface tension and gravity might also aid in pulling the water away from the membrane. **END EDIT** If enough were stacked, would this allow for transporting water higher than the maximum that trees can transport (about 138m according to this article)?


Why is a laserpointer able to "erase" a glow-in-the-dark sticker?

a while ago I tried to charge a glow-in-the-dark sticker using a simple red laser pointer. It was a large sticker, of the type used to mark emergency exits and fire extinguishers here in Germany. I thought I could draw a picture this way, with glowing strokes. To my surprise, the exact opposite happened - the sticker was already glowing a little bit and the areas I illuminated with my laser turned dark instantly, as if the charge of the sticker was removed by the laserlight. The effect was reversible, the darkened areas would charge and glow as usual if exposed to normal light. So I was able to draw a picture after all - however, it was a negative. Can anyone explain why the sticker was discharged instead of charged by the laserlight?


How much does it cost every time your car stops for a traffic light?

Every time we have to stop the car, it is costing us extra money, because we have to then accelerate to full speed again. I would like to know how much. In order to simplify the situation, we can make these assumptions.   * we disregard cost of car maintenance (brake pads wearing out etc.). This is focused entirely on fuel economy.   * A car is always traveling at 60km/h when it needs to stop   * The car's fuel economy is 8L/100kms when traveling at 60km   * The cost of fuel is $1.25 per litre.   * The car weighs 1000kg I will be happy with either a definitive answer, an explanation of how to arrive at the answer, or an explanation of why there is not enough information in the question to come up with the answer.


Can smoke stay still in the air?

Can a small amount of smoke be dense enough to stay in the air keeping its shape for a minute or so?   Or does it always dissipate quickly?   If not smoke, can anything else stay in the air for a minute while keeping its shape?


What happens to the absorbed light energy?

When light comes across with a solid material, some of it is reflected, some of it passes through and some of it is absorbed. I understand the reflection and passing through, but I don't understand what happens when light is absorbed. Suppose that there is an enclosed box. Its material is thick enough so that no light can escape out. We put a Led diode in it whose internal resistance is zero (there is no loss as heat energy, all energy dissipated is given out as light). What are the possible steady state scenarios that can happen? Why and how some wavelengths of sun light heats up black objects while some other wave lengths do not? Why and how some wavelengths of light pulls the outer most electrons of atoms to higher energy levels while other wavelengths have no such effect? (I understand that energy of a photon must be enough to take electron to higher energy level, but why doesn't it take the electron temporarily a littler higher in the current energy level and then make it return back? I understand that an electron cannot stay between two energy levels, because those are unstable regions; but why doesn't electrons stay there even if it is as short as an instant?)


Pollen Particle Attracted to TV due to Which Force?

A pollen particle has no charge so I cannot understand how the Lorentz force $\bar{F} = q \bar{E} + q(\bar{v} \times \bar{B} )$ could explain the event. I speculated that it is because of the electric field that is generated to the dipole with a charge in the TV and the distance, more here. I have not yet confirmed that it would attract the pollen particle. Any better ideas?


quantization with constraints

let be a Hamiltonian system $ H= H(x,p) $ for this system there is a conserved quantity namely $ C=xp $ so the total system is invariant under rotation if we 'quantizy' this function $ Cf(x)=\lambda _{n}f(x) $ the result is known and $ f(x)= Ax^{{1/2}+i\lambda _{n}} $ for some constant 'A' then how is this function $ f(x) $ related to the quantization of the Hamiltonian $ H\Psi (x,t)= E_{n}\Psi (x,t) $ for example if the system has a SYMMETRY so there is a conserved quantity (there can be more constants of motion of course) how does this affect to the quantization of the TOTAL hamiltonian ??


FFT distortion, harmonics (singing wine glass)

I'm doing a school assignment on Singing Wine glasses (you rub the rim of the wine glass with a wet finger and it produces a pure tone). I have recorded $30\,\text{ms}$ of the "singing" at a sampling rate of $10\,\text{kHz}$ (total $300\,\text{samples}$) and have the following Sound pressure and FFT graphs: ![Sound pressure graph](http://i.stack.imgur.com/OInFM.png) Sound pressure graph ![FFT graph](http://i.stack.imgur.com/wvusd.png) FFT graph In the FFT graph, I'm assuming that the first peak is the fundamental frequency of the wine glass (natural frequency), but I'm not sure of the three others (they are integer multiples apart from the first peak). Are they due to the harmonics of the wine glass or the distortion? Also, if I were to have distortion in the graph, would it only occur at odd multiples of the fundamental frequency? **EDIT** : So the three peaks are harmonics. What are they caused by? Has it got something to do with modes of vibrations, distortion or something completely different? (this was my first post on SE, so please don't be harsh on me if I got it all wrong :) )


Ising model. What is large fluctuations of magnetization?

My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical Mechanics by Sacha Friedli and Yvan Velenik (The Book Project can be seen here) that talked about **magnetization $M_N$** (chapter 1 pages 17 and 20). My question about the Ising model is the following. > What conceptually mean **fluctuation of the magnetization $M_N$**? And > **large fluctuations of $M_N$**? **Up date:** Surely this question is related to another concept: fluctuations of spins.