title: Does Heisenberg's uncertainty under time evolution always grow?

text: Recently there have been some interesting questions on standard QM and especially on uncertainty principle and I enjoyed reviewing these basic concepts. And I came to realize I have an interesting question of my own. I guess the answer should be known but I wasn't able to resolve the problem myself so I hope it's not entirely trivial. So, what do we know about the error of simultaneous measurement under time evolution? More precisely, is it always true that for $t \geq 0$ $$\left<x(t)^2\right>\left<p(t)^2\right> \geq \left<x(0)^2\right>\left<p(0)^2\right>$$ (here argument $(t)$ denotes expectation in evolved state $\psi(t)$, or equivalently for operator in Heisenberg picture). I tried to get general bounds from Schrodinger equation and decomposition into energy eigenstates, etc. but I don't see any way of proving this. I know this statement is true for a free Gaussian wave packet. In this case we obtain equality, in fact (because the packet stays Gaussian and because it minimizes HUP). I believe this is in fact the best we can get and for other distributions we would obtain strict inequality. So, to summarize the questions >   1. Is the statement true? >   2. If so, how does one prove it? And is there an intuitive way to see it > is true? >


title: Light travels a straight line write down the principle in which this is manitested

text: Light traveles a straight line write down the principle in which this is manifested.


title: electron hole exchange

text: If exchange is an interaction between indistinguishable particles, how can there be an exchange interaction between electrons and holes? I see mention of e-h exchange often in the literature.


title: Inflating a balloon (expansion resistance)

text: I am doing a quick calculation on how to calculate the pressure needed to inflate a perfectly spherical balloon to a certain volume, however I have difficulties with the fact that the balloon (rubber) has resistance to stretching and how this affects the pressure needed. It has to do with the E-modulus of the material I think, but I can not think of a proper way to calculate it. EDIT: Looking for a few hours in my materials books now, but after posting it here I found an answer online already: http://www.colorado.edu/engineering/CAS/courses.d/Structures.d/ASEN3112.Lect05.d/ASEN3112.Lect05.pdf This one has an example in it which actually answers my question.


title: Flow of water and flow of electrons, how this analogy works?

text: If **flow of electrons** analogy can be imagined as flow of water, how to imagine electricity, that comes in this whole picture? When plug from bottom of sink is taken out, gravity pulls water molecules, creating pressure difference, in sink there is larger pressure than in open hole, making water to move to place, where is less pressure, until pressure is equal in all places, water can flow. As I have understood, electricity is some field around each electron. Power of field is called **electric charge** , mesured in _columbs_ , every electron has some charge, eaven those, who are sitting tight, that is called static electricity? That charge is generated when electrons rub/hit against each other, when they are "made to move", when **electrical potencial** , or pressure difference is made, by connecting to medium, another medium, that has... What that connected medium has, that makes electrons flow? Less electrons? Less electrons with electric field around them? If that is field, that can have some maximum ammount of charge, can charge vary, how that affect flow? I don't think, it can be explained with water, as water isn't carrying... anything... What is mesured in amperes? What is rate of flow, is it a speed of water/electrons flow? Are electrons same as water, in manner of, they are just some sort of matter, that is flowing in another **medium** , but water has much larger **particle size** , so its hard to make is analogy in my mind - there is no medium, in which water can flow, water is medium by itself. If I forget, that water is medium, but pretend, that water can only flow in... air, places where air can go in... Then how does wire connections work? If There is one wire, that divides in two, as some sort of connection, **does in each wire, goes same ammount of electrons** (if we pretend ideal/same conditions in both wires)? Does that mean, there will be half of electrons in one wire, and other half in another wire? The more wires I connect, the less electrons will be in each wire? If one of wires will have damaged lattice or resistor sitting middle of it, will electrons "run way back" to connection place and go into other wires, where is less resistance or they will stay at same place, just building up pressure, constantly making denser electron cloud in resistance area... Ehh... I know, I'm asking too many questions, that touches too many sides of electricity, but please, I want some analogy explanation, that would allow me better understand this whole "stuff". :) Maybe, someone can suggest some visual materials (video, pictures), for this?


title: Energy in magnetic fields

text: If I calculate the energy contained in the electric field for an electric dipole p in an electric field E, I get (ignoring the terms independent of orientation): $U = - \vec{p} \cdot \vec{E}$ which is as expected. However, if I do the same for a magnetic dipole m in a magnetic field B, I get (again ignoring the terms independent of orientation): $U = \vec{m} \cdot \vec{B}$ which clearly has the wrong sign. Does one have to be careful in interpreting energy in the magnetic field? A colleague pointed out that David Griffiths mentioned this problem in passing in "Dipoles at Rest" (AJP 60, 979, 1992). But it wasn't very satisfying, as he seems to be referring to the terms which are independent of the orientation to try to argue it fixes the sign somehow. It didn't make sense to me, maybe because it was only mentioned briefly in passing. Can anyone expand upon this? Also, if I look at the Lagrangian for electrodynamics, I notice the energy in the electric fields has an overall negative sign (like a potential energy) while the energy in the magnetic fields has an overall positive sign (like a kinetic energy). So is this a hint I'm not supposed to treat the energy in a magnetic field on the same footing as the energy in an electric field?


title: Is there a rest frame for the Higgs boson?

text: If there is a non-zero expectation value for the Higgs boson even in "vacuum", since the Higgs boson has a mass unlike photons, then I would expect it to have a rest frame. So why doesn't a non-zero expectation value for the Higgs boson not only break electroweak symmetry, but also break Lorentz symmetry?


title: Physical representation of magnetic vector potential

text: For time varying potential $$ E= - \nabla(v)- \frac{\partial A}{\partial t} $$ now for scalar potential v we can represent the equipotential surface as a perpendicular surface of the direction of derivative. such as $$ E(x)=- \frac{\partial V}{\partial x} $$ & the equipotential surface is as a perpendicular of $E(x)$ or $\frac{\partial V}{\partial x}.$ then how can I represent the vector potential A having equal in every where. like wise the above is it perpendicular to time?


title: Storing kinetic energy instead of potential energy - practically possible?

text: One of the big problems today considering **energy** is its **storage** (e.g. batteries are not that efficient, very expensive and polluting). Energy is classically mostly stored as some kind of **potential** (in a battery, a high- level water tank, ...). Compare it with the equivalence between a condensator and a coil: a condensator holds a potential energy of $1/2CV^2$ and a coil holds a kinetic energy of $1/2LI^2$. We use batteries to **store a voltage** as a potential energy, but is there a way to store current (e.g. in a hypothetical superconductor that superconducts at regular temperatures)? I could imagine one example where kinetic energy is actually "stored", i.e. thermal energy storage (as used e.g. in solar thermal electricity systems). But are there other ways to **store kinetic energy** , and **in particular an electric current**? Or is this inherently a less attractive option due to thermodynamics (i.e. due to thermalization the kinetic energy will get useless)? The question may boil down to: is it inherently physically more attractive to store energy as potential energy, or are we till now just hold back by practical limits (such that in the future we may be able to store kinetic energy in an efficient way)? *Some context: the reason why I came up with this question is that energy transportation is also a big issue. Energy is of course transported as a kinetic energy (a current through the grid); but if it would be possible to also store it kinetically, less conversion would be needed. Moreover, energy would be stored (in some kind of PEC storage loops) _and_ transported by the electricity grid.*


title: Who of these cyclist travel takes less time?

text: There are two cyclist. They start off with equal velocity $v_0$. The first one bikes a straight path, while the other bikes through a valley, something like this: ![Like this ______/](http://i.stack.imgur.com/pQ8pp.jpg) We assume friction doesn't affect either cyclist, so only gravitational potential energy plays a role here. Who should arrive first? I think its about to find the angles of the second way where the time its a minimun. Someone said I should use the conservation of mechanical energy, but I don't understand how could add the two different velocities (one simply contant, while the other is related to the gravitational potential).


title: Does a light cone only effect the time an object has lived?

text: I'm confused about light cones and I've driven a crazy scenario to try to represent it. Let's say I can move through my past light cone to the exact time of my birth. If I kept on moving back could I move to a time before I was born? Therefore my question is, when they show light cones in space-time diagrams do they apply to our _own_ past our the past of the time throughout the universe. Does this mean that in the -t direction, time for us only goes as far back as our birth. Sorry if this sounds too confusing.


title: Why Liouville's theorem is obvious?

text: In Florian Scheck's _Mechanics_ , he stated the local form of Liouville's theorem as follows: Let $\Phi_{t,s}(x)$ be the flow of the differential equation $-J\frac{d}{dt}x=H_{x}$. Then for all $x,t,s$ for which the flow is defined, we have $$D\Phi_{t,s}(x)\in Sp_{2f}.$$ In his proof he claimed that $$\frac{d}{dt}[D\Phi_{t,s}(x)^{T}JD\Phi_{t,s}(x)]=0$$ Thus since $D\Phi_{t,s}(x)^{T}JD\Phi_{t,s}(x)=J$ when $t=s$, we proved the theorem. My question is: Why at $t=s$, $D\Phi_{s,s}(x)^{T}JD\Phi_{s,s}(x)=J$ holds? The author claimed that this is `obvious', but it is not obvious to me. Mathematically $t=s$ just means the flow starts at the time $t=s$ for which it is defined. So we can use $s=0$ without losing generality. But why would Hamilton's equation $$-J\frac{dD\Phi_{t,s,t=s}(x)}{dt}=DH_{x}\circ D\Phi_{t,s,t=s}(x)$$ imply $$D\Phi_{s,s}(x)^{T}JD\Phi_{s,s}(x)=J?$$ Writing out this in block matrix form we should have this equal to $det[D\Phi_{s,s}]J$ instead. And we do not know as prior $det[D\Phi_{s,s}]=1$.


title: RLC circuit, turning off the voltage source

text: ![RLC](http://i.imgur.com/54z9L7u.png) An RLC circuit (pictured above) is governed by two equations: $$ -iR=-L \frac{dj}{dt} = \frac{q}{C}+V(t) $$ $$\frac{dq}{dt}=i+j$$ q satisfies the equation: $$\frac{d^2q}{dt^2}+\frac{1}{RC}\frac{dq}{dt}+\frac{1}{LC}q=-\frac{1}{R}\frac{dV}{dt}-\frac{1}{L}V $$ The system is held in a steady state (i.e. $\frac{dq}{dt}=0$ and $V(t)=\frac{Q}{C}$) for negative time. At t=0 the voltage is switched off and $V(t) = 0$ for $t \geq 0$. **Question: how to derive the initial conditions for the system, i.e. $q(0)=Q$ and $\dot{q}(0)=\frac{Q}{RC}$ ?** My attempt: to calculate the charge in the steady state (just before t=0), I can set all derivatives with respect to time to 0. Then I get $V=-\frac{C}{q}$ and I can define $Q=-\frac{C}{V}$. I don't know how to handle the discontinuity at t=0 to obtain $\dot{q}(0)$ though.


title: Does a photon interfere only with itself?

text: I sometimes hear statements like that: > Quantum-mechanically, interference pattern occurs due to quantum > interference of wavefunction of a photon. Wavefunction of a single photon > only interferes with itself. Different photons (for example from different > atoms) do not interfere. First of all -- is this correct? If it is correct -- how do we explain basic classical interference, when we don't care about where do the plane waves came from? I heard that there are experiments with interference of two different lasers -- is this considered as a refutation of the statement? If it is -- how one should formally describe such process of interference of different photons? Finally -- such statements are usually attributed to Dirac. Did Dirac really say something like that?


title: Use of the mathematical concept 'function' in theoretical physics

text: The mathematical concept of function is used in physics to represent different physical quantities. For example the air pressure variation with time and space is called an acoustic wave. We use a function to represent a charge distribution (or even electric field strength) in space and time.In gravitation we use it to represent a mass distribution (and momentum distribution) in space and time. In Quantum mechanics we use it to represent a Quantum state and hence the probability distribution of position and momentum of a particle in space and time. Most of the time we do a variety of mathematically well defined operations on these functions to make some conclusions and to answer some questions regarding a physical system.Even the fundamental laws of physics give the mathematical relation between functions representing different physical quantities. Now if i ask a question on the **_mathematical nature_** of a function that represents a physical quantity (say for example a mass distribution in space and time), would it be possible to find an answer ? Does every such question has a physical interpretation ? **EDIT 1** Here i give a sample question ? Q. let a function $p(t)$ represent the acoustic pressure variation at a given point in space.Is the function well behaved ? Mathematically speaking "Is $p(t)$ a smooth function ?"


title: Why are carbon nanotubes are so difficult to create?

text: I have heard that the future of the techonolgy are the carbon nanotubes due to their resistance and conductivity, but why are they so difficult to create?


Does there exist a laser that is tunable over the whole visible spectrum? If so does there exist one that is solid state? This is to settle a score with my dumb workmates.


title: Jupiter radiation belt: where >MeV particles comes from?

text: When I read some discussion about exploration of Jupiter moons, or possibility of life there, a common argument is high dose of radiation in Jupiter's radiation belt (several orders of magnitude higher than outside Jupiter's magnetosphere). If we speak about charged particles, dangerous is just radiation faster than let's say 1 MeV ( other are shielded very easily by thin protection) I would like to know what is the mechanism which create these fast particles inside Jupiter's magnetosphere. I would expect that particles from Sun/Cosmic radiation are rather repelled by the magnetosphere bubble, and the few which are caught slow down by emitting EM radiation oscillating around magnetic field lines (so ther would never accumulate much of them) I found in some papers that the slow particles (~10 keV) are accelerated by plasma currents generated by the rotation of the magnetosphere/ moons and jupiter. However this does not explain the fast particles which only does matter for radiation hazard and are hard to shield.


title: Why is steam used to spin turbines?

text: The ideal gas law tells us that the relationship between Pressure (P), Volume (V), Temprature (T), and quantity/amount (n) is $$ PV = nRT $$ where R is the gas constant. Say your an engineer who only cares about efficiency (cost is not an option). Your general goal should then be to find a fluid which, given a fixed volume, is under the most pressure for all temperatures (or the range of temperature for a given fuel). Any material then, with a greater atomic mass number with a less then or equal to boiling point then water would seem to be a better fit. So I'm wondering, is water really the best tool for the job?


title: Where does the Berry phase of $\pi$ come from in a topological insulator?

text: The Berry connection and the Berry phase should be related. Now for a topological insulator (TI) (or to be more precise, for a quantum spin hall state, but I think the Chern parities are calculated in the same fashion for a 3D TI). I can follow the argument up to defining the Chern parity $\nu$, where the Berry connection $\textbf{A}$ is explicitly within this equation where it gets integrated over half the Brillouin zone as it was described in Liang Fu's thesis from 2009 on page 31 to calculate the Chern parity or the $Z_2$ invariant(http://repository.upenn.edu/dissertations/AAI3363356/): $\nu = \frac{1}{2\pi} \left( \oint\limits_{\partial(A + B)} d\textbf{k} \cdot \textbf{A} - \iint\limits_{A + B} dk_x dk_y \nabla \times \textbf{A} \right) \text{mod } 2 $ It is known that the Berry phase for the surface state is $\pi$ and it is also known how the Berry connection $\textbf{A}$ leads to a Berry phase (http://en.wikipedia.org/wiki/Berry_connection_and_curvature). But I can't see how this is equal to $\pi$: $\left( \oint\limits_{\partial(A + B)} d\textbf{k} \cdot \textbf{A} - \iint\limits_{A + B} dk_x dk_y \nabla \times \textbf{A} \right) \text{mod } 2 = \pi$ ? Is there a simple way to show that the surface states of a topological insulator must have a $\pi$ Berry phase? Maybe by invoking time-reversal symmetry on this equation? For the Integer Quantum Hall Effect the conductance was used to show how the Berry phase is connected to the Berry connection. But I would like to avoid using charge polarization, I just want to see the direct relation between the Berry connection on the BZ and the resulting Berry phase of the wavefunctions that is exactly equal to $\pi$, e.g. a fermion must undergo two complete rotations to acquire a phase of $2\pi$. Is there a simple argument to relate this equation with the time reversal contraint to the Berry phase?


title: What can we learn about physics by doing experiments at the end of the heliosphere?

text: My question is very naive, as I do not know cosmology and astrophysics. I am asking it just for general curiosity. All of us know that Voyager I is now going out of heliosphere, and now sending data regarding this very boundary. Can we expect some interesting / new physical discoveries? By this I mean, certain results which can give us deeper insights on physical laws or open new avenues of work. (I believe, I am not very clear here and shall get a few angry comments for spamming. Advanced apologies for that. I remember the 1998 observations on distance–redshift relation for Type Ia supernovae. I want to know whether we can expect some data which are similarly striking.)


title: Light dispersion in water

text: Simple question: Water is clearly not disspersive if we have it, for example, in a glass of water. We don't see the rainbow through a glass of water. However drops of water disperse light in the atmosphere and allow us to see the rainbow, am I right? Why is this? In which conditions is water disspersive and in which conditions it's not?.


title: Deformation due to isostatic compression

text: When loading a solid material in the shape of a cylinder in isostatic compression, what is the relationship for the change in length versus change in diameter? For example. If I know that when I apply an isostatic load of 6000 psi to a cylindrical core of rock that is initially at a volume of 11,351 cc the deformation will be ~10.8 cc. Knowing the initial length and diameter of my cylinder, how do I predict the new length and diameter?


title: How exactly to show that s-matrix elements diverges because time-ordering is not well determined?

text: Let's have s-matrix: $$ S_{\alpha \beta} = \langle \alpha | \hat {S} | \beta \rangle , $$ $$\hat{S} = \hat{T}e^{-i\int \hat{L}(x)d^{4}x}, \quad \hat{T} \left( \hat{\Psi}(t) \hat{\Psi}(t') \right) = \theta (t - t')\hat{\Psi}(t)\hat{\Psi}(t') \pm \theta (t' - t)\hat{\Psi}(t')\hat{\Psi}(t). $$ How to show that matrix elements diverges because time ordering is not well-defined operation when $t=t'$?


title: Deriving Statistical Mechanics laws from Quantum Mechanics?

text: Since the law of individual molecule is governed by Quantum Mechanics, and the interaction of large number of molecule is governed by Statistical Mechanics, can we derive Statistical Mechanics from Quantum Mechanics?


title: Dynamic Light Scattering

text: In the Dynamic Light Scattering experiment, how is the intensity distribution plotted against time, keeping in view the multiple scattering of photon particles in laser ?


title: What is the physical process (if any) behind magnetic attraction?

text: I understand that the electromagnetic force can be described as the exchange of virtual photons. I also understand that it's possible for virtual photons, unlike their real counterparts, to have mass (for various complicated reasons.) I'm quite new to all this, so I'm finding it hard to believe that photon exchange is powerful enough to move macroscopic objects (or hold up a train), so I'm convinced I'm looking at it the wrong way. So specifically:   1. Are the virtual photons just a useful way to imagine what's actually happening, or are actual photons being exchanged?   2. Can the force applied to magnetically attracted/repelled macroscopic objects be described purely in the QED sense of virtual particle exchange, or is it the result of something else we can point to, or is it voodoo from the metaphorical aether?   3. Can force simply be spontaneously created by a field interacting with objects within it (as far as I can tell that's not what fields are/do) And very generally:   * Where does the force to move macroscopic objects originate (at the most fundamental level)?


title: What happened to the idea of tachyonic or other superluminal neutrinos?

text: While hunting around for information about the recent OPERA measurement that hints at superluminal neutrinos, I discovered that this idea was actually considered back in the 1980s. Wikipedia lists as references two papers by Chodos et al. (unfortunately they're paywalled so I can't access them right now), and some more recent ones dealing with the Standard Model Extension. I'm curious: what happened to this line of inquiry? Did it get conclusively disproven at some point, or just ignored because there was never any reason to believe that tachyons exist? Or are there still people doing legitimate research on it?


title: Why does a firebrand glow brightest before it burns out?

text: I've noticed this in match-sticks, and mango wood. After the flames die out, the brand glows red for a while. The glow is brightest right before it dies out. My guess is that immediately before the glow dies out, any air channels in the wood are fully dried by the heat to the extent that the 'reverse wind' sweeps in to oxygenate the burning portion. This wind is so strong that the burn cannot advance and therefore glows brightest right where it is before burning itself out. This is just my guess. Why does it glow brightest before it dies out?


title: Why Does Gravity Work?

text: I'm trying to work out if energy has gravity, because if it does, then it will all get sucked into black holes, including dark energy, meaning that there will be no pushing effect left, and that the extra gravity of all the dark energy and dark matter in black holes will be enough to cause the big crunch. It also means that black holes cannot evaporate, and that the ultimate fate of the universe will not be photons flying around for all eternity, it will be the collapse of the universe in a big crunch, which causes the next big bang and so on forever. I was told that energy gets converted into mass by the Higgs effect, and that somehow means that the same energy now has gravity, where it had none before. Why is that? Can somebody explain why this particle of energy causes other particles of energy to form into something which has a completely different property to the particles of energy by themselves? Is there any real testing of the hypothesis that energy particles do not have gravity unless they are formed into mass? I understand the warping of space time, to some degree, it's like a three dimensional curve, like rolling down a hill, except there's nothing there in between the objects, and rolling down a hill is caused by gravity. http://simple.wikipedia.org/wiki/Higgs_field I'm not a physicist, but I've been looking at pages like this, and half the time I understand it, and the rest of the time, it goes way over my head and I imagine that there are a handful of people in the world who can really understand it, or I think it's actually just nonsense. It matters to me because I believe that the universe is eternal, and that the only way the big bang could have happened in the first place is if there was this eternal cycle, and that means that death is probably not the end, because the same energy will be formed in the same way over and over again, into my brain, and my consciousness.


title: Confusion regarding the principle of least action in Landau's "The Classical Theory of Fields"

text: Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in the points 1. and 2. below. * * * I understand that "principle of least action" is somewhat of a misnomer, since we find that to determine the path taken by a system, we need only impose the condition that the action be stationary, i.e., that $\delta S$ should vanish to first order for small variations of the path, and this leads to the Euler- Lagrange equations. In _The Classical Theory of Fields_ , Landau discusses the relativistic action for a free particle: > So for a free particle the action must have the form > > $$S = -\alpha \int_a^b ds$$ > > (...) It is easy to see that $\alpha$ must be a positive quantity for all > particles. In fact, as we saw [earlier], $\int_a^b ds$ has its maximum value > along a straight world line; by integrating along a curved world line we can > make the integral arbitrarily small. Thus the integral $\int_a^b ds$ with > the positive sign cannot have a minimum; with the opposite sign it clearly > has a minimum, along the straight world line. There is also a footnote, addressed a couple of paragraphs earlier, but which is relevant: > Strictly speaking, the principle of least action asserts that the integral > $S$ must be a minimum only for infinitesimal lengths of the path of > integration. For paths of arbitrary length we can say only that $S$ must be > an extremum, not necessarily a minimum. I have two questions regarding this:   1. How is the condition "the action must be a minimum for infinitesimal displacements" formulated? I've never heard of that outside of Landau's books, and in _Mechanics_ he mentions it as well but doesn't go into detail. Is this discussed a bit more somewhere?   2. If for the whole path the action only needs to be stationary, how can we make the argument for the negative sign? If the action had to be a minimum then it would make sense, but surely the fact that $\delta S$ = 0 isn't affected by an overall sign?


title: What is up and down conversion in photonics?

text: I have heard the terms up and down conversion in photonics/photovoltaics articles. What do the terms mean?


title: Weird Kinematics Homework

text: Here's another "hard" homework question I was given on how printers work. (I find it more confusing than it is hard.) ![enter image description here](http://i.stack.imgur.com/AhN24.jpg) I'm supposed to find the horizontal velocity of a charged droplet as it leaves the electric plates. This question is worth one single mark. I tried using the potential difference between the electric plates to compute the acceleration the droplets faced while within the plates, but the potential difference is unknown and the charge of the droplet is unknown. Most importantly, this is too much work for one single mark, and I therefore suspect that I am missing out on something small yet very important. Any ideas?


title: How do you calculate the anomalous precession of Mercury?

text: One of the three classic tests of general relativity is the calculation of the precession of the perihelion of Mercury's orbit. This precession rate had been precisely measured using data collected since the 1600's, and it was later found that Newton's theory of gravity predicts a value that differs from the observed value. That difference, which I am calling the _anomalous precession_ , was estimated to be about 43 arcseconds per century in Einstein's time. I have heard that general relativity predicts an additional correction that is almost exactly sufficient to account for that 43"/century difference, but I've never seen that calculation done, at least not correctly. Can anyone supply the details?


title: What categorical mathematical structure(s) best describe the space of “localized events” in “relational quantum mechanics”?

text: In a recent (and to me, very enlightening) paper, entitled "Relational EPR", Smerlak and Rovelli present a way of thinking about EPR which relies upon Rovelli's previously published work on relational quantum mechanics (see http://arxiv.org/abs/quant-ph/9609002 ). In relational quantum mechanics, there is no non-locality, but the definition of when an event occurs is weakened from Einstein's strict definition and instead is localized to each observer-measurement apparatus, including subsequent observers. There are (informal) coherence assumptions to ensure the consistency of reports from different subsequent observers (all possible friends of Wigner). All of this seems very similar to various results in modern categorical mathematics. Is there a standard mathematical structure which well describes the structure of the space of localized measurements which Rovelli has envisioned? I know of Isham's work on topos theory and quantum mechanics, but I think he is aiming at something a little different. PS I first asked this on mathunderflow, then on mathoverflow but to no avail, I am therefore reposting it here.


title: What are some approaches to discrete space-time used in modern physics?

text: This thought gave rise to some new questions in my mind. What are the consequences for:   1. How would it affect duality i.e. particle, wave property of photons?   2. How does this statement affect the information theoretical aspect (entropy) of the universe? **Update:** Given a volume V of space, is the entropy (maximum information that can be store) in this volume changed when this statement is applied?   3. How is a black hole affect by this statement? **Update** How is entropy changed inside the black hole?   4. Could one consequence be that the universe is hologram, since the construction isn’t continues?   5. Would the smallest quantified space be planck's constant? Is there an equivalent constant for time? I hope to get some of your feedbacks regarding this statement.


title: Does mutual gravitational attraction imply a negative pressure?

text: Imagine a small ball of gravitating dust particles initially at rest at the center of a large volume $V$. Following John Baez, Einstein's field equations say (in units of $c=8 \pi G=1$): $$\frac{\ddot{V}}{V} = - \frac{1}{2} (\rho + 3 p)$$ Now traditionally dust particles have a pressure $p=0$. However the dust particles have a mutual gravitational attraction for each other. Could this mutual attraction be described within the framework of GR by assigning a negative pressure $p$ to the ball of dust particles? Another way of looking at it is to say that the ball of dust particles has a certain amount of negative gravitational self-energy which counteracts some of the gravitational effects of its positive rest mass energy. Apparently the concept of gravitational energy in GR is complex so maybe negative pressure is a better way to think about it.


title: Spaceships travelling through space and debris

text: How can a spaceship travel through space if there is space debris flying around at very high speeds? Wouldn't even a small rock crack through the spaceship?


title: Quantum Fourier Transform question

text: We can formulate a Quantum Fourier Transfrom which is derived from a DFT. This DFT performs a polynomial operation by interpolating over specific sample points, and then when we read the output from the DFT one gets the coefficients of the whole polynomial operation using a DFT. The DFT pair maps to the Quantum analog, we can write the QFT analog for the DFT in question. There are two questions to this scheme: 1> In the DFT case to get the output, we read the output vector, to get the resultant poly- nomial. How can this be achieved in the the case of the Quantum Fourier Transfrom - is it possible at all, I mean if for the DFT output, we have a sequence of numbers sampled at points 1,2,3,etc, to get the coeffs of a polynomial at x^0,x^2,X^3,etc..., what way can this be done in the quantum Fourier transfrom, as in the QFT case it is just a superposition of states? 2> Also, what would be the complexity of such a quantum operation, we know DFTs with (n^2) operations use (log n)^2 QFT gates(??).Also, what is the time complexity of such an operation?


title: Spacecraft momentum question

text: Assume you're sitting in your spacecraft. The mass of you and the spacecraft is 2000 kg. You're traveling at 200km/h through the vacuum of space. You have a thruster pointing in the direction you're traveling at, so when turning it on it will slow you down. It produces 300N of thrust. How long does it have to stay on to slow you down to 0km/h. How do you calculate this, and the momentum of the spacecraft? This question would learn me a lot about momentum.


title: If the sun stopped burning, would we ever know it?

text: I read somewhere that since gravity moves at the speed of light, if the sun were to leave its position we would "know" about it through the absence of light and its gravitational effects on our planet at the same time. If this is the case, would we ever even know? Would the effects of its gravity change on our planet kill us all before we realized the light went out? Thanks


title: Tension on a string pulled by unequal forces

text: > Suppose two cases where masses are attached to massless, inextensible > strings. > > In the first case a body which has a weight of 20 Newtons(downwards) is > attached to a string which is acted upon by a force of 100 Newtons upwards. > > In the second case, a body of weight 10 Newtons is attached to a string and > again a force of 100 Newtons upwards is applied on the string. These two cases are identical except for the magnitudes of the weights attached to the strings. However, I think that the tension in both strings will equal 100 Newtons(the reaction force for the upward force). If this is correct, how is it that the string has the same tension when different forces are applied on it? Intuitively, shouldn't the string stretch more and have more tension when a larger force acts on it on one side. And if the tension in both cases is not equal then how can the tension in the strings be calculated?


title: Dimensional transmutation in QED?

text: I am familiar with the QCD dimensional transmutation (QCD is dimensionless theory but via renormalisation we get dimensional parameter; we have to choose some referent scale...), but I'm not sure if there exists dimensional transmutation for QED? If not, why not?


title: Time reversal invariance and statistics

text: To what extend does the behaviour of time reversal invariance depend on the statistics of the particle under consideration? More explicitly: To what extend does the action of the time reversal operator depend on the commutation relations of say fermions, bosons, etc.? Given a certain Hilbert space (say $\mathbb{C}^N$) with $N>2$ (so we are not talking Spin 1/2). What is the general way to construct a Time reversal symmetry operator? I am looking forward to your response.


title: Lowest point of a loose cable with a pulley/mass hanging from it

text: This is part of a homework question which I've been stuck on for several hours. I've tried googling "lowest point of rope", "lowest point of hanging cable", "lowest point of pulley", and a bunch of other combinations without luck. > Cable ABC has a length of 5m. The cable is attached to a wall on the left at > A, and attached to a wall on the right at C, 0.75m above the vertical > position of A (so C is attached at a higher location on the wall). The > distance between the walls is 3.5m. A 100kg sack is hanging by a pulley on > this cable at equilibrium, at B. Find the horizontal distance x of the > pulley from the left wall (neglect the size of the pulley). Intuitively I think the the pulley would hang at the location where it's closest to the ground (hence "lowest point of loose cable..."). However, I have no idea how to calculate it. We're only allowed scientific calculators (no graphing) and whenever I try to set up an equation it blows up. Once I figure out x it should be relatively easy to calculate the component forces for equilibrium. I tried looking for examples in the textbook and internet for something like this without luck.               | ---- 3.5m -----|     ---D-------------* <- C     |  |            /|     | <- 0.75m   /   |     * <- A    /      |     |\ |   /         F     | \|/     |  * <- B     E  |       _______      | 100kg |     |--| <- x     Length of cable: 5m      Here's a text diagram, as best as I could make it **Update** : Found a hint from the textbook - `(3.5 - x)/cos(o) + x/cos(o) = 5`. Not quite sure what to make of it, but it does kinda remind me of an ellipse at a slant... http://math.stackexchange.com/questions/108270/what-is- the-equation-of-an-ellipse-that-is-not-aligned-with-the-axis **Update 2** : Upon closer inspection of aufkag's angle-suggestion and the hint from the textbook, I believe he is correct about the angles being equal - the formula calculates the two segments of the rope from the adjacent sides `x` and `3.5 - x`. By the way, how can it be explained or "proved" or what's the law that says the angles between AB and the wall and AC and the wall in a setup like this are equal? **Update 3** : (after solved, see comment for aufkag): Added D, E, F. ABD = BAE and CBD = BCF, but can anyone prove or point out the law that says ABD = CBD or BAE = BCF? Anyways, the steps are:               o = angle AB and the horizontal or BC and the horizontal     x / cos(o) + (3.5 - x) / cos(o) = 5 (sum of segments of rope is 5)     tension in AB = tension in BC, therefore they share the same "load" of the mass, so we can calculate the tension in just one side     100 * 9.81 / 2 / sin(o) = 687N (approximately - first half of answer)     0.75 + xtan(o) = (3.5 - x)tan(o) (equal lengths for line segment BD)     solve for x to get 1.38m


title: the physical properties of leak testing.

text: Description: To test for leaks a pressure bubble test is performed. This is adding a specified pressure and submerging the test object under water to see if air leaks emerge. The requirement is that no leaks shall be detected when a certain pressure 1 is applied during a predefined time 1. I’m currently looking for a way to speed up this process. When decreasing the time, pressure should logically increase to draw the same conclusions. However what I would like to know is if there is more know about this relationship or/and if it is possible to superimpose this if this relationships is too complicated.


title: About the hump on galaxy rotation curves

text: The past days I have been studying the rotation curves of disk galaxies and I am currently trying to understand how we can extract information about the dark matter of a galaxy by looking its rotation curve. A typical and well behaved rotation curve of a disk galaxy rises fast at the start, then it peaks and produces a "hump"/"bump" and then it remains constant (or slightly declining). I would like to ask what exactly causes the "hump"/"bump" on the rotation curve and what it can tell us about the galaxy.


title: Ski Jumper's vertical velocity after $246.5m$ record?

text: What would be the vertical velocity of this ski jumper (ski flyer), after he first touches down, after he breaks the record with a $246.5m$ jump? What g force would he experience as he slows down? Video (the last video) I think he gets at least 6 seconds of airtime from $26$ to $32$ second mark. The ramp gradient at take off is listed at $11$ degrees and the take off speed is about $105km/h$. Some statistics] are here. [1] [2]


title: Why doesn't the existence of proper-time $\tau$ imply a preferred reference frame?

text: A proper time interval $\Delta\tau$ for a given observer is a relativistic invariant. However, the calculation of $\Delta\tau$ requires reference to some arbitrary coordinate time t: $\Delta\tau$ = $\int_{t_1}^{t_2} \\! \frac{\mathrm{d}t}{\gamma}$ Doesn't the invariance of $\Delta\tau$ require a "preferred" reference coordinate time? According to Wikipedia:   _Proper time is the pseudo-Riemannian arc length of world lines in four- dimensional spacetime._ Doesn't a unique arc-length require a fixed (ie preferred) metric? For example, when discussing the twin "paradox", solutions typically involve drawing world lines against a fixed metric, where the different arc lengths are obvious. Does this not violate the spirit of SR? Is there a better way to look at it that does not involve a preferred reference frame against which arc lengths are defined?


title: What sort of experiment would directly test time reversal invariance?

text: I guess the title says it all: how could/would you experimentally test whether our universe is truly time reversal invariant, without relying on the CPT theorem? What experiments have been proposed to check this? Have any of them been performed? I know that there are _indirect_ tests of time reversal invariance by observing CP violation, in the decay $K_L \to 2\pi$ for example. Then if you assume that the necessary conditions for CPT symmetry are satisfied in our universe, that means there must be time reversal symmetry violation as well. But I'm curious about ways to test time reversal invariance without relying on CPT. Basically, how could we distinguish between the standard model, which predicts T violation, and some hypothetical other theory that matches current experimental results as well as the SM, but in which CPT symmetry does not hold? P.S. This may be more of a research-level question, but I'm hoping it won't be _too_ obscure for this site ;-)


title: Covariant Quantisation and the Time Operator in String Theory

text: Covariant quantisation in string theory is accomplished by giving the commutator relations $[X^\mu(\sigma,\tau),P^\nu(\sigma',\tau)] = i \eta^{\mu\nu} \delta(\sigma - \sigma')$. Although string theory is not a field theory this approach is identical to the quantisation of fields $X^\mu$ in 1+1 dimensions. From this point of view it is also clear how to proceed from here (e.g. getting rid of the negative norm states due to the "wrong" sign of the zeroth component). However, there are two issues that I do not quite understand. Physical states are supposed to have positive energy, i.e. $P^0 \geq 0$. Especially when supersymmetry comes into the game, the algebra so to say dictates positive energies. But when the energy is bounded from below it is not possible to have a time operator obeying the commutator relation $[x^0,p^0] = -i$ where $x$ and $p$ are the above Operators $X$ and $P$ integrated over $\sigma$. For the case of quantum mechanics this has been proved by Pauli in 1933. The prove goes roughly like this: For an operator $H$ which is bounded from below let there be a Hermitian time operator $T$ with $[T,H] = i$ It is possible to shift the spectrum of H because of $e^{-i\epsilon T} H e^{i\epsilon T} = H - \epsilon$ for arbitrary $\epsilon$. That means for an eigenstate $|\psi\rangle$ with $H|\psi\rangle = E|\psi\rangle$ there is also an eigenstate $|\phi\rangle = e^{i\epsilon T}|\psi\rangle$ with $H|\phi\rangle = (E-\epsilon)|\phi\rangle$ For $\epsilon > E$ one has to either conclude that H can not be bounded from below or that T is not a Hermitian operator because it would generate states that lie outside of the Hilbert space. One possible solution could be to allow negative $p^0$ and to apply some kind of Feynman-Stueckelberg approach by reversing the sign of the world-sheet coordinate $\tau$. In this sense the decay of the vacuum into a positive and negative energy state is simply the propagator of a free state. However, this would not be possible in the supersymmetric case where the states have $p^0>0$. The other issue related to defining the zeroth component of the commutator is the construction of the Hilbert space of the physical states. In his book String Theory Polchinski starts with a "vacuum" state $|0;k\rangle$ with the norm $ \langle 0;k|0;k'\rangle \sim \delta^{26}(k-k')$ However, when integrating over $k$ one ends up with a superficial delta function because of the additional mass shell constraint. Polchinski solves the issue by introducing a reduced product $ \langle 0;k||0;k'\rangle \sim \delta^{25}(k-k')$ This seems to be a logical step because selecting the physical states by $L_0|\psi\rangle = \alpha'(p^2+m^2)|\psi\rangle = 0$ yields a Hilbert space whose functions depend on 25 momentum components. Still, the full Hilbert space is not normalisable (this differs from what is usually done in QFT during gauge fixing, where the Hilbert space is constructed via an equivalence relation for the gauge and not by selecting a subspace). The question is whether the Hilbert space constructed in such a way does exist at all. Also it seems as if the number of spacetime operators is reduced by one, thus rendering the steps taken for the covariant quantisation needless. (REMARK: I edited my question to make the point a bit clearer. This is not meant to be a criticism against string theory. It is just that during studying string theory I was confronted by someone with this issue. I just want to understand this detail of the basics because I haven't yet been able to resolve it. I hope somebody can help me.)


title: Can a trajectory between planets accelerate a space craft?

text: I read that if some spacecraft's trajectory is carefully planned, i.e. if it can slingshot (at loss of a better word) a massive body like a planet, it can gain speed. Is that correct ? Does solar system actually lose some energy to such a space craft in this way ?


title: Embedding of $F(4)$ in $OSp(8|4)$?

text: Is the superconformal algebra in five dimensions, $F(4)$, a subalgebra of the (maximal) six-dimensional superconformal algebra $OSp(8|4)$?


title: Real representation is physically real?

text: In Peskin & Schroder, Introduction to Quantum Field Theory  equation (15.82) states that $$ t^a_{\bar{r}} = -(t^a_{r})^* = (t^a_{r})^T $$ Why is the representation which satisfies $$ t_{\overline{r}}^{a}=Ut_{r}^{a}U^{\dagger} $$ called real? Does this real means something physically real?


title: Why do the anticommutation relations imply Fermi–Dirac statistics (Pauli Exclusion Principle) for the field quanta?

text: I was reading the following article Fermion FIelds and discovered the following passage not fully explained to me : > It is these anticommutation relations that imply Fermi–Dirac statistics for > the field quanta. They also result in the Pauli exclusion principle: two > fermionic particles cannot occupy the same state at the same time. What is the proof that the anticommutation relations of the Fermion Field gives rise to the Pauli Exclusion Principle?


title: Dyson Series Second Order Term Importance vs. Time

text: Given a time ordered Dyson series expansion of $$H_I=e^{-\frac{i}{\hbar}\sigma_3t}V_0\sin(\omega t)\sigma_1e^{\frac{i}{\hbar}\sigma_3t}$$ $${\cal T}\exp\left[-\frac{i}{\hbar}\int_0^tH_I(t')dt'\right]=I-\frac{i}{\hbar}\int_0^t dt' V_0\sin(\omega t')\sigma_1e^{\frac{2i}{\hbar}\Delta\sigma_3t'}+\ldots.$$ where $\sigma_i$ are the Pauli matrices, what is the condition for the second or higher order terms to become non-negligible? I know it scales like $V_0>V_0^2$ for the first to second order, but what is the role of the time? at very long times, the second term must become more and more important, what is that time scale? (based on this question: Rigorous justification for rotating wave approximation )


title: Effect of gravitation on light

text: Einstein predicted that the gravitational force can act on light. This was verified in one solar eclipse that light from a star near to the sun's disc bent due to Sun's gravity as predicted. Since Sun's corona is very hot, there should be hot gases filled beyond the corona through thousands of miles forming a convex-lens. Can it be refraction through convex lens that causes bending of light from the star rather than Sun's gravity?


title: What's the source of electricity for the human brain?

text: I keep hearing that there's always electrical activity taking place inside the human brain. Our heart and various other organs function because it receives electrical signals called impulse. But, what's the "voltage source" for the brain? How does it receive signals? Does it generate on it's own? If so, how?


title: The resultant of two forces acting at any angle?

text: I am studying about forces as vectors. And they give me this equation:   $c^2 = a^2 + b^2 - 2ab \cos C$ Can anybody explain me the second part of the equation? I perfectly understand $c^2 = a^2 + b^2$ but what's with the $-2ab \,\mathrm{cos}\, C$?


title: 3D Quantum harmonic oscillator

text: For an _isotropic_ 3D QHO in a potential $V(x,y,z)={1\over 2}m\omega^2(x^2+y^2+z^2)$. I can see by independence of the potential in the $x,y,z$ coordinates that the solution to the Schrodinger equation would be of the form $\psi(x,y,z)=f(x)g(y)h(z)$. Explicitly, what would it be? Is it $\psi(x,y,z) = cH_{n_x}H_{n_y}H_{n_z}e^{-{m\omega\over2\hbar}(x^2+y^2+z^2)}$, where $H_{n_i}$ are the $ith$ Hermite polynomial? (A side query, surely since the potential is radial, there is a polar coordinate form of solution which might be better? But this is not asked for in the question. Also, does _isotropic_ just mean that the potential is spherically symmetric?) How many linearly independent states have energy $E=\hbar\omega({3\over2}+N)$? Am I supposed to be counting the number of combinations of $n_x,n_y,n_z$ s.t. $n_x+n_y+n_z = N$? I vaguely remember some notion $(n,l)$ mentioned once, but I can't remember what it is nor find the bit of notes on this. Thanks in advance.


title: Transparency of materials

text: Is transparency of material has something to do with inter- or intra-molecular bonding? E.g. both graphite and diamond are carbon, but graphite is opaque and diamond transparent.


title: Crystal Field Theory

text: I am literally lost with this question: > Suppose that within the set of (2L+1)(2S+1) lowest-lying ionic states the > crystal field can be represented in the form **a(L_x)^2 + b(L_y)^2 + > c(L_z)^2** , with a, b, and c all different. Show in the special case L = 1 > that if the crystal field is the dominant perturbation (compared with the > spin-orbit coupling), then it will yield a (2S+1)-fold degenerate set of > ground states in which every matrix element of every component of L > vanishes.


title: Easy to obtain liquid with freezing point a couple of degrees above 0 Celsius

text: Please advice me a liquid whose freezing point is 2-5 Celsius. I know that the solution of salt in water can have freezing point of about -3 Celsius. I would like to know if similar liquid but with freezing point slightly above zero can be obtained. The liquid has to be created from readily available materials, like a mixture of water and something else. It also have to be non-explosive, non-poisonous and not easy to start fire on (so it is allowed to be sent via mail). Why I need this: A friend of mine is going to send some sweet potatoes to me to grow (this is a new culture in my county). But we fear that it can freeze. My friend will insulate the box with polystyrene. But I doubt that insulation will be useful without having a descent amount of heat inside the box. The idea is to put some phase-change thermal accumulator inside the insulated box, so that the inside keeps above zero for several days while the temperature outside is several degrees below zero Celsius. In case temperature outside will drop below zero, the liquid will begin to freeze and while it is freezing the temperature inside will keep at its freezing point.


title: Berry curvature of Landau levels

text: If we consider an electron on a two dimensional surface with a magnetic field normal to the surface, we know the states the electron can occupy are Landau levels. If we additionally impose periodic boundary conditions, i.e., that these states are eigenstates of the magnetic translation operators, then our surface becomes a torus, and the eigenstates are generalized Bloch states $\psi_{\mathbf{k}}(x,y) = e^{i\mathbf{k}\cdot\mathbf{r}}u_{\mathbf{k}}(x,y)$, with $k_i$ taking values in $\frac{2\pi}{L_i}n, 1 < n < N_{\Phi}$, where $L_i$ are the system dimensions, and $N_{\Phi}$ is the number of flux quanta passing through the area $L_x L_y$. For this boundary condition to be meaningful, we further require that the magnetic translation operators in either direction commute, so that $L_x L_y = 2\pi N_{\Phi} \ell^2$ ($\ell$ is the magnetic length). We can write down wavefunctions $\psi_{\mathbf{k}}(x,y)$ that statisfy these boundary conditions, as done, for example, by Yoshioka (http://prb.aps.org/pdf/PRB/v29/i12/p6833_1) and Haldane and Rezayi (http://prb.aps.org/pdf/PRB/v31/i4/p2529_1). To calculate the Berry curvature, one could simply calculate the Berry connection in some gauge, $$ \mathbf{A} = \int d^2x \,\, u_{\mathbf{k}}^*(\mathbf{r}) \nabla_k u_{\mathbf{k}}^*(\mathbf{r}) $$ and then the curvature $$ F_{xy} = \partial_{k_x}A_y - \partial{k_y}Ax $$ We know the Berry curvature for the Landau levels should be constant in $\mathbf{k}$. My question is, how does one do this in practice? It seems that the calculation of the Berry connection (in the Landau gauge $A = -Bx\hat{k_y}$) reduces to calculating the expectation value of the x position $\left<x\right>$. However, while this calculation would be trivial in an infinite plane, with periodic boundary conditions the wavefunctions become much more complicated.


title: Can the Lamb shift be expressed in more-or-less closed form in terms of the renormalized 2-, 3-,...,n-point VEVs of QED?

text: I see here that there are three contributions to the Lamb shift, from vacuum polarization (-27 MHz), from electron mass renormalization(+1017 MHz), and from the anomalous magnetic moment (+68 MHz). These look to be the renormalized 2-point photon propagator, the renormalized 2-point Dirac spinor propagator, and the renormalized 3-point VEV for two Dirac spinors and a photon. In my experience, derivations of the Lamb shift are somewhat long and messy. If we take the derivation of some set of renormalized n-point VEVs for granted, is the derivation of the Lamb shift from that point forward relatively short and clean? Although someone might feel like deriving this relation (or showing that there is no such relation) in a few lines as an Answer, and I _would_ be interested if it can be done briefly and convincingly, I would probably prefer a reference to somewhere that derives the Lamb shift in terms of the renormalized VEVs. Failing that, a reference to your favorite derivation of the Lamb shift, either in Comments or as an Answer, would be Useful to me, even if it doesn't conform to the prejudices you can see on display above. Finally, if the Question seems ill-put, as I suspect it might be, please feel very free to tell me so. Wanna learn.


title: Why do balls in a spinning ellipsoid move to the minor axis plane?

text: There is a question concerning the Physics of a small child's tall that has been bothering me for some time now. I have investigated this to a small degree, but I have not been able to find a satisfactory answer and I believe the resulting answer must be of an elementary nature. My newborn son has a small plastic toy that is an ellipsoid filled with small, plastic balls (approximately 10-15 balls). The ellipsoid can be revolved around an axis of revolution (the axis of revolution is the major axis of the planar ellipse) and when one spins the ellipsoid, the small, plastic balls find there way (almost immediately) to the plane that is perpendicular to the axis of revolution and contains the minor axis of the planar ellipse where they continue to spin in said plane as long as their speed is sufficiently large. ![Spinning ellipsoid](http://i.stack.imgur.com/popDF.png) In the image, the red curve is a metal rod (elephant's arms) that keep the ellipsoid in suspension, the green line is the axis of revolution, and the blue curve is the curve that the small, plastic, balls move to (almost immediately) and rotate along as long as the speed is sufficiently fast enough. Is there an elementary explanation (elementary = 2 undergraduate courses in Physics) for what I am observing? I am also interested in any explanation of what I am observing that would lead me to learning something new.


title: How much energy is contained in a 40 meter wave?

text: Consider a wave that stands 40 meters high in the sea on very deep water. How much energy would approximately be contained in this wave if it was 100 meters wide and had been produced by wind? Is this question even answerable? I read somewhere that the tsunami that caused massive destruction in South-East Asia a few years ago, was just something like a meter tall in open sea..


title: The effect of an EMP on circuits

text: Which of these is the current (also, what about voltage?) induced by an EMP pulse within a circuit most dependent on?   1. The area of the region enclosed by the circuit   2. The orientation of that area with respect to the originating direction of the pulse   3. The total length of the circuit (e.g. a wire with two conductors potentially connected together at the ends has lots of length but not much area enclosed within the loop) Suppose I were hypothetically trying to shield my computer and an iPhone connected to a USB cable to that computer from a high-altitude nuclear event. Does the thinness of the USB cord allow me to extend the cord outside the computer's Faraday cage and still have it be relatively safe? The phone would need to be in its own Faraday cage in this case, of course. What I'm wondering is if the exposed cable would have voltages induced in it.


title: How might clock synchronization work with RSA SecurID tokens?

text: ![enter image description here](http://i.stack.imgur.com/SO3v4.jpg) My workplace uses these things to generate one-time passwords which only work within a short time period. I have always been curious about how the clock synchronisation between the authentication server and the token might work. I'm not sure whether there is any communication between the token and the outside world at all, but I would doubt it because they are small, light, and they must make these things to be as cheap as possible for lowest unit cost. So, maybe there isn't any synchronization at all? But then, wouldn't the clocks gradually drift apart, especially if the battery was running down, eventually resulting in a bricked token?


title: What is the relationship between Force and Kinetic Energy?

text: I am an Middle-School (Grade 8) student, who is self-learning classical mechanics. I saw this equation from Classical Mechanics: $\vec F=m \vec a$, the following equation is pretty straight forward Force equals to mass x acceleration but I as a newbie to this subject am left very confused. As you may see the $a$ in the formula is an vector and so is the $F$. That in mind, it must mean force & acceleration is an direction we apply to an object. That seems extremely familiar to Kinetic Energy as Kinetic energy tends to be applied to an object in an direction, yet its equation is $E = \frac{1} {2}mv^2 $ is not too similar except from it pertaining to do with mass and movement. That in mind, my question is what is the relationship between Kinetic Energy & Force?


What is the energy distribution of light if it has an infinite length? ![Electromagnetic wave](http://i.stack.imgur.com/wgZiU.png) I have read in one of the answers here on phys.SE that light has actually an infinite length. But then what is the energy distribution of that electromagnetic wave?


How does band gap vary with the cell volume? is there a relation? If the volume is compressed, the interaction between atoms would be more, therefore the perturbation is higher hence the splitting would be more. Is my assumption right? What is the mathematical background? Any help would be greatly appreciated.


title: Does Feynman path integral include discontinuous trajectories?

text: While reading this derivation of relation of Schrödinger equation to Feynman path integral, I noticed that $q_i$ can differ form $q_{i+1}$ very much, and when the limit of $N\to\infty$ is taken, there remain lots of paths, which are discontinuous (almost) everywhere — i.e. paths consisting of disconnected points. Do I understand this wrongly? How do such discontinuous paths disappear on taking the limit? Or maybe they have zero contribution to integral?


title: Statics with ladder and wall

text: > _A uniform ladder of mass m and length L rests against the wall. The > coefficients of static friction between the floor and the ladder and between > the wall and the ladder are equal to each other (μ). What is the maximum > value of angle θ that the ladder can make with the wall without sliding._ My way to solve this: since ladder is not moving Torque on the ladder $$ -\frac{mgL}{2}\sin\theta-\mu N_{f}L\cos\theta+N_{f}L\sin\theta=0$$ Horizontal forces $$ N_{w}-f_{f}=0$$ Vertical forces $$ N_{f}+f_{w}-mg=0$$ where $N_{f}$ and $N_{w}$ is normal forcé due to floor and Wall, $f_{w}$ and $f_{f}$ friction due to Wall and floor. Now I solve for $N_{f}$ the first equation, to get: $$N_{f}=\frac{mg\tan\theta}{2(\tan\theta-\mu)}$$ Sincé the angle is the situation where the ladder is about to start sliding, friction forces will have their máximum value, so: $$f_{f}=\mu N_{f}$$ from 2º equation: $$N_{w}=f_{f}$$ and for same reason like befor $$f_{w}=\mu N_{w}$$ substituting all this values in the 3º equation I get: $$\frac{\tan\theta}{2(\tan\theta-\mu)}(1+\mu^{2})=1$$ and solving this for $\tan\theta$: $$\tan\theta=\frac{2\mu}{1+\mu^{2}}$$ but aparently this is wrong. Could someone check this and point where is the mistake. Ty


title: Whether nuclear physics or nuclear engineering is suitable for doing research in nuclear fusion?

text: I want to do research in making nuclear fusion sustainable for electrical energy production , which field I should choose? and it is worth doing research in fusion now, since many of them are saying we are technologically more backward to make fusion for commercial energy production. Additional details:Now I am in 3rd year electrical electronics engineering.


title: Why does a Resistor cause a potential drop?

text: I need to know the underlying physics of what exactly happens different with the electric field in the resistor than in superconducting wires. Why is it that when I connect a resistor, potential drops across its(resistor's) ends? Sorry for the silly question but I can't figure it out. I do know, energy will be dissipated and hence the voltage will drop but I'm looking for a more insightful and detailed answer.


title: Probability of spontaneous Boltzmann brain formation

text: I was reading through: http://www.scottaaronson.com/papers/giqtm3.pdf But I can't make sense of page 61 discussing Boltzmann brains. Specifically the fact that it says: > But the problem is worse. Since in an eternal universe, you would have > inﬁnitely many Boltzmann-brain doppelgängers, any observer with your > memories and experiences seems inﬁnitely more likely to be a Boltzmann > brain, than to have arisen via the “normal” processes of Darwinian evolution > and so on starting from a Big Bang! I don't understand what this last statement follows from and it seems very unintuitive. A Boltzmann-doppelgänger brain arising by chance seems very improbable since that would require the formation of a brain with a full brain state, i.e. essentially all the individual atoms/molecules appearing in the exact (or at least close enough) configuration. In other words, a very high level of organization. Whereas the Big Bang scenario merely assumes a hydrogen/helium cloud and that the basic laws of nature are in place. This seems to be a much simpler object as a starting point and hence much more probable. This starting point, once it has occurred (maybe due to chance) then evolves (through the relatively simple laws of nature) into the state we have now, and gives rise to processes like natural selection etc. which eventually bring about intelligent life and the very high level of organization in the brain. Evolution through natural selection, while fundamentally also depending on stochastic events, seems much more probable since natural selection guides the process, allowing it to "tune in" on the target state, rather than there being a requirement of the target state just emerging in one step as with the Boltzmann-doppelgänger. Another argument is that the human brain, while seemingly a very complex structure, is probably the result (as part of fetus/child development) from a much simpler process, described in the human DNA. Like how a seemingly complex fractal can emerge from a simple equation. Hence, it seems a much easier way of producing a brain by chance is to produce this simpler mechanism by chance "and let it run" until it forms a brain, rather than demanding that a full brain itself appears by chance as in the Boltzmann case. But given Scott Aaronson is very smart there must be something about this I'm missing. Because I'm reading the statement as saying that the Boltzmann- doppelgänger are more probable than the big bang, but to me it seems the converse is true.


title: Why do grey body radiators not heat up?

text: So I'm doing so work on the earth's climate system, and modelling it as a grey body radiators, and I've come across the phrase: "$62\%$ of the outgoing energy is lost to space and the other $32\%$ is absorbed by earth's atmosphere". Surely is energy is constantly being absorbed by the Earth it would just keep heating up for ever?


title: Question on Conformal Field Theory

text: Since every question has to be asked in a seperate topic, I'm asking a question refering to the following topic: Beginners questions concerning Conformal Field Theory In particula I'm refering to the subsection "Implementing a symmetry on operators" of the answer given by Lubos Motl. It is clear to me that we obtain $\delta\phi=i\epsilon [L_{m},\phi]=i \epsilon z^{m+1} \partial_{z} \phi$ and that $z^{m+1} \partial_{z}$ are the generators of conformal symmetry. What confuses me though is that these generators fulfill the Witt-Algebra and not the Virasoro Algebra. Since we're in the quantum case and we want to show that the theory is invariant on a quantum level, shouldn't we get generators that fulfill the Virasoro Algebra? Thanks in advance for the responses. Best regards.


title: When do we expect to get results from the LHC?

text: At the current LHC luminosities, will it take years to detect the Higgs boson, superpartners, or any other forms of new physics at the LHC? What should particle physicists do in the meantime? We particle physicists have been waiting too long now for experimental input.


title: Give me examples of crackpots who were right after all

text: I am interested in examples of crackpots coming up with correct results in physics. Why do mainstream physicists look down so much upon "crackpots"?


title: Fuel and heated iron?

text: If I have a pile full of fuel (gasoline) - and I also have heated iron ( very very hot - color orange) and I put the Iron in the pile , Would the gasoline will burn ? I mean - does gasoline need heat or actual fire in order to burn ? nb - I can't test it since I don't have the means to do it.


title: Field interaction betweeen two point charges?

text: [SOLVED] Consider two particles _A_ and _B_ having equal charges and placed at some distance. The particle _A_ is slightly displaced towards _B_. So, * Does the EM force on _B_ increase(+/-) **as soon as** the particle _A_ is displaced? * Does the EM force on _A_ increase(+/-) **as soon as** it is displaced? The first question is a straight no, since the field don't interact instantaneously, however what about the second question? P.S: This from the short answer section of the chapter 29 from Concepts of Physics (Part 2) H.C.Verma (ISBN-13: 978-8177092325)


title: Does one square centimenter of the sun core really radiate this amount of energy?

text: I have been thinking that since the core of the sun maintains its temperature at 15 million degrees Kelvin, then every cubic centimeter of this core is receiving a certain amount of energy to keep it at this temperature. So I was thinking what would happen if we could take a small sphere, say, 0.6 cm in radius (so the area is 1 square cm) and put it in the earth's atmosphere. Would it radiate the same energy that it consumed to get to 15 million degrees in the first place ? I made some calculations using Stefan-Boltzmann law, here's what I got : $$ P = Area \times 5.67 \times 10^{-8} \times e \times T^4 $$ So for easier calculations let's assume that it is a black body, and the surrounding temperature is negligible compared to 15 million degrees. so I got : $$ P = .0001 \times 5.7*10^{-8} \times ({15*10^{6}})^4 = 2.9\times10^{17} \,\mathrm{joules/second} $$ Now, isn't this a huge amount of energy ? I know the body has to be maintained at 15 million degrees to keep radiating energy at this rate, about 0.8 cubic cm of the sun core is about 120 kilograms, so the more important question is for how long will this rate of radiation continue. I honestly feel that there are mistakes in what I have calculated, so please any correction would be greatly appreciated.


title: Why doesn't sound infinitely loop?

text: Let say we have a microphone and a speaker. The microphone will receive the surrounding sound, and the speaker will amplify it. Assume we have unlimited power for the microphone and speaker, so they can work forever. When we speak to the microphone, the sound should be repeated by the speaker. While the speaker generates sound, the sound should input to the microphone, and the microphone should repeat to the speaker. So, the sound should never stop, in a loop. But in reality, we don't have this issue. What's going on? Do my assumptions have something missing? Thanks.


title: Why does burning things make them black?

text: It's not clear to me how burning process can transform a material which was previously capable both of absorbing and emitting photon to one which can only absorb them. I would like to hear an educated explanation for how the burning process alters that property of matter: what is happening to the energy levels that the material used to have before it was burned?


title: Einstein-de Sitter - confusing constant of integration

text: I'm struggling to understand this derivation of the Einstein-de Sitter universe model It starts with $$\int R^{1/2}dR=\int H_{0}R_{0}^{3/2}dt.$$ Evaluating this integral gives$$\frac{2}{3}R^{3/2}=H_{0}R_{0}^{3/2}t+K,$$ where $K$ is a constant of integration. $$R\left(t\right)=\frac{3}{2}R_{0}\left(H_{0}tK\right)^{2/3}.$$ Let $t=t_{0}$ when $R=R_{0}$, this becomes $$R_{0}=\frac{3}{2}R_{0}\left(H_{0}t_{0}K\right)^{2/3}.$$ Dividing the third equation by the fourth equation gives$$R\left(t\right)=R_{0}\left(\frac{t}{t_{0}}\right)^{2/3}$$ What I don't understand is how the constant of integration disappears. In the second equation it's added to the right-hand side, but in the third equation its multiplied by the right-hand side, and then cancels to give the final (correct) equation. How does that work? Apologies if I've missed the obvious.


title: Covariant derivative of a covariant tensor wrt superscript

text: Is it true that when you take the covariant derivative of a covariant tensor, do you always have to do with a subscript? What if you do it wrt a superscript?Does the first term (with the partial derivative) take a minus sign? More specifically, is this true? $$\nabla^{\mu}R_{\mu\nu} = -\frac{\partial R_{\mu\nu}}{{\partial x_{\mu}}} + \text{(Christoffels)}$$ Where does the minus sign come from? Is there a proof for this, or is it just a definition? Also, is there a change in the signs for Christoffel symbols(not the change if the the tensor's indices change position, but the change _when the index of the covariant differential changes_ )? I want to know the PROOF/REASON behind the minus sign.


title: Angular displacement and the displacement vector

text: I've been recently introduced to angular displacement, and I'm a little bit confused about it. I think that _displacement_ which is a vector and which is defined as the shortest distance between any two points is different from _angular displacement_. Angular displacement is measured in radian or in other words it measures the 'angle' that a rotating body goes through. However, _displacement vector_ is measured in meter. Angular displacement has the dimension of $1$; however, displacement vector has the dimension $L$. Is there any concept of the-shortest-distance-covered in angular displacement? I think angular displacement may just mean the change of position of a rotating body w.r.t. the angle subtended by the arc, traveled by it, at the center of the circle around which it is rotating. ![enter image description here](http://i.stack.imgur.com/o6LgA.jpg) If a body is rotating about the axis of a circle, and it moves from point A to B making an arc of length S, then the distance it covered is given by $S = θr$. However, the shortest distance it could have covered to reach point B can be given by the length of the vector D.


title: Does a AAA battery have a dipole moment?

text: Does a AAA or D battery have an electric dipole moment? Why don't the opposite poles of two batteries attract each other like that of magnet's?


title: Electric Field Lines between two non parallel plates

text: **A potential difference is applied between two metal plates that are not parallel. Which diagram shows the electric field between the plates?** ![enter image description here](http://i.stack.imgur.com/lFmHv.png) A is the answer BUT WHY explanation needed !


title: Orbital angular momentum and multielectron atoms energies

text: Explain why states with diﬀerent orbital angular momentum quantum number have diﬀerent energies for multielectron atoms but are degenerate in energy for hydrogen Can anyone explain?


title: Normal mode of a coupled pendulum: why the constant $\psi_1$, $\psi_2$

text: I need to solve a problem that tells me to find out the motion of both the pendulums that appear in the first 45 seconds of this video I think this kind of motion is described by a system of differential equation of the form: $$\ddot{x} + \omega^2x = \epsilon y$$ $$\ddot{y} + \omega^2 y = \epsilon x$$ where all constants like the mass of the pendulum and so on are missing and $x$ describes the motion of the first pendulum and $y$ the motion of the second one. To solve the problem one needs to assume $\epsilon$ very small and $\epsilon \lt \omega^2$. I've tried to solve this problem analytically, but it was a little too complicated so i tried the physical approach by following the example given here under the section coupled oscillator. I think that i've understood almost everything except the fact that when we evaluate the normal modes we add the constant $\psi_1$ and $\psi_2$ and get the solutions $$\vec{\nu}_1 = c_1 \begin{pmatrix} 1 \\\ 1 \end{pmatrix}\cos(\omega_1 t + \psi_1)$$ $$\vec{\nu}_2 = c_2 \begin{pmatrix} 1 \\\ -1 \end{pmatrix}\cos(\omega_2 t + \psi_2)$$ My question is: why do we have those two constant $\psi_1, \psi_2$? I understand the fact that we are interested only in the real valued part of the solution $Ae^{i\omega t}$, but I don't understand where do these constant come from, is there a physical or better mathematical explanation for this?


title: Bernoulli Equation and Flow in a pipe - paradox

text: I am studying Bernoulli equation and am facing a problem. The Bernoulli equation is applicable along a streamline and in steady flow condition (I guess this condition is to make sure it can be applied at all times). Now say I want to calculate the flow velocity at a particular cross section of a pipe of varying cross sections. Now assume, I have put a Gauge pressure meter between these two particular cross sections, which gives me the change in pressure between these two cross sections along the pipe. So, $\Delta P = \frac{\rho (v_1^2 - v_2^2)}{2} + \rho g \Delta z$ Here, $v_2$ is the velocity at the cross section at which we want to calculate the velocity. Now we know $\Delta P$, we know $\Delta z$ (assume we are calculating along a horizontal streamline). Now interestingly, in all the literature the velocity they calculate, everyone assumes it to be uniform over the cross section. Why? The Bernoulli equation is applicable along a streamline, and every starting point will have a different ending point, and hence a different streamline. Why on earth, everyone assumes the velocity is uniform over cross section?


title: Constructing Ward identity associated with conserved currents

text: Consider constructing the Ward identity associated with Lorentz invariance. It is possible to find a 3rd rank tensor $B^{\rho \mu \nu}$ antisymmetric in the first two indices, then the stress-energy tensor can be made symmetric. Once done, the conserved current coming from the classical analysis is of the form $$j^{\mu \nu \rho} = T_B^{\mu \nu}x^{\rho} - T_B^{\mu \rho}x^{\nu}$$ This ensures the symmetry of the conserved current which can be seen most easily be invoking the conservation law $$\partial_{\mu}j^{\mu \nu \rho} = 0 $$ and $$\partial_{\mu}T_B^{\mu \nu} =\partial_{\mu} (T^{\mu \nu}_C + \partial_{\rho}B^{\rho \mu \nu}) = 0.$$ Let $X$ denote a set of $n$ fields. The Ward identity associated with Lorentz invariance is then $$\partial_{\mu} \langle (T^{\mu}x^{\rho} - T^{\mu \rho}x^{\nu})X\rangle = \sum_i \delta(x-x_i)\left[ x^{\nu}_i \partial^{\rho}_i - x^{\rho}_i\partial^{\nu}_i\langle X \rangle - iS^{\nu \rho}_i \langle X \rangle\right].\tag{1}$$ This is then equal to $$\langle (T^{\rho \nu} - T^{\nu \rho})X \rangle = -i\sum_i \delta (x-x_i)S^{\nu \rho}_i\langle X \rangle,$$ which states that the stress tensor is symmetric within correlation functions, except at the position of the other fields of the correlator. My question is: how is this last equation and statement derived? I think the Ward identity associated with translation invariance is used after perhaps splitting (1) up like so: $$\sum_i^n x^{\nu}_i \sum_i^n \delta(x-x_i)\partial^{\rho}_i \langle X \rangle - \sum_i^n x^{\rho}_i \sum_i^n \delta(x-x_i)\partial^{\nu}_i \langle X \rangle - i\sum_i^n\delta(x-x_i)S^{\nu \rho}_i\langle X \rangle $$ and then replacing $$\partial_{\mu}\langle T^{\mu}_{\,\,\,\rho}X \rangle = -\sum_i \delta (x-x_i)\frac{\partial}{\partial x^{\rho}_i} \langle X \rangle$$ for example. The result I am getting is that $$\langle ((\partial_{\mu}T^{\mu \nu})x^{\rho} - (\partial_{\mu}T^{\mu \rho})x^{\nu} + T^{\rho \nu} - T^{\nu \rho})X \rangle = \sum_i x^{\nu}_i \partial_{\mu}\langle T^{\mu \rho}X \rangle + \sum_i x^{\rho}_i \partial_{\mu} \langle T^{\mu \nu} X \rangle - i\sum_i\delta(x-x_i)S^{\nu \rho}_i\langle X \rangle$$ To obtain the required result, this means that e.g$$ \sum_i x^{\nu}_i \partial_{\mu} \langle T^{\mu \rho}X \rangle = \langle(\partial_{\mu}T^{\mu \rho})x^{\nu} X \rangle,$$ but why is this the case? Regarding the statement at the end, do they mean that when the position in space $x$ happens to coincide with one of the points where the field $\Phi_i \in X$ takes on the value $x_i$ (so $x = x_i$) then the r.h.s tends to infinity and the equation is then nonsensical?


title: Is this theory about Universe information true?

text: I recently saw this video about information and randomness. At some point, it states that a completely predictable universe would infringe the second law of thermodynamics, because it would imply that the overall information of the Universe would be conserved throughout time, thus leading to a costant entropy Universe. Also, it states that the additionally information that is increasing entropy is coming from QM randomness. I recognize it's a really fascinating theory, but is it true? Is the equivalence between information and entropy sensible?


title: Why does a wine glass with less water resonate at a higher frequency?

text: In this video https://www.youtube.com/watch?v=hWwM7F-zaHs, Professor Lewin showed that for the tube, the less water there is, the longer the effective length of the tube and therefore, the lower the frequency. He then demonstrates an opposite effect for a wine glass. Namely, an empty wine glass resonates at a higher frequency than a filled one. Why is that so?


title: Action of the Poincare Group on a Scalar Function

text: Let $F(x^\mu)$ is a scalar function; i.e. $F(x^\mu): \mathbb{R}^{1,3} \rightarrow \mathbb{R}$. How the Poincare Group $P(1,3)$ will act on it; i.e., by which formula I can calculate it for a specific function $F(x^\mu)$? Edit 1: We know that a subgroup of Poincare group $P(1,3)$ leaves the hypersurface $\Sigma: x^+ = 0$ invariant where $x^+ \equiv x^0 + x^3$. To show this a formula is needed.


title: Temperature of thermochemical reaction between propane and nitrous oxide

text: I'm trying to calculate the properties of the combustion process using propane and nitrous oxide. When I tried to nail down the combustion temperature, the result looks just off to me. I went through several times with the process but since the reaction should produce less enthalpy change than using pure oxygen gas and my results is above the standard combustion temperature with pure oxygen, it is definitely wrong somewhere. The process, how I got my solution is the following: $$C_3H_8 + 10 N_2O => 3 CO_2 + 4 H_2O + 10 N_2 + \Delta_rH$$ $$\Delta_rH = \Delta_fH_p - \Delta_fH_r$$ Where the r subscript means reactants and p is for products. $$\Delta_fH(C_3H_8) = -104.7 kJ/mol$$ $$\Delta_fH(CO_2) = -393.5 kJ/mol$$ $$\Delta_fH(H_2O) = -241.8 kJ/mol$$ $$\Delta_fH(N_2O) = +82.05 kJ/mol$$ $$\Delta_fH(N_2) = 0 kJ/mol$$ Which amounts to the following conclusion: $$\Delta_rH = (3 * -393.5 kJ + 4 * -241.8 kJ) - (1 * -104.7 kJ + 10 * 82.05 kJ) = -2863.5 kJ$$ $$\Delta_rH = -2863.5 kJ / 0.484 kg = -5916.3223 kJ/kg $$ This value is for 10 mols of Nitrous Oxide and 1 mol Propane. Since both molecules have the molar mass around 44 g / mol, it's essentially the stoichometric ratio of 1 to the 10. So far, so good (I think). The result seems reasonable to me, as I went through the same process using only O2, which ended up considerable more as expected (it only takes 5 part of O2 so the reaction produces more enthalpy with the same mass, plus O2 molar weight is 32.) In the next step I used the following formula: $$\Delta_rH = \sum_{i=1}^m n_i \int_{T_0}^{T_r}C_pdT $$ I assumed here that the: $$\int_{T_0}^{T_r}C_pdT$$ part can be simplified with the assumption that the Cp won't change with the temperature. I'm well aware that this isn't the exact case, and I've found that for example water vapour has a particular big swing over the temperature in terms of heat capacity on a constant pressure. However, I tried to work with the values I could find around the internet, and in the case of water vapour I worked with the temperature that looked like a quite good mean value. So I continued like this: $$\int_{T_0}^{T_r}C_pdT = \Delta T * \sum_{i=1}^m n_iC_p$$ $$T * \sum_{i=1}^m n_iC_p = \Delta_rH$$ $$T = \frac{\Delta_rH} {\sum_{i=1}^m n_iC_p}$$ $$T = 2863500 J / (3 * 37.135 J/K + 4 * 53.1 J/K + 10 * 29.12 J/K) = 4656.06 K$$ This value is obviously not good, given that the pure oxygen reaction combustion temperature with propane is 3093 K Ref. Now, is there some deeply flawed assumption in my process? Can it be that the simplification of that integral expression led me down on a wrong calculation in the first place? If so, how can I access to the exact functions of these heat capacities for the gases I'm using?


title: Can symmetry generators anticommute with the S-matrix?

text: In Coleman and Mandula's proof of the Coleman-Mandula theorem, they define a symmetry transformation as an unitary $U$ which,   1. turns one-particle states into one-particle states,   2. acts on many-particle states as if they were tensor product of one-particle states,   3. commutes with $S$, the $S$-matrix. I think this means that if $T$ is a generator of symmetry, then $$[T,S]=0.$$ If we relaxed the 3rd point so that $T$ can also anti-commute with $S$, what would be the consequences? In particular, would the theorem still hold?


title: Feynman diagrams in effective theories

text: I've been seeing many feynman diagrams lately that I can't quite interpret yet. I've heard a basic Quantum Field Theory lecture and so to me, a Feynman diagram is simply a mnemonic picture to quickly write down (and remember) all of the possible terms in the perturbation series of the matrix element in scattering. But they seem to be much more than that. Consider for example this diagram of proton-neutron scattering via pion exchange. The picture seems to have an intuitive meaning, but how can it be a valid Feynman diagram? Wouldn't that imply that there is an unterlying theory with a proper Lagrangian from which Feynman rules can be derived that would assign a number to this diagram? **Question: When describing nucleon-nucleon interactions in this way, do people actually write down a Lagrangian and derive those rules?** (I am confused because I've seen diagrams like that in several books and they usually write down the cross sections simply from analogy arguments to other theories.) Any clarification will be greatly appreciated, David


title: Measuring the magnitude of the magnetic field of a single electron due to its spin

text: Is it possible to measure the magnitude of the magnetic field of a single electron due to its spin? The electron's intrinsic magnetic field is not dependent upon the amount of energy it has does it? Does this require a SQUID, a Superconducting Quantum Interference Device? What published papers or experiments have been done to answer this question?


title: Has somebody ever tried to measure the gravity oscillations of nearby rotating masses?

text: I'd like to extend this question: Are Newton's gravity waves detectable by a laser interferometer? but with some changes. Has somebody ever tried to measure the gravity oscillations nearby (< some meters) of such rotating masses (as in Carl Brannens question)? Say some kgs or grams rotating on a beam with the highest rpm technically possible? (In a vacuum chamber of course!) I dont know what will "radiate" stronger , some grams at 100 000 rpm or some kg at say, 5000 rpm (and some cm distance), therefore, has anybody ever tried something like that in lab? I am aware, that such a experiment is plagued by mechanical (elastic) coupling through air, supporting structures etc, but I think that one can make use of mechanical resonance in the detecting device, helping a lot for selectivity. The fact that the oscillations come from a quadrupole(frequency doubling) , whereas mechanical coupling is not at double frequency, might help to "see" something. As often, its a question of signal/noise ratio :=(


title: Why work is a scalar and not a vector?

text: > Work (in physics) is a scalar but why? and why not a vector?


title: What is the difference between broken and unbroken sypersymmetry?

text: In a physics article I read recently, the author introduces the notion of supersymmetry by saying basically that the system described by the Hamiltonian $H$ is supersymmetric if $H$ can be decomposed as $H=QQ^\dagger + Q^\dagger Q$ with $Q^2=0$. This condition then leads to a nice splitting of the underlying Hilbert space, which seems to help a lot when working with $H$. Even from the point of view of simple linear algebra, this property is obviously interesting. Then, I heard that the symmetry is said to be broken or unbroken depending on whether or not $H$ has any ground states, or in other words if the null space of $H$ is non-trivial. I can understand this as a definition, but why would this be interesting? In particular, what consequences are there to supersymmetry being (un)broken (preferably at the low level)? Which systems are "better"?


title: Why fermions have a first order (Dirac) equation and bosons a second order one?

text: Is there a deep reason for a fermion to have a first order equation in the derivative while the bosons have a second order one? Does this imply deep theoretical differences (like space phase dimesion etc)? I understand that for a fermion, with half integer spin, you can form another Lorentz invariant using the gamma matrices $\gamma^\nu\partial_\nu $, which contracted with a partial derivative are kind of the square root of the D'Alembertian $\partial^\nu\partial_\nu$. Why can't we do the same for a boson? Finally, how is this treated in a Supersymmetric theory? Do a particle and its superpartner share a same order equation or not?


title: Feynman's Infinite Amount of Logic for One Tiny Bit of Space

text: Watching one of Feynman's lectures, I came across something that puzzled me. What was Feynman referring to when he said the following? > What goes on in no matter how tiny a region of space and no matter how tiny > a region of time, according to the laws as we understand them today, takes a > computing machine an infinite number of logical operations to figure out. > Now, how could all that be going on in that tiny space? Why should it take > an infinite amount of logic to figure out what one stinky little bit of > space-time is going to do?   >  -- Richard Feynman **Edit:** I see a close vote was cast, the reason being that the question is unclear. My question is, why would Feynman say it would take an infinite amount of logic to simulate even a small region of space-time?


title: How does the frequency of a particle manifest itself?

text: In terms of wave-particle duality for, let's say a photon; how would the frequency practically manifest/demonstrate itself? Like, i understand that the frequency is related to the energy a particle has, but frequency in my mind suggests oscillation about a point. Is the photon physically oscillating through space as it travels? I wouldnt imagine so. Which periodic occurrence is referred to when one talks about the frequency of a particle?


title: Difference Between Algebra of Infinitesimal Conformal Transformations & Conformal Algebra

text: in Blumenhagen Book on conformal field theory, It is mentioned that the algebra of infinitesimal conformal transformation is different from the conformal algebra and on page 11, conformal algebra is defined by a redefinition of generators of infinitesimal conformal transformation. I have three question about this :   * How this is possible that by a redefinition of generators, one could obtain a sub-algebra of an algebra? in this case one obtain conformal algebra as a sub-algebra of algebra of generators of infinitesimal conformal transformations?   * Does this is related to «special conformal transformation» which is not globally defined?   * How are these related to topological properties of conformal group? Any comment or reference would greatly be appreciated!


title: Getting the Lagrangian from the action in curved spacetime

text: Suppose I have this action: $$ S = \int \mathrm d^4 x\sqrt{-g}\times \text{something}$$ where $g$ is the determinant of the metric. Should I take the Lagrangian to be: $$ \mathcal L = \sqrt{-g} \times \text{something} $$ or: $$ \mathcal L = \text{something}$$ instead? Yes, this is a stupid question.


title: Is there an alternative to solving the equation for a bead on a hoop with friction?

text: > Given a circular horizontal loop of radius R and coefficient of friction > $\mu$, and a bead which slides along the loop with some velocity, determine > the initial velocity $v_o$, that should be given to the bead so that it > makes exactly one full turn before stopping. I believe the set up looks something like this: ![Setup](http://i.imgur.com/KxSf1vx.png) I will work in cylindrical polar coordinates (r,$\phi$,z). The normal force N can be written as: $$N(\phi) \hat{r} +N_z \hat{z}$$ I arrive at the following set of equations: \begin{align} F_r &= -m r \dot{\phi } (t)^2 = -N _r (\phi) \\\ F_\phi &= m r \ddot{\phi } (t) = -f = -\mu \lvert N\rvert \\\ F_z &= ma_z = N_z-mg \end{align} Immediately it can be deduced that $a_z=0$ so $N_z=mg$. I use the first equation to express $\lvert N \rvert$ as follows: $$\lvert N \rvert = \sqrt{\bigl(mr\dot{\phi}(t)^2\bigr)^2+(mg)^2}=m\sqrt{r^2\dot{\phi}(t)^4+g^2}$$ I sub $\lvert N\rvert$ into the second equation and arrive at: $$r\ddot{\phi}(t) = -\mu \sqrt{r^2\dot{\phi}(t)^4+g^2}$$ I'm not sure how to work with this differential equation. In an ideal world I would have the initial conditions be $\phi (0) = 0$ and $\dot{\phi}(0)=\frac{v_o}{R}$ and there would be an analytic solution. I would then chose $v_o$ so that the time at which $\phi (t) = 2\pi$ is the time at which $\dot{\phi}(t)=0$ which ensures the single turn condition. Is there some alternative procedure that would be less complicated?


title: What are the current contenders/most promising approaches to High Tc Superconductivity?

text: I want to know what kinds of things theorists are currently looking at. Specifically, I want to know more about the promise that field-theoretic methods are showing. I am studying superconductivity at an advanced undergraduate/beginning graduate level. Links to review papers/papers appreciated. Thanks.


title: Which quantum models violate the third law of thermodynamics and have an ergodic ground state?

text: Which any condensed matter quantum spin models over a finite lattice of size N which violates the third law of thermodynamics with ergodic mixings for the ground state?