Can additional airfoil enable a commercial liner to reach 100km altitude?

Assuming that it's engines are incapable of dying out at 100km altitude, would mere addition of airfoil area enable a commercial liner e.g. B787 to reach that altitude?


Could we use particle colliders as fusion generators?

So I know the basic gist is that fusion power's main issue is sustaining the fusion. I also know that there are two methods. The Torus method and the laser method. The torus magnetically contains plasma and heats it with radiation and accelerates the plasma around to make strong enough collisions that protons fuse. The laser method uses 192 lasers and focuses it on tiny frozen hydrogen pellets and aims to initiate fusion each time pellets are dropped. The though struck me when we could sorta combine the two designs together. The torus doesn't have to worry about making fusion happen at a specific location but it has issues in that the plasma is unevenly heated and leaks. On the other hand, the laser design is extremely complicated in the level of precision needed and would have to repeat this for every pellet. This lead me to think to make something precise and contained at the same time. I see that particle colliders are able to direct two beams of protons and have them collide at a specific spot with a very precise energy. Couldn't we tune the energy of the two beams of protons to the energy required for them to fuse? We have the ability to smash them into bits, surely we have the ability to have them fuse. (I'm thinking about the type of collider that circles two beams in opposite directions) It would be at much lower energies than normal colliders and would be very precise and it would be possible to fuse at a specific location that has greater leeway because for protons that missed collision, they'd just circle around again! Thus protons would efficiently be used and very little would be wasted. There wouldn't be problems of plasma leakage because we are focusing them in a thin tight beam. It seems that this idea has girth, or I feel this way at least, can someone back me up by offering some calculations on how to calculate the efficiency? How would I go about calculating the two circling beams of protons and at what specific velocity would be needed? etc.


Different batteries connected in parallel

If we have 2 batteries one of emf x and the other is of emf y and we connect them in series we get an effective emf of x+y. But what if we connect them in parallel, how to calculate the emf now?


Work on Ferromagnetic Object Due to Solenoid

I've been going through some equations and such trying to determine the work done by a solenoid on a ferromagnetic object. I have the following: Magnetic field due to solenoid: $\vec{B} = \langle0,0,\mu_0nI\rangle$ (Assuming coils are on xy-plane and current is counter-clockwise) Force of magnetic field: $ F = q\vec{v} \times \vec{B} $ Work: $ W = \int F \cdot dl $ Work of Magnetic Field: $ W = \int_c(q\vec{v} \times \langle0,0,\mu_onI\rangle) \cdot d\vec{r} $ For one, this seems to indicate a work of 0 if the object is not charged, which I have seen in some places but just doesn't seem right. Also, this does not take into account the properties of the object, such as relative permeability, which I guess could have some effect with the charge value. I'm trying to calculate the acceleration of a ferromagnetic object from a magnetic field, is there a better way to do this? I've thought about the following: $ \vec{a} = \frac{q\vec{v} \times \vec{B}}{m} $ However, this is where I started running into the charge issue and thought to calculate it from the work done.


Intelligent(?) Particles

Quite a while ago I read about a series of experiments that basically suggested that a certain kind of particle/atom/(something) were "intelligent" and could appear in two places at once, or essentially could "tell the future" when it came to navigating a "maze" ...I think it might have involved lasers or mirrors? Does any one a) know what I'm talking about, and b) have links/further information on it? Really don't have much more recollection than that I'm afraid. This will probably come across as a rather vague question so my apologies but hopefully someone will know what I'm talking about!


Deriving the "total" Bose Einstein density of states, including the condensate

Is is possible to derive the Bose-Einstein density of states containing the delta function representing the BE condensate?


How to tackle 'dot' product for spin matrices

I read a textbook today on quantum mechanics regarding the Pauli spin matrices for two particles, it gives the Hamiltonian as $$ H = \alpha[\sigma_z^1 + \sigma_z^2] + \gamma\vec{\sigma}^1\cdot\vec{\sigma}^2 $$ where $\vec{\sigma}^1$ and $\vec{\sigma}^2$ are the Pauli spin matrices for two particles separately. I think $\sigma_z$ is the z component, I found that $$ \sigma_z = \left( \begin{matrix} 1 & 0 \\\ 0 & -1 \end{matrix} \right) $$ which is 2x2 matrix. I am wondering if the $\sigma_z$ is the same for particle 1 and 2? if so, $$ \sigma_z^1 + \sigma_z^2 = 2\left( \begin{matrix} 1 & 0 \\\ 0 & -1 \end{matrix} \right) $$ Is that right? The most confusing part is $\vec{\sigma}^1\cdot\vec{\sigma}^2$, there are two matrices involved, so how does the dot product work? I am trying solve for the eigenvalues of H, it looks like to me that each $\sigma_z^1$ and $\sigma_z^2$ is 2x2, so there are two eigenvalues, is that correct?


What's the highest speed one can obtain safely at home?

Among common household appliances, things one can make from stuff in the garage or hardware store, and reasonably safe, e.g. within reach of hobbyists and high school kids entering a science fair, what is the highest speed of motion of any bit of matter one can obtain? The bit of matter, or surface points of some object, should be macroscopic - big enough to see, time the motion of somehow, make collisions with other bits of matter. Electrons aren't big enough! Fluids are fine too. Guns, dynamite would be too dangerous. The tips of a fan blade or shutter edges in a camera are fine. Using a drill to make something spin real fast might be okay if all mad scientists involved are careful.


Tension of rope in the gravitational field of earth

> Two balls of mass $m$ each one are connected with mass-less rope with the > same length as the radius of earth. The system is in free fall. Prove that > the tension of the rope when the nearest (to the earth) ball's distance from > the earth surface is $R_E/2$ is: $T = \frac{32}{225} mg$ ![Illustration](http://i.stack.imgur.com/TgZjm.png) What I did is the following: $F_1$ is a gravitation force exerted on the nearest ball by the earth: $F_1=G \frac{M_Em}{(1.5R_E)^2}$ $F_2$ is a gravitation force exerted on the farthest ball by the earth: $F_2=G \frac{M_E m}{(2.5R_E)^2}$ $T=F_1-F_2=G \frac{M_E m}{(1.5R_E)^2}-G \frac{M_E m}{(2.5R_E)^2}=\frac{G M_E m}{R_E^2} \left (\frac{4}{9} - \frac{4}{25} \right)=\frac{64}{225} mg$ However, my answer is somehow twice bigger than what is expected. Where am I wrong? What am I missing?


1. Has martian sunset same spectra than this earthly bluish-violet sunset?    2. What about sunset on Mercury?


Help an aspiring physicists what to self-study

This is probably not the kind of question you'll often encounter on this forum, but I think a bit of background is needed for this question to make sense and not seem like a duplicate: 2012 has been an annus horribilis in my life. I have lost a lot of close relatives in a sudden surge of cardiovascular diseases in my family. I also discovered I inherited genetic diseases and that I'll probably undergo the same fate sooner or later. One of the people I've lost is my father. We used to talk about physics all the time, and ever since I was 5 I kept telling him my dream was contributing to the field. When I lost him a couple of months ago, I used studying as an emotional outlet. He always emphasized the importance of academic excellence, and for this reason I got obsessed with studying and getting high grades even more than I ever did. I now am 1/80 in a top high school, but I am frustrated enormously. I find that I waste my time at high school, especially since I probably won't have as much time here as many other people do. I find the mathematics and physics boring and easy, and I feel like I'm wasting my time with certain classes which don't interest me at all (for example Latin). So I decided to study physics and mathematics outside of school. My school has been somewhat supportive, granting me a day per week off to do whatever I want, basically. I of course have a considerable amount of free time in addition to that day, since I ace almost every test without too much studying and without making my homework (not because I don't want to, but because I don't need to). I decided to self-study because I decided that life is too short (and mine will be even shorter, if I reach 50 I'd be lucky) to waste time. So my plan is to do at least the first 2 years of undergraduate physics in the 2 years I've got left at my high school. My main objective is to gain a mathematical and physical understanding of quantum mechanics, as advanced as I possibly can. I am currently studying Linear Algebra and Statistics, but I have a problem. I don't know what to study and, especially, in what order to study it. I have read literally read dozens of questions and answers as to what should be the mathematical/physical background for Quantum Mechanics (my future field of interest). But I find these to be too general, and I often am overwhelmed by it. In the same way you can get overwhelmed when you need to clean your house, but it’s so dirty that you don’t know where to start. So I would like your help. My current mathematical background:   * Basic differential calculus and no integral calculus, we will get that later on this year, however, I think it’s best for me to study it myself before we get it at school since it is crucial in physics. To show my level of differential calculus, this is about the toughest homework question we had to solve algebraically: _Given are the functions $f_p(x) = \dfrac{9\sqrt{x^2+p}}{x^2+2}$. The line $k$ with slope $2.5$ touches the function of $f_p$ at point $A$ with $x_A=-1$. Get the function of $k$ algebraically._   * Trigonometry and trigonometric functions. Again, as above, one of the toughest question we had to solve: _Given are the functions $f(x)=-3+2cos(x)$ and $g(x)=cos(x-0.25\pi)-2$. Get the functions $s(x)=f(x)+g(x)$ and $v(x) = f(x)-g(x)$ in the form $y(x)=a+bcos(c(x-d))$._   * Analytic Geometry (conic sections, tangency, bisections, you know the drill).   * And of course everything below this level. I probably forgot some things, but you can ask my in the comments if I know certain fields. We will get a lot more mathematics in the coming years, but I want you to disregard that fact when answering that questions. I want to self-study as much as I can, and my mathematics teacher is very fond of me, so if I know a topic before we get it in class, he will let me do other mathematics that I want (he even said this). So I won’t lose time by self-studying subjects we’ll get eventually, so don’t worry about that.  My current physics background (names of the chapters we discussed):   * Newton’s laws, Mechanical energy/forces    * Pressure and Heath    * Signal processing    * Electric currents (Ohm’s law, Series and parallel circuits, etc.)   * Again, everything below this level too (again, I’m probably forgetting stuff). Here exactly the same thing counts as with mathematics, we will get a lot more physics in the coming year, but again, disregard that. My physics teacher adores me, even more so than my mathematics teacher, so again, he won’t mind if I do something else if I know the material he’s discussing already. This is of higher level than American AP classes and British A-levels, keep that in mind. Now my question is, what mathematics and physics do I need to study, and my importantly, in which order do I need to study it, in order to have a basic understanding of quantum mechanics in 2 years? I know basic is a very general term, but I think you people, as people who studied it themselves, know what is realistic and achievable. I know this might seem like a duplicate of hundreds of previous questions, but it isn’t. All the other people asking this question have gotten answers that I don’t find suitable for me. Mostly the answers are from people who assume that you have to ‘have a basic understanding of this, a basic understanding of that’, etc. But how do I know what ‘basic means’? Also, now that you guys know exactly what I know and what I don’t, you can more finely tune the answers into my personal situation. As I said, currently I am doing Linear Algebra and Statistics, so you can omit those 2 from your answers, and start from the point I finished those 2 (which will be around January).   * p.s. If you want to recommend certain books, be my guest. If it's a good book, than money is no issue, I've saved up enough money throughout the years


Residues in QFT propagator

It is a well known fact that the location of the pole of a propagator (in QFT) can be interpreted as the physical mass. Is there an interpretation for the residue of the propagator? **Note:** I´m thinking of generalised propagator, not necessarily a propagator of a fundamental field.


Is the quantum analog of a probability distribution the wave function or the density matrix?

Classically, probability distributions are nonnegative real measures over the space of all possible outcomes which add up to 1. What they mean is open to debate between Bayesians, frequentists and ensemble interpretations. A degenerate distribution is the least random distribution with a probability of 1 for a given fixed event, and 0 for everything else. What is the analog of a classical probability distribution in quantum mechanics? Is it a wave function augmented with the Born interpretation for probabilities, or is it the density matrix? Does a pure density matrix correspond to a degenerate distribution?


is the nature of particle beam weapons in science fiction true to the reality of particle physics?

I am referring to the use of specific particle types such as an antiproton beam, positron beam, meson beam or muon beam for example in the likes of shows like star trek. I was curious if a beam of a certain particle would produce specific effects or is this purely wishful thinking. I am by no means a physicist so straightforward answers would be great if possible. If the answer could describe what effect each particle would have on materials, which particles are of particular use and which ones are impractical. Would it matter if the particle is normal or antimatter? I understand there is a lot of variables and factors like the way a particle decays, the particle half life and velocity affects its range distance, the energy of each particle, the materials the particles interact with, etc etc so any input is appreciated. To summarize, i am asking in terms of the realistic attribution of weapon effects to certain particle types and also non-weapon effects.


How does Earth's interior dynamo work?

I'm interested in getting a basic physical understanding of how Earth's magnetic field is generated. I understand that it's a "dynamo" type of effect, driven by convection currents in the molten outer core. These currents cause charges to move, and this generates the field. However, what I can't find a good explanation of is why there is a separation of charges in the first place. Presumably, moving neutrally charged molten iron would have the same effect as moving any other neutrally charged thing, i.e. it wouldn't create a field. And presumably, if the fluid wasn't moving then it would become neutral pretty quickly, since molten iron is a good electrical conductor. So am I right in thinking that the charge separation is the result of positive feedback, in that an intial deviation from neutrality would generate a field, and this would (somehow) cause a greater separation of charges, resulting in a kind of self-maintaining charge separation? Or is there another explanation? In either case, does anyone know of a good resource that explains the basic principles in physical terms? I know that the interior dynamo is a very complex phenomenon, but I'd like something that gives a good physical picture of how the electromagnetic and fluid dynamical phenomena interact, rather than diving straight into partial differential equations.


Why is spacetime curved by mass but not charge?

It is written everywhere that gravity is curvature of spacetime caused by the mass of the objects or something to the same effect. This raises a question with me: why isn't spacetime curved due to other forces or aspects of bodies? Why isn't it that there are curvatures related to the charge of a body or the spin of particles or any other characteristics?


What does the notation $|x_1,x_2\rangle$ mean?

I would like clarification on an equation in the paper "Free matter wave packet teleportation via cold-molecule dynamics", L. Fisch and G. Kurizki, _Europhysics Letters_ **75** (2006), pp. 847-853, DOI: 10.1209/epl/i2006-10205-7. The paper talks about entangling two particles translationally, meaning that two particles' position and momenta are correlated such that a precise measurement of particle 1 will cause particle 2's spread in momenta to be uncertain, vice versa. So the equation is equation (2) in the paper, $$\langle x_1, x_2 | \Psi \rangle= N e^{-\left({x_+}/{2\Delta x_+}\right)^2}N e^{-\left({x_-}/{2\Delta x_-}\right)^2}$$ where $x_+ = (x_1 + x_2)/2$, $x_- = x_1 - x_2$, and $N$ is a normalization constant. I'm assuming that the $\Delta x_\pm$ are the standard deviations of $x_\pm$. I've never seen bra-ket notation with "$\langle x_1,x_2|$" in it. This confuses me a lot! It doesn't make sense to have $x_1$ (comma) $x_2$. What the heck does this mean? I am interpreting this as the expectation value of the positions of the two entangled particles where $|\Psi\rangle$ is the wave function of two translationally entangled particles. Can someone please help me?


What would happen if the Earth was tidally locked with the Sun?

I'm thinking of writing a short story set on a version of Earth that is tidally locked to the Sun. I'm not exactly sure how to research the topic. Here's a number of questions about what would happen:   * How hot would the light side get? Are we talking ocean-boiling levels? I imagine that life would eventually flourish, given the massive constant energy source. Is this accurate?     * On that note, I imagine massive thunderstorms along all the coasts due to increased evaporation. How bad would they get? Would the ground ever see the Sun, or only rainfall?   * How cold would the dark side get? Is it conceivable that any life could still exist there? (Life has proven itself quite versitile in the past, i.e. life at the bottom of the ocean.)   * What wind speed would the twilight zone experience? I imagine the atmosphere would transfer heat from one side to the other, but would the wind speeds be bearable? In what direction would air flow?   * I hear that the oceans would recede into disjoint northern and southern oceans if the world stopped spinning. Would this also happen if the Earth became tidally locked?   * Would the Sun create a 'tidal' bulge in the ocean at the apex of the light side? Would this or the above dominate ocean behavior?   * Would we completely lose the magnetic field? Would life be able to survive without such shielding from magnetic radiation?   * Would the Moon eventually unlock the Earth? What state would the Moon have to be in for there to be both a locking between the Sun and the Earth as well as the Earth and the Moon?   * What other radical differences would exist between our Earth and a tidally locked alternative?


What amount of force is needed to topple a person?

Assuming no sliding and that the shoulder is 1.2m from the feet, what force is required to topple a person weighing 70 Kg standing with his feet spread 0.9 m? If possible, please include an explanation about your answer.


Why is speed/position relative but acceleration not?

I think i understand it now, if found this: link I know that position and speed are relative. There is no such thing as universal coordinates. Then why is acceleration absolute? Is the 3th and 4th derivative of position to time also absolute? Where/how can i see this in the math/laws of motion? For example: you are in a rocket and you have an accelerometer with you, and someone else is standing on an astroid that is not attracted by gravity towards something else, so it has no net force on it. If the engines of the rocket are turned on, then you will see that on the accelerometer, and you will know that it is you that is accelerating, not the astroid. Also if the universe were completely empty, except for a bucket of water. If the water would be pushed towards the edges of the bucket, then we would know that the bucket is rotating around its axis. But what would happen if you could rotate space itself around the bucket? It probably is because $F=ma$ and not something else like $F=m^2a^3+2a+...$, is that correct? Can $F=ma$ be deduces from deeper principles, or is it an experimental law?


How do photon emitters and photon detectors work?

The interpretation of the double slit experiment is very strange and i want to understand how they did it before I give up my concept of reality. With the double slit experiment a interference pattern is created even when you emit just one photon. However, when you use photon detectors to find out which slit the photon went though, the photon goes in straight line. So firstly I want to know how do the photon emitters work and secondly I want to know how these photon detectors work. How are you even meant to detect a photon without even touching it? also how big the the slits?


Topological Phases and Confinement

I recently attended a talk in which the speaker defined a topological phase as "A phase which has a gap above the ground state for bulk excitations in the thermodynamic limit." I am interested in what sense then can we think of confinement in non-Abelian Yang-Mills theories as topological phases. What I'm looking for are the analogies; what would the **thermodynamic limit** and the **bulk excitations** mean if we were talking about a YM theory (QCD, for instance). The thermodynamic limit is the number of particles $N\to\infty$, which I suppose we can think of as the number of Feynman diagrams (order of the loops) growing as large as possible. "The bulk" seems a bit more vague (which is perhaps because of my definition), but it seems like bound states of quarks is the appropriate notion for that. So, is it possible to (correctly) say something like "QCD is a topological phase for the standard model"? If not, is there a clear reason why this is not the case?


Can open, unsafe nuclear fusion reaction burn the atmosphere?

I happened to hear people saying that the nuclear fusion bomb tests could set the atmosphere on fire. I have some serious doubts about that - but I have no facts.   Nuclear fusion reaction requires $15*10^{6}$ kelvins to start. If we produce such temperature in " _open air_ " would the atmosphere become a fuel for further fusion? Shouldn't the whole thing just be torn apart by its terrible pressure?


Quantum Mechanical Effects of an object accelerating near speed of light $c$?

Consider a space ship, undergoing constant acceleration (which for our purposes means that the same amount of energy is being used per second to increase its speed). According to special relativity the ship will accelerate but in such a way that it will approach the speed of light $c$, but never reach the speed itself or cross it. This means however that the more time we spend accelerating the space ship, the closer and closer it will get to the speed of light. Which basically amounts to: our knowledge, or accuracy of our velocity is going to steadily go up. Heisenberg's Uncertainty principle states that there is limit to how accurately we can know our velocity before we need to give up some information about our position? What does this mean in our context? Say we reach the critical threshold where we are accurate to some 35+ significant digits aka 0.999999999999999999999999999999999999999999999999999999999999999999c is our speed. We need to lose accuracy of our position between our start and endpoint (assuming this trip has a definite endpoint)? Whats happening? Is the ship suddenly making jumps to random locations? Is it spreading out like a wave, where we the faster we go, the less likely we are to know when we reached our endpoint? I'm very very curious. * * * ## EXTENSION: Additional Thought Consider an object in circular orbit around a black hole, outside of the event horizon (the black hole itself is stationary) and these are the only 2 systems present, with the object in question having very negligible mass compared to the black hole. As the object is brought closer and closer to the black hole, the centripetal force it experiences, obviously goes up, causing to orbit at a faster speed. The closer you bring it towards the center of the black hole, the faster the object will orbit, allowing you to bring it arbitrary close to value of C. According to heisenberg as the velocity increases to an accuracy beyond the reduced planck's constant (0.9999...)c the position of the object becomes increasingly unknown. It would start to "smear" out in a circle around the orbit, transforming into a haze which can be observed. Or So I think... Is this correct intuition?


Accuracy and Error of Atomic Clocks

I'm quoting a passage from my notes: > The development of clocks based on atomic oscillations allowed measures of > timing with accuracy on the order of $1$ part in $10^{14}$, corresponding to > errors of less than one microsecond (one millionth of a second) per year. I do not understand what the accuracy of $1$ part in $10^{14}$ means. Does it mean that the atomic clocks can tell us the time accurate and ceratain to $10^{-14}s$? How should I understand this? Moreover, what is meant by the error of one microsecond per year? Is it a kind of uncertainty in measurement? How should I understand it? I googled this topic and found information about the atomic clocks and also reviewed the definitions of accuracy and error; however, I'm not able to make any sensisble connection between the concepts. Please help me, thank you.


What is negative about negative energy states in the Dirac equation?

This question is a follow up to What was missing in Dirac's argument to come up with the modern interpretation of the positron? There still is some confusion in my mind about the so-called "negative energy" solutions to the Dirac equation. Solving the Dirac equation one finds the spectrum of allowed energies includes both positive and negative solutions. What does this negativity refer to? Given that the Dirac equation is symmetric under charge conjugation, the convention to call one positive and the other negative appears perfectly arbitrary. Would it be therefore correct to refer to the electrons as "negative energy positrons" ? In a similar spirit, physicists used to be worried about the "negative energy" solutions decaying into infinity through emission of photons. By the same symmetry argument, this should also be a problem for photons. It is not entirely clear to me how the quantization of the field supresses this issue : is the "photon emission" for the negative state re-interpreted as photon absorption by a positron ? My understanding is that the whole discussion about "positive" or "negative" energy solutions is misleading : what matters is the physical content through the QED interaction hamiltonian, which does not predict this infinite descent. Is this correct? Edit: I think I understand the source of my confusion after the comments. If I get it right, the Dirac sea picture is equivalent to the freedom of choice in the formally infinite vacuum energy one observes after quantization of the QED Hamiltonian. Holes in the sea are positive-energy positrons, equivalent to the action of the positron creation operator on the vacuum. Is this correct?


Why does the thickness of a wire affect resistance?

For small thicknesses of wire, it's pretty obvious why resistance affects thickness. (The electronics squeeze to get through). But after a certain thickness shouldn't the thickness become irrelevant? For example if your trying to pour a bucket of water through a straw, the thickness of the straw is obviously gonna be a bottle neck- the bigger the straw, the easier it is for water to get through. But if you try to pour a bucket of water through a tunnel - the size of the tunnel doesn't really matter, because the tunnel is already big. So after a certain thickness shouldn't the thickness stop mattering?


Relativity question: frequency shift under constant acceleration

Okay, my buddy tells me this: Let there be a starship, ovoid, and me and my buddy stand each at the extremities of the ship, him below the roof, me on the floor. We start a journey and the ship accelerates at a constant rate, let's say $1g$, in the direction of the axis of the ship. _My buddy says_ : since the ship is accelerating, when he strobe (on off on off) a light from the room, back to me, at a frequency $F$, I'll see a shifted frequency $F' = F + \delta f$. If he switches the light at $1Hz$, I'll see $1.01Hz$ for instance. _My take on the thing_ tells me that in this case, there's no shift: we're both immobile in our referential, and the light will travel at $c$ in this referential. Who's wrong?


Why does a coulomb explosion induce fusion?

If you strip the valence electrons apart with a very short intense electromagnetic field the remaining core explodes in a so called coulomb explosion. But experiments have shown that under certain cases fusion does occur in a manner, that the ions are accelerated and you get a non maxwellian velocity distribution. Can you explain the process a little bit more and show how it is possible to overcome the nuclear repulsion for fusion? The wikipedia page to this topic is a little bit missleading, so I give you a paper Efficient fusion neutron generation from heteronuclear clusters in intense femtosecond laser fields that this kind of fusion is indeed possible and experimentally proven.


We tend to think the action of a constant force...?

This is a school exercise. We tend to think that the action of a constant force produces a constant movement speed as well. How can you explain this situation in accordance with Newton's second law? Because as the force will end up in a certain time that means there will not be a movement of constant speed; I'm correct?


How do we recognize hardware used in accelerator physics

When I see a new accelerator in real life or on a picture, I always find it interesting to see how many thing I can recognize. In that way, I can also get a small first idea of how the accelerator is working. Here is a picture, I have taken of LEIR at CERN![LEIR](http://i.stack.imgur.com/d8t7B.jpg) Help me to be able to recognize even more stuff, than I can now(I will post a few answers myself) Suggested answer form:   * **Title**   * **Images**   * **One line description**   * **Link**


Light pulses and energy-time uncertainty principle

Suppose we have a monochromatic light beam. We put an obstacle between source and observer and remove it repeatedly by certain frequency such that observer sees an oscillating intensity of light. Will the observer see different frequencies or only the original frequency? Does the energy-time uncertainty principle apply in this case?


Impurities involved in nucleation centres

When magmas begin to crystallise, a first step is the formation of a crystal nucleus around an impurity (nucleation centre), whereby a few of the right atoms get together to form a speck of a crystal. I know that impurities are not always necessary for crystallisation to occur but I'm curious to know what these impurities are?


Charges and their configurations

Can we treat any charge configuration as small point charges by using superimposition principle to derive electric fields, forces and other things ? For example suppose we have a symmetrically charged cylinder, from the distance outside the cylinder, we can treat it like a line charge along the axis of the cylinder. We know that in the original charge distribution the charges do not sit together at 0 distance from one another, but when we consider it as a line charge we do not think about the quantisation therein; We treat the line charge as one continous thread of point charges placed at 0 distance from one another. Back to my question, since this line charge is just an assumption, can we extend our assumption and treat it like individual point charges sitting next to each other, is there any limitation to this assumption ?


How do I show that all Brillouin zones have the same volume?

I have read in a few books that all Brillouin zones have the same volume, and I can vaguely see how it works, but have not been able to think up a formal proof. Help?


Is it possible that QM is just GR?

The more I learn about General Relativity, the more it seems like it isn't fully understood. It seems that before it's full consequences were exhaustively understood, not 10 years after its discovery, QM came on the scene and stole the limelight. Now it seems like a "boring" field without much funding, even though all but the most trivial and artificial types of solutions to the field equations are known. Here, for example, @Ron Maimon describes how classically a type of black hole allows solutions in which a particle can cross the event horizon, and then exit the event horizon at an earlier time, seemingly leading to causal paradoxes. It sounds like this is an issue that was never fully resolved. It seems the sort of very messy thing that, once properly understood, could lead to some very odd physical behavior. Is it possible that all particles are just extremal black holes, and that Quantum Mechanics is just an emergent property of the solution to Einstein's field equations for the interactions between extremal black holes going backwards and forwards and time? Does something like Bell's inequality rule out this sort of idea? **EDIT** : There are some papers purporting to do this. Mitchel Porter pointed out these: McCorkle, Hadley I also found: McCorkle And then there is Mendel Sachs who has written a number of books purporting to derive QM from GR.


Physical interpretation of normalization of wave fuctions

Does normalization of wave function mean that we are getting our state vector to unit length? If that's the case what does it mean physically? Also is the underlying vector space finite dimensional? If yes, then what is the dimension and how do I find the basis vectors?


Determing what is differnece beetwen eigenvalues for attractive Coulomb Field (Hydrogen) calculated by exact method and WKB aproach

I have task to compare eignevalues gained by exact calculation on electron in Coulomb attractive field (hydrogen) and gained by WKB method.. As far as I get, eigenvalues gained with exact method are E=13.6 / (n^2) and for WKB method all i find is exact same answer E=13.6 / (n+l+1)^2 exept there is l. I Don't understand what does it means exactlly...


Street Light Interference Phenomenon

Is there a scientific approach that can explain the street light interference phenomenon? Everytime I walk past a Streetlight it turns off.


How does a holographic object change perspective when the image is rotated?

Fundamentally i want to know: **How do holograms work?** The problem with that question is that normally you will end up with pages and pages talking about:   * a laser   * a beam splitter   * a diffuser   * the object being imaged   * object beam   * reference beam   * mirror   * holographic emulsion Even Wikipedia is heavy on _how to make a hologram_, rather than **how does a hologram work**. * * * Other people have mentioned stereoscopic vision; how having two eyes gives the illusion of a 3d object. That is also irrelavent, since someone with one eye (or, in my case, one eye closed) can still experience a hologram. What i am trying to figure out is _how does a hologram work?_. More to the point, how is it that rotating a **flat** holographic sticker allows the virtual object to change orientation - allowing me to see content that was not there a moment ago? * * * Wikipedia has an image that mentions _reconstructing a virtual 3d object_ : ![enter image description here](http://i.stack.imgur.com/tEyZM.png) Some problems that that image, though, is that my credit card:   * has no _reference beam_   * is not being viewed at a 45 degree angle (meaning no interference can happen) Assuming i have a holographic image of a simple cube. If i am looking at the holographic plate straight on, i will only see a square (i.e. the face of the cube closest to me): ![enter image description here](http://i.stack.imgur.com/BHgQO.png) If i rotate the holographic plate, so the right side of the plate is further away, the virtual cube will rotate, and i will actually be able to see the **_left_** face of the cube: ![enter image description here](http://i.stack.imgur.com/1XT9U.png) What is happening in the **flat, 2-dimensional, holographic sticker** that it can display _continuously_ different information as i rotate it? What is the mechanics of this holographic _"paper"_ that it can present my eye different images?


How are quantum potential wells fabricated?

Potential wells, such as infinite and finite potential well, have been the standard examples in quantum mechanics textbooks for tens of years. They started being only theoretical toy models but as time progresses scientists succeeded in fabricated them which resulted in the nanotechnology revolution. 1-Is the fabrication process too technical to be explained to the undergraduate students who are taking a course in quantum mechanics? 2-How such potential wells are fabricated in practice ? 3-Why engineering potentials of certain shapes became only possible recently, what changed in science that made it possible (since obviously on the theoretical level quantum mechanics did not change) ?


States diagonal in the tensor product of Bell states.

Bell-diagonal states are 2-qubit states that are diagonal in the Bell basis. Since those states lie in $\mathbb{C}^{2} \otimes \mathbb{C}^{2}$, the Peres- Horodecki criterion is a sufficient condition to show separability and it's also pretty easy to check: $\rho = \sum_{i \in [0,3]}\lambda_i|\psi_{i}\rangle\langle\psi_{i}| $ is PPT (or separable) if and only if $Tr(\rho) \geq 2\lambda_i \geq 0$ for every $i$. (Here {$|\psi_{i}\rangle$} are the Bell states) In my research I am dealing with a generalization of those states. In particular, my question is about states in $\mathbb{C}^{2^d} \otimes \mathbb{C}^{2^d}$ that are diagonal in the basis given by the $d$-fold tensor product of Bell states. For example, for $d=2$, the states I am considering are diagonal in the basis: $$ |\psi_{0}\rangle\otimes|\psi_{0}\rangle,|\psi_{0}\rangle\otimes|\psi_{1}\rangle, \ldots,|\psi_{3}\rangle\otimes|\psi_{3}\rangle. $$ I am wondering the following: > are there some nice criteria already known to check when these states are > PPT or separable? Notice that those states are in general different from the states diagonal in what is called the generalized Bell basis in literature.


General procedure for Clebsch-Gordan expansions

I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps an example derivation of the well known expression of spherical harmonics would be helpful)? I know it has something to do with being able to compute the multiplicities of the tensor product of the irreducible representations, but I don't know how one would do that.


partial trace with sparse matrices

Let $\rho_{ABCD}$ be a sparse matrix of 4 systems each in a $d$-dimensional Hilbert space. For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the code proposed in http://www3.imperial.ac.uk/people/m.tame/research. I would need an efficient algorithm for calculating $\rho_{AD}$ where $d\geq7$. The algorithm of the site above does not exploit any properties of the matrix and it requires a lot of permutations and rearrangements. Do you know an efficient algorithm for calculating the partial trace of qudit which uses the fact that the matrix is sparse? It would also be interesting if the algorithm can take advantage of parallel computation. Thank you very much in advance for your answers. Regards, Silvio


Kramer's-Kronig relations for the electron Self-Energy Σ

I'm currently studying an article by Maslov, in particular the first section about higher corrections to Fermi-liquid behavior of interacting electron systems. Unfortunately, I've hit a snag when trying to understand an argument concerning the (retarded) self-energy $\Sigma^R(ε,k)$. Maslov states that in a Fermi liquid, the real part and the imaginary part of the self-energy $\Sigma^R(ε,k)$ are given by $$ \mathop{\text{Re}}\Sigma^R(ε,k) = -Aε + B\xi_k + \dots $$ $$ -\mathop{\text{Im}}\Sigma^R(ε,k) = C(ε^2 + \pi^2T^2) + \dots $$ (equations 2.4a and 2.4b). These equations seem reasonable: when plugged into the fermion propagator, $$ G^R(ε,k) = \frac1{ε + i\delta - \xi_k - \Sigma^R(ε,k)} $$ the real part slightly modifies the dispersion relation $ε = \xi_k$ slightly and the imaginary part slightly broadens the peak. That's what I'd call a Fermi liquid: the bare electron peaks are smeared out a bit, but everything else stays as usual. Now, Maslov goes on to derive higher-order corrections to the imaginary part of the self-energy, for instance of the form $$ \mathop{\text{Im}}\Sigma^R(ε) = Cε^2 + D|ε|^3 + \dots .$$ First, I do not quite understand how to interpret this expansion. > How am I to understand the expansions in orders of $ε$? I suppose that $ε$ > is small, but in relation to what? The Fermi level seems to be given by > $ε=0$. Second, he states that this expansion is to be understood "on the mass-shell". > I take it that "on the mass shell" means to set $\xi_k=ε$? But what does the > expansion mean, then? Maybe I am supposed to expand in orders of > $(ε-\xi_k)$? Now the question that is the most important to me. Maslov argues that the real part of the self-energy can be obtained via the Kramers-Kronig relation from the imaginary part of self-energy. My problem is that the corresponding integrals diverge. > How can $$ \mathop{\text{Re}}\Sigma^R(ε,k) = > \mathcal{P}\frac1{\pi}\int_{-\infty}^{\infty} d\omega > \frac{\mathop{\text{Im}}\Sigma^R(\omega,k)}{\omega-ε} $$ be understood for > non-integrable functions like $\mathop{\text{Im}}\Sigma^R(ε,k) = ε^2$? It probably has to do with $ε$ being small, but I don't really understand what is going on. * * * I should probably mention my motivation for these questions: I have calculated the imaginary part of the self-energy for the one-dimensional Luttinger liquid $\xi_k=|k|$ as $$ \mathop{\text{Im}}\Sigma^R(ε,k) = (|ε|-|k|)θ(|ε|-|k|)\mathop{\text{sgn}}(ε) $$ and would like to make the connection to Maslov's interpretation and results. In particular, I want to calculate the imaginary part of the self-energy with the Kramers-Kronig relations.


What is Hawking radiation and how does it cause a black hole to evaporate?

My understanding is that Hawking radiation isn't _really_ radiated from a black hole, but rather occurs when a particle anti-particle pair spontaneously pop into existence, and before they can annihilate each other, the antiparticle gets sucked into the black hole while the particle escapes. In this way it appears that matter has escaped the black hole because it has lost some mass and that amount of mass is now zipping away from it. Is this correct? If so, wouldn't it be equally likely that the particle be trapped in the black hole and the antiparticle go zipping away, appearing as if the black hole is spontaneously growing and emitting antimatter? How is it that this process can become unbalanced and cause a black hole to eventually emerge from its event horizon and evaporate into cosmic soup over eons?


How does the energy of a sound wave decrease with the distance

More precisely, how small is the potency a listener hears, compared to the potency of the emitter. I'd like to present a simple and yet reasonable approximation, to a high school audience (I am a teacher) Intuitively, it should decrease with a square (of distance; because of the expansion of the area the wave covers) and exponentially (because of accumulation losses in the way) .Here, they mention both decreases: http://www.sfu.ca/sonic-studio/handbook/Sound_Propagation.html . The air absorption component is linear in dB (which, as far as I know, means exponential on energy) I am just not sure of how to put them together, and if there are other ideas that a first approximation should cover.


Discussions of the axioms of AQFT

The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 **38** 771-846, "Outline of axiomatic relativistic quantum field theory". I'm looking for any more recent review that seriously discusses the axioms. A critique of the Haag-Kastler axioms would also be welcome, but I would prefer to stay close enough to Lagrangian QFT to allow relatively immediate characterization of the difference between models of the reduced axiomatic system and the standard models that are relatively empirically successful. I'm specially interested in any reviews that include a discussion of what models are possible if one relinquishes the existence of a lowest energy vacuum state (we know that, at least, this weakening allows the construction of thermal sectors of the free field, and that such a sector contains a thermal state that is thermodynamically stable even though it is not minimum energy, and that a Poincaré invariant "extra quantum fluctuations" sector is also possible—I'd like to know what is the full gamut of such models?). [Added: This question was partly inspired by a Cosmic Variance post on the subject of QFT, particularly the link to John Norton, obviously with my research interests added.]


How to prove quantum N=4 Super-Yang-Mills is superconformal?

I'm especially interested in elegant illuminating proofs which don't involve a lot of straightforward technical computations Also, does a non-perturbative proof exist?


What force is responsible for anti-gravity?

I've seen several video which claims that is anti-gravity. I am sure at least one of them, use a kind of electricity to lift an object! (triangle lifter), I would guess electricity lift that object by air. But what is the equation?, I have no idea.


Phase Structure of (Quantum) Gauge Theory

> **Question** : How to **classify/characterize the phase structure of > (quantum) gauge theory**? Gauge Theory (say with a gauge group $G_g$) is a powerful quantum field theoretic(QFT) tool to describe many-body quantum nature (because QFT naturally serves for understanding many-body quantum problem with (quasi-)particle creation/annihilation). **Classification of gauge theory** shall be something profound, in a sense that gauge fields (p-form $A_\mu$, $B_{\mu\nu}$, or connections of $G_g$-bundle etc) are just mediators propagating the interactions between matter fields (fermion $\psi$, boson $\phi$). Thus, effectively, we may "integrate out" or "smooth over" the matter fields, to obtain an effective gauge theory described purely by gauge fields ($A_\mu$, $B_{\mu\nu}$, etc). **Characterization of gauge theory** should NOT simply rely on its gauge group $G_g$, due to "Gauge symmetry is not a symmetry". We should not classify (its distinct or the same phases) or characterize (its properties) ONLY by the gauge group $G_g$. What I have been taught is that some familiar terms to describe the phase structure of (quantum) gauge theories, are: (1) confined or deconfined (2) gapped or gapless (3) Higgs phase (4) Coulomb phase (5) topological or not. (6) weakly-coupling or strongly-coupling > **sub-Question A.** : Is this list above (1)-(6) somehow enough to address > the phase structure of gauge theory? What are other important properties > people look for to classify/characterize the phase structure of gauge > theory? Like entanglement? How? (for example, in **2+1D gapped deconfined weak-coupling topological gauge theory** with finite ground state degeneracy on the $\mathbb{T}^2$ torus describes anyons can be classified/characterized by braiding statistics $S$ matrix (mutual statistics) and $T$ (topological spin) matrix.) > **sub-Question B.** : Are these properties (1)-(6) somehow related instead > of independent to each other? It seems to me that **confined** of gauge fields implies that the matter fields are **gapped**? Such as 3+1D Non-Abelian Yang-Mills at IR low energy has **confinement** , then we have the Millennium prize's Yang–Mills(YM) existence and mass gap induced **gapped** mass $\Delta>0$ for the least massive particle, both(?) for the matter field or the gauge fields (glueball?). So **confinement** and **gapped** mass $\Delta>0$ are related for 3+1D YM theory. Intuitively, I thought **confinement $\leftrightarrow$ gapped** , **deconfinement $\leftrightarrow$ gapless**. However, in 2+1D, condensed matter people study $Z_2$, U(1) spin-liquids, certain kind of 2+1D gauge theory, one may need to ask whether it is (1) confined or deconfined, (2) gapped or gapless, separate issues. So in 2+1D case, **the deconfined can be gapped**? **the confined can be gapless?** Why is that? Should one uses Renormalization group(RG) argument by Polyakov? how 2+1D/3+1D RG flow differently affect this (1) confined or deconfined, (2) gapped or gapless, separate issues? > **sub-Question C.** : are there **known mathematical objects to classify > gauge theory**? perhaps, say **other than/beyond the recently-more-familiar group cohomology** : either topological group cohomology $H^{d+1}(BG_g,U(1))$ using classifying space $BG_g$ of $G_g$, or Borel group cohomology $\mathcal{H}^{d+1}(G_g,U(1))$ recently studied in SPT and topological gauge theory and Dijkgraaf-Witten?


Cosmological redshift in a lab?

I want to consider a thought experiment. Lets ignore technical problems of actually performing such an experiment. Consider two photons having the same wavelength. We send 1 photon to a distant galaxy (millions of light years away). The photon would hit a mirror there and return to Earth. On Earth (I assume) a cosmological redshift would be detected. At the same time we keep the second photon on Earth in small container with perfect mirrors where it bounces back and forth. Would the photon in the container exhibit the same cosmological redshift as the photon that traveled to the distant galaxy and back? If so, (now back to technical problems) could the redshift be ever measured in the lab or is the effect many orders of magnitude too small to be ever measured in a lab on Earth, not to mention the problem of constructing a perfect mirror to keep the photon?


Computing an average escape distance for a particle

Somewhere in a two dimensional convex bulk of particles (pic related) on a random position a reaction takes place and a particle is sent out in a random direction with a constant velocity $v$. What is the average distance such a particle travels until it leaves the bulk? ![enter image description here](http://i.imgur.com/PxTWz.gif) Might be codable if one puts a grid over the planes and weightens with a yes/no function if the stating position is within the bulk. Then I'd cut that object with n corners (8 in the pic) into pizza slices and do some geometry to compute the distances in all directions and integrate over all of these and all staring point. I really wonder if there is a good way to do this on a piece of paper, the problem being how to parametrize the points which are inside and not counting these outside. Monte-Carlo computations for regular polygons would be an interesting semi- solution too. Edit: Not that it matters much, but the question is motivated by the question Mean free path of UV photon and is part of me wondering about the escape route for particle entering a bunch of mass, and there specifically on the the dependence on the two length characteristica cloud dimensions and mean free path derived by the clouds constitution. Given that the direction of a particle after a collision is random and so it will probably have to make a detour through the cloud, what is the relation between the average cloud radius to the mean free patch such that the particle is able to leave after only one reaction. Because a collision is almost a reset, I have the suspicion that the escape time only falls slowly with the number of collisions a particles had to endure. The simulation of this might be a more standard question, i.e. starting at a random position and choosing a random direction after the mean free path traveled, how manny mean free paths does it take for a particle to escape a random polygon with characteristic measure being some multiple of the mean free path.


Why is the BCS trial function valid across the BEC-BCS crossover?

In one of the two main theoretical approaches used in describing ultracold Fermi gases and the BEC-BCS crossover, the so-called BCS-Leggett approach, the starting point is the BCS trial wavefunction: $$ \mid BCS \rangle \equiv \prod_{\mathbf{k}} \left( u_{\mathbf{k}} + v_{\mathbf{k}} P^\dagger_{\mathbf{k}} \right) \mid 0 \rangle $$ where the $P^\dagger_{\mathbf{k}}$ operator creates a Cooper pair. It is often asserted that this wavefunction, which may seem tailored for a BCS-like problem, has far greater validity and can also be successfully exploited in describing the BEC-BCS crossover (see for instance: http://arxiv.org/abs/cond- mat/0404274). Even looking at the original articles by Leggett and Eagles (cited in the reference above) I cannot see why $\mid BCS \rangle$ should be valid in the BEC regime: I am looking for a review article (or even a textbook) addressing this issue.


Photon in a weighted superposition of states

Consider an experiment that produces photons in an entangled state such as $1/\sqrt{2}(|{H,H}\rangle+|{V,V}\rangle)$. The photons are in a superposition of horizontal and vertical polarization, and the way we analyze this is to say that the photons are in **both** states at the same time. Though this is odd, I can eventually reconcile it. However, the photons can also be in an entangled state such as $\sqrt{0.2}|H,H\rangle+\sqrt{0.8}|V,V\rangle$. Again, the photons are in **both** states at the same time, but do we say that they is somehow more in one state than the other? How can we think of this unevenly weighted superposition of states?


Have negative pressures any physical meaning?

Some cubic thermodynamical equations of state predict negative pressures, have negative pressures any physical meaning? Could they be related to negative mass?


The value of current and voltage in a circuit

![enter image description here](http://i.stack.imgur.com/s2KzU.png) The picture is just for example. I don't know why $i$ and $i_1$ have different directions and $i+i_1=0$ according to KCL. Also, the value of voltage at each element. I mean in why the $V$ of the end of $R_1$ is negative but the start of $R_2$ is positive. Is the sign is just to indicate the direction of current, where the voltage is higher than the other at each element but not tell its value is positive or negative. Moreover, does the $V$ value of each element is define by its difference in $V$ which mean $\Delta V$.


current induced in magnetic field

"If a wire loop is completely in magnetic field no current is induced as voltage induced is balanced by an equal and opposite voltage. " My guess for this statement is that the loop wire must be stationary and that voltage is zero if its equal on both sides of the wire my question is if current will stil be induced if the wire loop is moving but is still completely in the magnetic field. (I know how as it enters and leaves induced current moves either clockwise or anti so what wil happen if its moving but not entering or leaving)


Can we change frame of reference twice in a single problem?

My question has an inclined plane of mass $M$ and simple block kept on it, of mass $m$ (Both on a table). All surfaces are friction-less. Both of the objects would move, block down the incline and inclined plane parallel to the table, somewhat opposite to the block. Can the two equations I make be from the Free Body Diagram (FBD) of incline, in GROUND frame, and FBD of block in the INCLINED-PLANE frame? Or do I need to solve in a single frame(either GROUND or INCLINED-PLANE)?


Double-slit experiment simulated with water waves?

We all know the explanation videos and other material using the water waves analogy to illustrate the propagation of electrons or photons and the interference patterns measured in the the single-slit and double-slits experiments. Being just an analogy it misses for sure many attributes by which light/electron waves differ from water waves. BUT: If limited only to use water-waves analogy would it be possible to simulate the impact of the observer/detector in the experiments by means of water waves (yes, i'm smiling my self at this a little ;) What would be the properties of such a detector-by-means-of-waves needed to simulate the collapse of the interference pattern, for example? In other words is it possible to rebuild the double-slit experiment with such a water-waves setup and with same known results? How about in theory? What ("strange") requirements are there? For starters maybe let's drop the switching the slit-result and let's assume when the observer is turned on the water wave shows to be originating always from the same slit... At what earliest point does this "model" break? How? Thanks!


Calculating Lyapunov exponents from a multi-dimensional experimental time series

Wolf's paper Determining Lyapunov Exponents from a Time Series states that: > Experimental data typically consist of discrete measurements of a single > observable. The well-known technique of phase space reconstruction with > delay coordinates [2, 33, 34] makes it possible to obtain from such a time > series an attractor whose Lyapunov spectrum is identical to that of the > original attractor. One of the cited papers, Geometry from a Time Series, elaborates: > The heuristic idea behind the reconstruction method is that to specify the > state of a three-dimensional system at any given time, the measurement of > _any_ three independent quantities should be sufficient [...]. The three > quantities typically used are the values of each state-space coordinate, > $x(t)$, $y(t)$, and $z(t)$. We have found that [...] one can obtain a > variety of three independent quantities which appear to yield a faithful > phase-space representation of the dynamics of the original $x$, $y$, $z$ > space. One possible set of three such quantities is the value of the > coordinate with its values at two previous times, e.g. $x(t)$, $x(t - > \tau)$, and $x(t - 2\tau)$. Finally, Rosenstein's paper A practical method for calculating largest Lyapunov exponents from small data sets states that: > The first step of our approach involves reconstructing the attractor > dynamics from a single time series. We use the method of delays [27, 37] > since one goal of our work is to develop a fast and easily implemented > algorithm. The reconstructed trajectory, X, can be expressed as a matrix > where each row is a phase-space vector. That is, $$ X = [X_1\;X_2\; > ...\,X_M]^T$$ where $X_i$ is the state of the system at discrete time $i$. All three papers seem to implicitly assume that the system under study has a multi-dimensional phase space, but that only one dimension can be measured experimentally, and therefore that the full phase space data must be reconstructed from a one-dimensional time series. However, what if the time series is multi-dimensional, indeed of the same dimension as the phase space, to begin with? For instance, consider the problem of showing experimentally that a simple pendulum is not chaotic. The phase space is 4-dimensional ($r$, $\dot r$, $\phi$, $\dot \phi$) and it is straight-forward to design an experiment which generates a 4-dimensional time series of the values of these variables at each time step. Is it possible to skip the reconstruction in this case, and use $X = [r\; \dot r\; \phi\; \dot \phi]^T$ in place of the reconstructed trajectory in Rosenstein's paper, with no additional modifications? Is there a simpler way to calculate Lyapunov exponents when the full phase-space state of the system is known?


What phenoma have "intuitive" explanations which are completely wrong?

Some phenomena in physics defy intuition. Others have very intuitive explanations which you could explain easily to a layman. Sometimes, these intuitive explanations are simply wrong. What phenomena in physics have intuitive, but totally wrong, explanations? An explanation you could use to easily convince your non-physicist spouse: something that would make them _think_ they understand what's happening while being incorrect? I'll present one (somewhat contrived) example: > Bernoulli's principle is often used to explain how airplanes fly. After > explaining Bernoulli's principle, the layman might ask "okay, so why does > the air on top of the wing move faster than the air below it?" A seemingly > intuitive explanation is that because the wing is curved, the top surface > has a longer length from leading edge to trailing edge than the bottom > surface. Therefore, if two air particles hit the leading edge > simultaneously, and one travels above the wing while the other travels below > it, the one traveling above must move faster in order to arrive at the > trailing edge at the same time as its under-wing counterpart. This > explanation is totally wrong because there is no rule of physics that states > the two particles have to arrive at the same time. (And a non-curved "barn > door" wing is quite capable of producing lift.) So the phenomenon here is > genuine -- a wing does generate lift, Bernoulli's principle is involved, and > the air above the wing is moving faster and has lower pressure than the air > below it. But the "two particles racing each other, ending in a tie" > explanation is simply wrong.


Where to get hard historical and trend data related to reentry of satellites like UARS

NASA is providing very brief updates on the reentry of the UARS satellite. They also published an extensive study of the Re-entry and risk assessment for the NASA Upper Atmosphere Research Satellite (UARS) The Planetary Society Blog has some nice coverage and a graph of altitude over time: Keeping track of UARS' reentry The well-known satellite tracking site Heavens Above site provides UARS - Visible Passes data which seems relatively up-to-date, but without information on the uncertainty. What I want is actual tabular historical data, e.g. the changes in the Orbital elements over the last months, weeks or days of its flight, and a characterization of how those elements other than altitude change over time. _**Update:_** The Center for Orbital and Reentry Debris Studies has a prediction and map for UARS orbits. _**Update 2:_** One authoritative source is Space-Track, run by United States Strategic Command (USSTRATCOM), but you need to be an "approved registered user"....


Error analysis of flux from telescope-CCD setup (photometric calibration)

I am doing photometric calibration of a telescope and am trying to work out the errors on the flux that I measure. I have attempted to work out the errors due to the process of removing bias, dark frames, etc. using Poisson statistics, but this gives a fractional error of about 0.7, which is poor. I may try this analysis again using Gaussian stats, but I also want a measure of the error on the raw flux in the image (ignoring processing). I have tried to do this by taking many observations of one star to look at the variation of flux; it roughly looks like a Gaussian, but I can't get a fit to it without altering the data. Is there a good way to find a flux variation from data I have taken?


Could a neutron star be active, fusioning neutrons into something more dense and releasing constant power?

Could a neutron star be a bit like our Sun or any other star? Just to have a different scale: A neutron star fusioning not hydrogen and other elements but neutrons and quarks in its core at a stable, constant speed, would release energy, and the neutron star would therefore be larger than just packed neutrons would be. It would shine with very high frequency electromagnetic waves like gamma rays and far beyond. Finally it would be burning all its "material" into someting weird and collapse. Would it be possible for the neutron star to explode as a supernova or gamma-ray burst?


From Computational Astrophysics to Finance

If for some reason, an Astrophysics graduate decides to shift to Finance will he/she be in a better position (given his/her overspecialization) to make a transition compared to his/her counterparts who've been doing Analytical/Observational Astrophysics?


Is quantum indeterministic?

The question might look clear from a viewpoint of a non-physics guy but let me be more specific. Can we say quantum leaps or waves or maybe the universe itself are completely indeterministic or do the scientists say that because of lack of information? I am asking this because there are people telling me the you cannot know whether it is indeterministic because you might not have all the information needed to calculate the behaviour of the phenomenon. Also, some people argue that chaos is completely indeterministic. Which is the case and why?


What is off-diagonal long range order in superfluid?

From Wikipedia: > _[...]Off-diagonal long-range order (ODLRO) [...] exists whenever there is a > macroscopically large factored component (eigenvalue) in a reduced density > matrix of any order._ How to understand the ODLRO in superfluidity?


How does fire create thrust in rocket?

All big rockets are burning either gas or fluid to create thrust. While this is so, I have filled up a plastic bottle with air at high pressure, and it can go long distances by blowing the pressurised air at reverse direction. If my bottle can do this without using any fire, why don't rockets just use air? How is the effect of combustion in thrust?


Capacitor in series?

Say you have two charged capacitors in series. Zoom in on one capacitor. For this specific capacitor, the charge on the two plates will be the same in magnitude, according to my textbook. My teacher said that the charge on the two plates won't be the same if the gap between the the plates is large. In fact, the charge on each plate in a capacitor is _never_ the same. They're only approximated to be the same if the gap is small. Why is the charge not the same on both plates on a capacitor in series if the gap is large? ![enter image description here](http://i.stack.imgur.com/u9x6F.png)


As I read in The Road to Reality by Roger Penrose, the Joukowsky transform $$w(z) = \frac12\left( z + \frac1z \right)$$ after Nikolai Zhukovsky (transcribed in several versions from Никола́й Его́рович Жуко́вский) can be used to **calculate the flow** of a non-viscious, incompressible and irrotational flow **around an airfoil**. This can be done since the solution of a potential flow around a cylinder is known in full analyticity and the given transform conformally maps a circle on an airfoil-like geometry. I don't understand this argumentation, so: > ### How is the Joukowsky Transform used to calculate the Flow of an Airfoil? An **example** of such a transformation is given in the mentioned Wikipedia article: ![RotatingDisc](http://upload.wikimedia.org/wikipedia/commons/d/d5/Jouktrans.png) Thank you in advance.


Is it possible to study solid state from kittel after taking only one course in quantum mechanics?

I have taken only QM I, which is the 1st half of Griffiths including the chapter on identical particles, will that be enough to understand Kittel's solid state? Should one have also taken a course in statistical mechanics before studying kittel? I have seen in some universities in the states that the prerequisite of an introductory course in solid state physics sometimes are QM I, II, SM, and other times are QM I only (or with SM and QM II are corequisite)


Magnetic force at the edge?

When sliding a magnet over a ferromagnetic surface there is no magnetic force at all, however,there is a magnetic force only at the edge, when the magnet is being pulled of I assume the magnetic field is trying to resist. However, a fact it noticeable, the sliding/lateral magnetic force at the edge is a lot less, by a factor of half - ten times less. What could be the reasons that detains the magnitude of the lateral force? Pelase do explain in detail. Thank you.


Tensor product of Hadamard Operators

The Hadamard Operator on one qubit is: \begin{align*} H = \tfrac{1}{\sqrt{2}}\left[\,\left(\color{darkgreen}{|0\rangle + |1\rangle}\right)\color{darkblue}{\langle 0|}+\left(\color{darkgreen}{|0\rangle - |1\rangle}\right)\color{darkblue}{\langle 1|}\,\right] \end{align*} Show that: \begin{align*} H^{\otimes n} = \frac{1}{\sqrt{2^n}}\sum_{x,y}(-1)^{x \cdot y}\,\left|x\rangle \langle y\right| \end{align*} I can evaluate things like $H \otimes H$ in practice, but I don't know how to get a general formula for $H^{\otimes n}$. Are there any tricks I could use?


Is it possible that black holes are also neutron stars, but so dark that we cannot see them?

1. Since the concept of the singularity in a black hole leads to infinite densities, I wonder if it is really certain that black holes exist?    2. Is there a possibility that massive objects (which are believed to be black holes) are in reality dense stars not emitting light (dark neutron stars)?   3. Is there a possibility to explain the observed facts without the use of black holes?   4. One more question: According to the mainstream, are neutron stars believed to eventually collapse to a black hole, or are they stable objects?


Physical meaning of the sign basis in quantum mechanics

If we take a hydrogen atom as qubit, let $\lvert0\rangle$ = unexcited state   $\lvert1\rangle$ = excited state then what is the meaning of measuring the qubit value in the sign basis? If the atom may only be in excited or unexcited state, but $\lvert+\rangle$ and $\lvert-\rangle$ are superpositions of those states — then what would the outcome of the measurement be — also a superposition of $\lvert+\rangle$ and $\lvert-\rangle$? Can anyone please help to understand the idea behind the sign basis?


Quantum mechanics on Cantor set?

Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) Cantor set. What is the right way to formulate QM of a particle on a Cantor set? I can only guess that: i) There will be no momentum operator. ii) Hilbert space will be spanned by position vectors corresponding to points of Cantor set. iii) Corresponding to any two points $x$ and $y$ in Cantor set there will be a unitary operator $P_{xy}$ (analog of the exponential of momentum operator) such that $P_{xy}|x>=|y>$; $P_{xy}=P_{yx}^{-1}$; and $P_{yz}P_{xy}=P_{xz}$ for all $x,y,z$. But I am not able to see what would be correct notion of free particle, and what would be corresponding Hamiltonian.


What is the mass of the emergent magnetic monopoles in spin ice and how is the mass of an emergent particle determined?

In solid state physics emergent particles are very common.   1. How one determines if they are gap-less excitations?    2. Do the defects in spin ice called magnetic monopoles have mass?    3. What is the mass of emergent particles in the fractional quantum hall effect (FQHE)?  I am not looking for a deep theory, just the general picture.


The mighty man and the bridge

Let us say we have a mighty man crossing a bridge, carrying 4 bags of concrete, each of which weighs 50 pounds. Let us say, for the sake of the argument, that the mighty man himself weighs 300 pounds. The support capacity of the bridge $x$ is less than the 500 pounds they weigh together - therefore, the mighty man cannot carry the concrete in a stack across the bridge - it will fall. However, the mighty man does have the ability to juggle all the concrete bags so that he is only in contact with one of them at a time. Is there such a value of $x$ possible that he can cross the bridge juggling all four bags of concrete at once, or will the bridge necessarily exceed its support capacity?


Which types of particles are affected by the wave-particle duality?

If we take the double slit experiment as a way of demonstrating the wave- particle duality, which types of particles would show an interference pattern? For example, I know that electrons show such a pattern. But do protons, too? What about atoms? Where is the boundary between "wavey particles" and "classical particles"?


Construction of the $\cal{N}=3$ supersymmetric Yang-Mills Chern-Simons theory in $2+1$ dimensions

I am stuck with understanding the following construction. I am breaking it up into segments which I think can be separately answered. This is related to an earlier question of mine. Note that this previous question was edited a lot after the initial comments came in.   * Firstly I would like to know how the following field multiplet is determined,  The gauge multiplet of $\cal{N}=3$ in $2+1$ dimensions is apparently , $A_\mu$, a massive vector field of spin $1$ $\lambda_a$, $3$ Majorana fermions of spin $\frac{1}{2}$ $C_a$, $3$ neutral scalar bosons $\chi$, a Majorana fermion of spin $\frac{1}{2}$ (I guess there should be another scalar field $D_a$ not mentioned in the above list)   * Its not clear to me as to what are the superfields one has in mind with the above multiplet structure that helps construct the lagrangians below.    * Like in the linked earlier question above one had to "know" what exactly is the meaning of doing the dimensional reduction on a given set of supersymmetric transformations, here its not clear to me as to what are the corresponding starting points. (I wonder if I can start from the $\cal{N}=2$ SYM in $3+1$ lagrangian that is given in say equation $27.9.3$ in Weinberg's QFT book)  Then dimensional reduction of $\cal{N}=2$ SYM in $3+1$ apparently gives the following $\cal{N}=3$ SYM in $2+1$, $L_{\cal{N}=3,2+1,SYM} = \frac{1}{g^2}Tr\left [ -\frac{1}{2}F_{\mu \nu} ^2 + (D_\mu C_a)^2 + (D_a)^2 + i \bar{\lambda_a}\gamma^\mu D_\mu \lambda_a + i \bar{\chi}\gamma^\mu D_\mu \chi \+ i\epsilon_{abc}\bar{\lambda_a}[\lambda_b,C_c] -2i\bar{\lambda_a}[\chi,C_a] - \frac{1}{2}[C_a,C_b][C_b,C_a] \right ]$ where the notation is, $D_\mu = \partial_\mu -iA_\mu$, $ab,c=1,2,3$. The gauge group generators in the fundamental representation satisfy $[T^m,T^n]=if^{lmn}T^l$ with normalization as $Tr{T^mT^n}=\frac{1}{2}\delta ^{mn}$ and $f^{kmn}f^{lmn}=c_v\delta^{kl}$. ($c_v$ being the quadratic Casimir) The fields belong to the adjoint representation and $A_\mu = A_\mu^mT^m$. The metric is given by $\eta_{\mu \nu} = diag(1,-1,-1)$. The purely imaginary gamma matrices satisfy, $\gamma^\mu \gamma ^\nu = \eta^{\mu \nu}-i\epsilon^{\mu \nu \rho}\gamma_\rho$.   * It is not clear to me as to how does one argue that the above has $\cal{N}=3$ supersymmetry.    * The dimensional reduction of the $\cal{N}=2$ supersymmetry somehow implies that the theory has the not-so-obvious $\cal{N}=4$ supersymmetry.  * * * One also notes that supersymmetrizing the Chern-Simon's terms one is supposed to get the Chern-Simon's lagrangian as, $L_{\cal{N}=3,2+1,SCS} = kTr\left [ \epsilon^{\mu \nu \rho}(A_\mu \partial_\nu A_\rho - \frac{2}{3}iA_\mu A_\nu A_\rho) - \bar{\lambda_a}\lambda_a + \bar{\chi}\chi \+ 2C_aD_a + \frac{i}{3}\epsilon_{abc}C_a[C_b,C_c] \right ]$   * In all these lagrangians apparently the corresponding $\cal{N}=2$ theories can be obtained by setting $C_1=C_2=D_1=D_2=\lambda_3 = \chi = 0$ and the $\cal{N}=1$ theories can be obtained from the $\cal{N}=2$ theories by further setting $C_3=\lambda_2=0$.  (I am unable to get the equations to wrap around properly!)


Apple falls for which of these 2 reasons?

Needles to say I am a visitor here. I do not belong to the science world;) But I have read both of these things before:   1. Apple falls to the ground because curved spacetime pushes it there (same force as keeps moon in orbit)   2. Apple 'falls' to ground because the ground is rushing up to meet the apple (which is actually suspended in space) because of Earth's acceleration through space. I don't think these can both be true. I'd appreciate any clarification - thank you.


Moment of inertia of a hollow sphere wrt the centre?

I've been trying to compute the moment of inertia of a uniform hollow sphere (thin walled) wrt the centre, but I'm not quite sure what was wrong with my initial attempt (I've come to the correct answer now with a different method). Ok, here was my first method: Consider a uniform hollow sphere of radius $R$ and mass $M$. On the hollow sphere, consider a concentric ring of radius $r$ and thickness $\text{d}x$. The mass of the ring is therefore $\text{d}m = \frac{M}{4\pi R^2}\cdot 2\pi r\cdot\text{d}x$. Now, use $r^2 = R^2 - x^2:$ $$\text{d}m = \frac{M}{4\pi R^2}\cdot 2\pi \left(R^2 - x^2 \right)^{1/2}\text{d}x$$ and the moment of inertia of a ring wrt the centre is $I = MR^2$, therefore: $$\text{d}I = \text{d}m\cdot r^2 = \frac{M}{4\pi R^2}\cdot 2\pi\left(R^2 - x^2\right)^{3/2}\text{d}x $$ Integrating to get the total moment of inertia: $$I = \int_{-R}^{R} \frac{M}{4\pi R^2} \cdot 2\pi\cdot \left(R^2 - x^2\right)^{3/2}\ \text{d}x = \frac{3MR^2 \pi}{16}$$ which obviously isn't correct as the real moment of inertia wrt the centre is $\frac{2MR^2}{3}$. What was wrong with this method? Was it how I constructed the element? Any help would be appreciated, thanks very much.


Quantum Mechanisms for Isotope Fractionation

Are there any quantum properties that would enable isotope fractionation? For example, atoms with odd versus even numbers of neutrons are fermions and bosons, respectively. Has any work been done using the distinct properties of fermions and bosons to isolate isotopes?


Lorentz boost matrix in terms of four-velocity

As I understand it, the value of a 4-vector $x$ in another reference frame ($x'$) with the same orientation can be derived using the Lorentz boost matrix $\bf{\lambda}$ by $x'=\lambda x$. More explicitly, $$\begin{bmatrix} x'_0\\\ x'_1\\\ x'_2\\\ x'_3\\\ \end{bmatrix} = \begin{bmatrix} \lambda_{00}&\lambda_{01}&\lambda_{02}&\lambda_{03}\\\ \lambda_{10}&\lambda_{11}&\lambda_{12}&\lambda_{13}\\\ \lambda_{20}&\lambda_{21}&\lambda_{22}&\lambda_{23}\\\ \lambda_{30}&\lambda_{31}&\lambda_{32}&\lambda_{33}\\\ \end{bmatrix} \begin{bmatrix} x_0\\\ x_1\\\ x_2\\\ x_3\\\ \end{bmatrix} $$ I have seen examples of these components written in terms of $\beta$ and $\gamma$, which are defined as $$\beta=\frac{v}{c}$$ $$\gamma=\frac{1}{\sqrt{1-\beta\cdot\beta}}$$ where $v$ is the 3-velocity and $c$ is the speed of light. My question is this: How can the components of $\lambda$ be written in terms of the 4-velocity $U$ alone? I know that $U_0=\gamma c$ and $U_i=\gamma v_i=\gamma c\beta_i$ for $i\in\\{1,2,3\\}$, but I'm having trouble deriving the components for $\lambda$ using the matrices based on $\beta$ and $\gamma$. An example of one of these matrices can be found at Wikipedia. How can I rewrite this matrix in terms of $U$ alone?


Calculate impulse based on mass, acceleration and time elapsed

I want to move to Sprite Kit framework offered by apple which has physics integrated right into it. The back bone of the physics engine is famous Box2D. Sprite Kit has made it pretty easy by wrapping C++ inside Objective-C but unfortunately some features lack in Sprite Kit. One them is GetReactionForce function, that returns the impulse applied on the body B of a joint. Just disregard the software related terms if you find it difficult to understand. Basically what I need is to create my own function that will calculate impulse. Here are the ingredients I have: Mass, gravity, delta time. P.S. Sorry for the tags, I couldn't find anything more suitable and I have no right to create new ones


How to calculate tortuosity of a signal?

Not sure which stack exchange forum to put this in. Moderators feel free to migrate it. One definition of the tortuosity $T$ of a curve is: $$T=\frac{C}{L}$$ Where $C$ is the chord length (distance between the ends of the curve) and $L$ is the total length of the curve. I am trying to calculate the tortuosity of a white noise signal. But it is not clear to me what the unit length should be. Here's what I mean: The white noise is a time series $X(t)$ of length $N$ of normally distributed random numbers with mean $0$ and standard deviation of $1$. To calculate the length $L$ of this signal I do the following: $$dy(t)=\left| X(t+1)-X(t) \right |$$ $$L=\sum_{t=1}^{N-1} \sqrt{dy(t)^2+dx^2}$$ Where $dx$ is the unit interval. The question is how to select a suitable value for $dx$. Should it just be $1$? Or perhaps the mean or minimum value of $dy(t)$? The chord length $C$ of this signal is $N/dx$, so it also depends upon the selection of $dx$.


Would it help if you jump inside a free falling elevator?

Imagine you're trapped inside a free falling elevator. Would you decrease your impact impulse by jumping during the fall? When?


Implications of unbounded operators in quantum mechanics

Quantum mechanical observables of a system are represented by self - adjoint operators in a separable complex Hilbert space $\mathcal{H}$. Now I understand a lot of operators employed in quantum mechanics are unbounded operators, in nutshell these operators cannot be defined for all vectors in $\mathcal{H}$. For example according to "Stone - von Neumann", the canonical commutation relation $[P, Q] =-i\hbar I$ has no solution for $P$ and $Q$ bounded ! My basic question is :   * If the state of our system $\psi$ is for example not in the domain of $P$ (because $P$ is unbounded), i.e., if $P\cdot \psi$ does not, mathematically, make sense, what does this mean ? Does it mean we cannot extract any information about $P$ when the system is in state $\psi$ ?


Quantization of Electron Spin

Why is electron spin quantized? I've seen the derivation for the Hydrogen atom's energy levels, but my professor jumped to electrons having spin 1/2 or -1/2 as experimental. Why do electrons obey the same quantization rules for angular momentum as the Hydrogen atom does? Why must the two states be one apart?


Double-spring mass system

We just had a lesson about elementary mass-spring systems (SHO), and I thought about a horizontal situation with two springs with the test mass oscillating in between. If we are to manually stretch the mass a distance $\Delta x<\Delta_0$ , we obtain opposing restoring forces, which yields the familiar SHO equation. But do thesee conditions change when we stretch it beyond $\Delta_0$(a little beyond, it's still elastic with Hooke's law), in some intervals the restoring forces point in the same direction and in others don't. Does the system retain its "SHO-ness"? ![System diagrams](http://i.imgur.com/g0rBIf3.png)


what is the difference between constant and changing magnetic and electric fields? How do they occur? How do they form an electromagnetic wave?


Does black hole complementarity apply to white holes?

If physics is time reversal invariant, there ought to be white hole complimentarity as well. Imagine a white hole so enormous that it is possible for life to evolve entirely within it for billions of years before emerging to tell their story about the interior of the white hole. Meanwhile, an external observer can observe and keep note of everything in the vicinity of the white hole and what comes out of it. Both observers can meet and compare notes. Can the external observer really claim the white hole interior doesn't exist?


Is charge density zero in a dielectric material and why?

I'm trying to solve a problem involving parallel capacitor. I can't decide whether to use poisson's formula or laplace's formula. ![enter image description here](http://i.stack.imgur.com/hArz0.png) The question is, is there $\rho_v$ in a piece of dielectric and why?


How to tell local and non-local in QFT?

I'm taking QFT course in this term. I'm quite curious that in QFT by which part of the mathematical expression can we tell a quantity or a theory is local or non-local?


Question on particles

Is there any theory in which every particle can be further subdivided into any number of particles and the total number of particles any where in the space time are infinity in theory and only due to practical constraints that we are capable of observing the known particles in the current World. Also could you please explain the nature of the two widely accepted theories which explain the small scale and large scale universe which are QP and GR repectively in the current context of the question.


Acceleration on an inclined rail

I have to use $\vec{P}+\vec{R_N}+\vec{F_f}=m\vec{a}$ with $\|\vec{F_f}\|=\mu\|\vec{R_N}\|$ to express the acceleration as $$a_{x'}=g\sin\alpha(1-\frac{\mu}{\tan\alpha})$$ The configuration is (sorry about the poor image) : ![scheme](http://www.beziaud.org/~work/upload/docs/131112083008.schema.jpg) I'm totally lost. How could I do that?


Why Inox Steel doesn't interact with magnets?

My dad has a HUGE magnet on his workshop. I love magnets, and when I saw it, I asked him what it was for. His reply was: "I don't know why, but inox steel bolts don't get attracted to it, so I use it to identify them." Thus I got curious, why a magnet don't attract inox steel bolts? Steel, even if a inox variation is still mostly iron, no?


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

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


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


Online QFT video lectures

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


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

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


Find the Unit Vector of a Three Dimensional Vector

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


Kinetic energy and potential energy variation over distance in SHM

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


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

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


Regulating the sum in Casimir Force

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


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

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


What happens to internal energy in high-density materials?

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


Strange behavior and motion of bubbles in a glass of beer

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


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

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


Is a plasma necessarily made of monoatomic ions?

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


Why diaphragm in diffraction experiment using electrons is quantum object?

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


Water-cooled fast neutron reactors

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


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

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


What is the momentum of these emitted photons?

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


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

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


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

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


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

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