title: Derivatives of fluctuations about a condensate

text: * Firstly I am not sure as to whether I am using the word "condensate" in the right context. In QFT contexts I think I see it getting used to mean the space-time independent solution which would solve the Euler-Lagrange equations of the action that would sit in the exponent in the path-integral - which in general might be different from the classical action. I would like to know why are these kinds of solutions so important - because this is picking out some special configurations among the entire space of classical solutions which would in general include non-trivially dynamical solutions.    * Now when one is doing a "small" fluctuation about the condensate and integrating out degrees of freedom to get an effective action for one of the fluctuation variables then there are two issues which confuse me -     * In multi component fields (like say complex ones which can be thought of as the modulus and the phase) what drives the choice as to which fluctuation is to be integrated out? (..in the complex case I guess in general people talk to the effective action for the phase fluctuation..)      * What is most confusing to me is to understand how to determine whether the space-time derivatives of the fluctuations are big or small. If one is doing the calculation to say second order then does one keep the products and squares of the derivatives of the fluctuation at the same level of perturbation as the squares and products of the fluctuation themselves? I can't see a natural scale for the derivatives of the fluctuations to which I can compare the derivatives to decide whether they are large or small.


title: Deflection of a membrane

text: I am currently working on a project which is described as the deflection of a circular membrane. What I am trying to model is the deflection of a piece of plastic film (E=200MPa,v=0.5) when placed under pressure. I would like some recomendations on the initial displacement field (w(r)) and the horizontal displacement field (u(r)). Keeping in mind that this membrane is not of a small size, but can vary from 5 cm upto 20 cm in diameter. It has a thinkness of 0.05 mm. Queit honestly I am not exactly sure what the difference is between theory of using a plate to model this and using a membrane. I hope to start a discussion this way and receive some input with which I can further my study. Experimental investigation has been completed however the theoretical model is still in progress and I need some help. I hope to hear more soon! If anything is unclear or I have forgotten something, please let me know.


title: About the theory of relativity

text: Why is speed of light constant in every non inertial frame of reference? Is there any theoretical explanation behind this postulate Since we cannot completely depend upon the experimental results?


title: About the general expression of trace anomaly and CFT partition functions

text: I have put up a question here, http://mathoverflow.net/questions/139685/proof- of-the-general-expression-for-anomaly-in-a-cft-and-its-partition-function Here I am putting up a slightly different version of that question, * * *   * I think the statement is that for any dimensional CFT the following is true,  $$\langle T^{\mu}_\mu \rangle = \sum B_n I_n - 2(-1)^{d/2}AE_d,$$ where $E_d$ is the `"Euler density" and $I_n$ are the independent "Weyl invariants of weight $-d$". (...I am not sure of the definition of the geometric quantities coming on the R.H.S and I wonder if the notion of the "Euler density" and ``Weyl invariants" are related to the ideas of the Weyl tensor and the Euler tensor..) * * *   * Also a similar sounding statement that I see is as in equation 15 (page 5) of http://arxiv.org/abs/hep-th/9806087 One can see the stark similarity between that the equation referred to in the linked paper and the statement of trace anomaly that I have typed in the first bullet point. * * * I can't find a reference to the derivation of these results and/or the relationship between these statements. It would be great if someone can help with this.


title: Torque of a winch with pulleys

text: I'm working on a project that involves using a remote-controlled electric winch to raise and lower my bicycle using a pulley system. The problem is that I don't know how much torque will be required of the electric motor in this system. A somewhat rudimentary diagram is as follows: ![enter image description here](http://i.stack.imgur.com/dR3xC.png) I haven't bought the winch yet, but it'll probably be more like 2-3 cm radius rather than 5 cm as labelled, so I'll assume 3 cm. My calculation is as follows: The pulley system has a 4:1 mechanical advantage, so the weight on the rope is ~50 N, and then $$T = rmg = (3\,\mathrm{cm})(50\,\mathrm{N}) = 1.5\,\mathrm{N\,m}$$ Which means that this motor should do the job. Is my reasoning correct?


title: Foucault pendulum explanation, rotating earth or rotating universe?

text: If we start from the assumption that all frames of reference are valid for describing motion, how can a foucault pendulum either prove or disprove that the earth rotates or is stationary? Couldn't it just as easily prove that the earth is stationary and that the whole universe (including the earth's atmosphere) rotates? what would be the difference in the observed Foucault pendulum? How can the observation prove one explanation over the other in light of my assumption? Is the rotating Earth model preferred for the sake of simplicity?


title: Can antimatter be used as fuel for nuclear reactors?

text: I completely understand the difficulties of making and storing antimatter, so I am not talking about the mechanism or the way of doing it here, I am just talking about the concept. As far as I know, nuclear power plants use the heat from the nuclear fission reaction to heat water and use the steam through turbines and generators to generate electricity. So, if we could **somehow** use the annihilation of matter-antimatter inside a reactor, would it still be a viable way of generating heat and thus electricity ? or is there something special for nuclear fission that is not available for matter-antimatter annihilation ?


title: How can I explain or demonstrate the Lorentz Force to a 12 year old?

text: I'm a space physicist. I've been working with a group of school students (aged between around 10 and 12) exploring the Sun, the Earth and the solar system. We've talked about some basics of magnetism and the fact that the Earth's magnetic field is vital in protecting us from the Solar wind. However, one canny student wanted more info on exactly _how_ this worked? After all, the magnets he was playing with seemed to only attract other objects, unless the object was a magnet and he tried to bring like poles together. He suggested maybe the solar wind was made up of tiny magnets, but then correctly suggested that if this was true, would they just turn around if they happened to be aligned the wrong way and then still be attracted to the Earth? Of course, what is really going on is the Lorentz force due to the Solar wind (and other high energy particles) being ionised. I took a stab at explaining the Lorentz force in the simplest possible terms but I don't think I was very successful! I've been thinking of how this could be shown with a simple demo, where by simple I'm ruling out any use of electron beams (cathode ray tubes etc). This is a primary school without access to such gear (and I don't have ready access through my work either). At a pinch an old CRT TV or computer monitor might be useful, but I'm a few years late. It's all flat screens at the school. We could play around with some simple motors and generators but I fear it's a little abstract trying to connect concepts from there to the solar wind and the magnetosphere. I've worked with high school students who've had a hard time getting their head around motors and generators so I think that might just be extra confusion for a 12 year old. Does anyone have a simple explanation or demo of the Lorentz force as it applies in the shielding of the solar wind by the Earth's magnetic field?


title: What is the relationship between strain and electric current?

text: Strain or stress can be caused by different sources. I categorized theses sources as mechanical, thermal and electrical loads and formulated the total stress as follows: $$ \epsilon_{total} = \epsilon_{mechanical} + \epsilon_{thermal} + \epsilon_{electrical} $$ I know that the thermo-mechanical stress-strain relationship can be expressed as follows: $$\epsilon_{x} = \frac{1}{E}\\{\sigma_{x} - v(\sigma_{y}+\sigma_{z})\\}+\alpha\Delta T\\\ \epsilon_{y} = \frac{1}{E}\\{\sigma_{y} - v(\sigma_{z}+\sigma_{x})\\}+\alpha\Delta T\\\ \epsilon_{z} = \frac{1}{E}\\{\sigma_{z} - v(\sigma_{x}+\sigma_{y})\\}+\alpha\Delta T $$ However, I'm wondering how the equations look like for a conducting material with high density current. In other words, I want to know what is $\epsilon_{electrical}$ in the following model: $$\epsilon_{x} = \frac{1}{E}\\{\sigma_{x} - v(\sigma_{y}+\sigma_{z})\\}+\alpha\Delta T + \epsilon_{electrical-x}\\\ \epsilon_{y} = \frac{1}{E}\\{\sigma_{y} - v(\sigma_{z}+\sigma_{x})\\}+\alpha\Delta T + \epsilon_{electrical-y}\\\ \epsilon_{z} = \frac{1}{E}\\{\sigma_{z} - v(\sigma_{x}+\sigma_{y})\\}+\alpha\Delta T +\epsilon_{electrical-z} $$


title: Dark age of universe when all fusion process ceases?

text: Some say we live in the golden age of the universe because there exits countless number of stars that shines in the dark universe. As the supply of gas for star formation is steadily being exhausted, it is estimated that star formation will cease in 100 trillion years. **Question:** Will there be a day that the universe becomes completly dark when all the stars burn out? Does all the cooled bodies eventually collide due to gravitational forces? Will black holes eventually dominate the universe?


title: electric field of unpolarized light after reflect?

text: Reflection and transmission (Fresnel equation) of polarized light are treated in many optics or electromagnetism books. If $E_s$ and $E_p$ is incident electric field with s-polarization and p-polarization, respectively, reflected electric field would be $E'_s = r_s E_s$ or $E'_p = r_p E_p$, where $r$ is reflection coefficient and $'$ means reflected field. Then electric field of any polarized light can be calculated by decomposition. For instance, since $E_{45^{\circ}} = \frac 1 {\sqrt{2}} ({ E_p + E_s })$, $E'_{45}$ would be $\frac{1}{\sqrt 2} (E'_p + E'_s )$ However, how can I express electric field of reflected unpolarized light?


title: Any projects to build a telescope in space?

text: Like in the title. With E-ELT we are pushing the limit of what we can build on the ground. With JWST we are pushing the limit of what can we launch into space. So instead, why don't we launch tools and materials to build a telescope and polish its mirror in orbit? This has several benefits. The environment is vacuum and microgravity, so very large components can be moved with small and light tools. The structure can be very light and fragile, bacause it doesn't have to survive the launch. It can be huge, because it doesn't have to fit into a rocket. Errors can corrected before it is commisioned. I am sure, I'm not the first one to have this idea, but I failed to find any existing projects (upcoming or future) on the web. Do you know any such projects being considered?


title: limits on a gauss box of light

text: Consider a wall defined by $w(x,y,z) = \Theta(x-L)$ which is nonzero in the infinite semi-space of $x \ge L$, as well as a coherent planar _standing_ EM wave travelling in the $z$ plane given by its electric field: $$E_x = \Theta(x - L) \sin(kz) \sin(\omega t), E_y = E_z = 0$$ Consider a complementary standing wave travelling in a opposite plane, in the region $x \le -L$: $$E_x = - \Theta(L - x) \sin(kz) \sin(\omega t), E_y = E_z = 0$$ now, if i take a small closed box in the region $-L- \epsilon \le x \le L + \epsilon$ and z such that $0 \le kz \le \pi$, the net electric flux over this box at any given moment of time is: $$ \frac{ 8 \Delta y \sin(\omega t) }{k} $$ Naively, it would seem "conceivable" to setup standing waves in this way and produce a net electric flux in a given region of vacuum _without any spatial charges anywhere_. Now, since this apparent flux increases with the wavelength, i suspect there is some optical bound in the coherence that the walls can sustain due to dispersion, i.e: something like $\Delta k_z \Delta x \ge \hbar $, but i can figure out exactly what is the reason this won't work. What i'm trying to figure out is how physical this solution is and what limits are imposed by optics in the realization of the charge-violating gauss box


title: What happens to a delta-wing plane when it's nose is tilted away from the line of motion 30 to 45 degrees horizontally?

text: Consider a delta-wing plane whose wing spread angle is 61 degrees (the plane looks like a flying equilateral triangle). What would happen if a cross-wind hits it, so that the direction of motion relative to the air suddenly changes, so that the nose is tilted in the horizontal flight-plane by 30 to 45 degrees? This is on a real jet aircraft, and an educated response would help us understand what we are seeing on a simulation.


How to show that higher derivative theories (mostly) breaks unitarity? Spinor field $\psi_{a_{1}...a_{n}\dot {b}_{1}..\dot {b}_{m}} $, which refer to the $\left( \frac{n}{2}, \frac{m}{2} \right)$ representation of the Lorentz group, must satisfy $$ (\partial^{2} + M^{2})\psi_{a_{1}...a_{n}\dot {b}_{1}..\dot {b}_{m}} = 0 , \quad \partial^{\dot {b}_{1}a_{1}}\psi_{a_{1}...a_{n}\dot {b}_{1}..\dot {b}_{m}} = 0 , $$ for representing the unitary one-particle state of the Poincare group with spin $n + m$, which can be integer or half-integer, and mass $M$. Then, these conditions can be combined in some field equation, which refers to the some Lagrangian. There is a requirement that the equation must not contain derivatives higher than second-order. If the requirement is violated, one says that it breaks the unitarity of the theory of corresponding field. So, the question: how exactly can be showed that it breaks the unitarity? And does it always break the unitarity?


title: Mean-field theory in 1D Ising model

text: A mean-field theory approach to the Ising-model gives a critical temperature $k_B T_C = q J$, where $q$ is the number of nearest neighbours and $J$ is the interaction in the Ising Hamiltonian. Setting $q = 2$ for the 1D case gives $k_B T_C = 2 J$. Based on this argument there would be a phase transition in the 1D Ising model. This is obviously wrong. Is mean-field-theory invalid for the 1D case? Am I missing something here?


title: How did Cook and other astronomers time the 1769 Venus transit?

text: The 1769 transit of Venus was observed and coordinated by over one hundred astronomers around the world. How did they measure time so accurately, key to the observations having any scientific value? I find little information online regarding 18th century timekeeping devices. I assume that they were mostly using clocks intended for nautical navigation, as I think those were the most accurate of the era.


title: Superconductor: What form of paramters (like London penetration depth) to use?

text: I am dealing with thin film and LN2 temperature, and am trying to calculate values such as the Pearl Length, but am trying to find clarification as to which value of $\lambda_L$ to use in this case. e.g. $\lambda_L(t,T)$ with T = 0 or T = 77K? I have other formula, such as the kinetic inductance for a CPW, but the articles I am pulling them from are somewhat unclear which forms of the parameters they are using. Any help is appreciated.


title: Can methane be used as a fuel to launch space vehicles?

text: Methane is apparently the most easily available hydrocarbon. It is also a flammable, and highly combustible fuel; does burning methane provide sufficient power-weight to be used to launch artificial satellites and their ilk into Earth Orbit?


title: Are normal light waves more dangerous than WiFi radiation?

text: I'm getting sort of tired of all the "wireless hysteria", so I thought this might be a nice comment. To the extent of my knowledge, WiFi uses microwaves, which have a lower frequency and hence carry less energy than light. Is normal light therefore more dangerous to us than WiFi waves?


title: Question about contraction with metric tensor

text: I just starting to study GR and I could not prove the following: if I have to tensors $T_{\mu\nu}$ and $Q_{\mu\nu}$ such that $T_{\mu\nu}=Q_{\mu\nu}$, why can I multiply both sides of the equation by $g^{\mu\nu}$, i.e., why is valid $g^{\mu\nu}T_{\mu\nu}=g^{\mu\nu}Q_{\mu\nu}$? Why some authors call it "tracing the equation with $g^{\mu\nu}$"?


title: Learning roadmap for picking up enough mathematical know-how in order to model "shape", "form" and "material properties"?

text: **I am interested in picking up enough mathematical background in order to easily understand a paper like this one:Growth, geometry and mechanics of a blooming lily, _and_ be easily able to create my own models when necessary. Therefore, a first-principles knowledge of the mathematics behind models for physics is not only aesthetically pleasing to me, but also necessary.** Here is how I have bumbled along thus far: I asked a question similar to this one on Mathematics StackExchange, which was soon closed. Before it was closed however, I gathered some interesting pointers on topics I could explore (see answer to that question):   * Discrete and Computational Geometry   * Geometric Folding Algorithms I also got pointers to check out general topics like _differential geometry_ and _topology_. I picked up some pretty good books, and on the way, got hooked onto _geometric algebra_. Oh, I loved it! A chance to be free from crappy tensor notation?! I'll take it! I even found a book that approaches differential geometry from a geometric algebra perspective. As I began to learn though, I became fascinated with the process of setting up an algebra rooted (initially) in the motivation to model physical phenomena. I spent a bit of time thinking about whether for instance, if it would be possible for me to develop an algebra that captures direction and magnitude separately. I wondered what it is about algebraic structures in particular that allows them to "model". I wanted to learn more about Grassmann's "General Theory of Forms". So I kept on going down the rabbit hole of abstraction. I read some preliminaries on lattice theory, and today I was about to start reading Ravi Vakil's notes on algebraic geometry. I thought about why it is I started down this road though, after reading the preface to the notes, which asked me to always remember this, and I wondered if I should ask for some feedback on my path so far. The fact that I feel a little lost right adds only further motivation to ask: **What are your comments on my path so far? Which direction would you point me in next?** I should note that being a structural engineering undergraduate student in the past, I have a pretty firm grip on the lightly-mathematical introduction undergraduate students get to concepts like "elasticity" and "plasticity".


title: Help Simplifying a Commutator Equation

text: For the SHO, our teacher told us to scale $$p\rightarrow \sqrt{m\omega\hbar} ~p$$ $$x\rightarrow \sqrt{\frac{\hbar}{m\omega}}~x$$ And then define the following $$K_1=\frac 14 (p^2-q^2)$$ $$K_2=\frac 14 (pq+qp)$$ $$J_3=\frac{H}{2\hbar\omega}=\frac 14(p^2+q^2)$$ The first part is to show that $$Q \equiv -K_1^2-K_2^2+J_3^2$$ IS a number. My approach: $$16Q=J_3^2-K_1^2-K_2^2=(p^2+q^2)^2-(p^2-q^2)^2-(pq+qp)^2$$ $$=p^4+q^4+p^2q^2+q^2p^2-(p^4+q^4-p^2q^2-q^2p^2)-((pq)^2+(qp)^2+pqqp+qpqp)$$ $$=2p^2q^2+2q^2p^2-pqpq-qpqp-pqqp-qppq$$ At least point, I am unsure of how to simplify any further. A lot of these look like the form of anticommutators, which does not seem to provide any useful information in turning Q into a number. Any help would be appreciated! EDIT:: This is how far I have gotten.   ![enter image description here](http://i.stack.imgur.com/GQsoK.jpg)


title: Regarding Electromagnetic Plane and Maxwell equations

text: I asked this on the math.stackechange but I was told that it might be a good idea to ask here too since my problem is physics/math! Here is the question: Hello everybody I am kind of struggling with an assignment question related to general relativity. I am just going to type what the question is and explain what I am having trouble with: Consider an electromagnetic plane wave in Minkowski space. We assume that in stationary coordinates $(t,x,y,z)$ the wave propagates in the positive $x$-direction, and that the components of the electric field $E$ and the magnetic field B are only a function of $u = t-x\ ($here $c = 1)$: $E = E_{y}(t-x)\frac{\partial}{\partial{y}}+E_{z}(t-x)\frac{\partial}{\partial{z}}$ $B = B_{y}(t-x)\frac{\partial}{\partial{y}}+B_{z}(t-x)\frac{\partial}{\partial{z}}.$ Moreover, we assume E and B are compactly supported in $u$. (1) Use Maxwell's equations to show that: $B_{y}=-E_{z},$ $\space$ $B_{z}=E_{y}$. First of all sorry if the formatting isn't that great. Now I am having trouble with this because I am not exactly sure what $E$ and $B$ are... by that I mean I know $E$ and $B$ are supposed to be vector fields but in that format they look like scalar fields. Is there another way to represent those two equations, I feel that if I understand the notation it would make doing this question pretty easy. Any help would be greatly appreciated. I just want to understand the notation properly and how to work with it so that I can actually apply Maxwell's equations on them and figure out those identities. Thank you and have a good day!


title: How many radiotherapy sessions would it take to boil one cup of water?

text: **Context** : Gray (Gy) is a unit dose used in radiotherapy. It is defined as the absorbed energy of 1J per kilogram of matter. There is a wide misconception that ionizing radiation acts by heating tissues, because after some sessions of radiotherapy the skin may become red due to inflammation, similarly to when we get a burn. **Goal** : I'd like to calculate how many standard sessions of radiation therapy would be required to boil one cup of water at standard ambient temperature and pressure. The standard daily dose is $1.8$Gy/day and we would assume that all sessions were given simultaneously (so that the water wouldn't cool off in the meantime). I've done my calculations by converting converting calories to Joule etc, but could please somebody provide his/her version of it? Just to cross-validate my results? If noone answers, I'll post mine.


title: Initial velocity to travel a certain distance

text: When launched from a planet with mass M and radius R, what initial velocity is necessary for an object to travel a distance r before it gravitates back towards the planet? Sort of like trying to find the escape velocity but with a finite distance.


title: How to get Intensity over a range of wavelengths from a Total Intensity

text: This is a theory vs experiment problem for me I think in that - as usual - I think I know the theory, but when it comes time to run an experiment, I can't actually extract squat. So, here is my light source: I am using the Cold White LED (MCWHL2). If you scroll down a bit, you'll see the LED normalized intensity vs. wavelength profiles for all the LEDs. The black line on this graph is my LED. As you can see, it meanders instead of being a simple Guassian-like thing. I measure the intensity of this light by using this power meter: Scientech Astral AD30 meter - which displays power and energy - with an AC2501 detector. Specs are here . So I'm calculating total intensity by dividing by the area of the beam. Now, here's my question: say I get a reading of $ 10\rm\frac{mW}{cm^2} $. If I want to know what is the intensity of the output only over the range 400nm to 455 nm, based on the Intensity vs Wavelength graphs and the characteristics of the meter and detector, what do I do? Now, Planck's equation for a black body was where I first looked. My procedure was to find the total intensity for the light temperature (6500 K) and integrate from 0 to infinity. I then numerically integrated from 440 nm to 455 nm and divided the two. Multiplying this by the output on the detector gave a ridiculous solution. Given the intensity profile - not really black bodyish - the ridiculous results make sense. It was at this point that I started searching and found nothing but Planck stuff. Thus, I humbly come before all of you. Please help! There must be some sort of standard procedure for those without specialized light analyzing equipment! Thanks! Sam


title: Viscosity tensor in Navier-Stokes equation?

text: In my Hydrodynamics notes the viscosity term in the Navier-Stokes equation is of the form: $$ \nabla\cdot(\underline{\underline{h}}\cdot\nabla)\mathbf{u} $$ where $\underline{\underline{h}}$ is the viscosity tensor and $\mathbf{u}$ is the velocity of the fluid. (The left hand side of the N-S equation is $\rho\frac{\partial \mathbf{u}}{\partial t}$.) Why does this term have this form? Is there a physical meaning? I have tried to look this up online but most pages consider the viscosity to be homogeneous and isotropic so that it can be taken outside the brackets: $$h \nabla^2\mathbf{u}$$.


title: random triggers

text: I understand that a small proportion of events at the LHC that would not trigger on any deterministic trigger are saved on what might be called a random trigger, so that, amongst other uses, proposed new triggers can be tested. What proportion of events are saved on deterministic and on random triggers? Also, how much is that data used and for what other purposes? This question was prompted by a Cosmic Variance Post, http://blogs.discovermagazine.com/cosmicvariance/2012/07/13/particle-physics- and-cosmology-in-auckland/, where this question may also be found.


title: Water Stream from a Horizontal Surface

text: If water was projected from a flat surface where gravity was equal all over the surface. What would happen when the water fell in on itself? The water is in a continuous stream and is perfectly perpendicular to the surface it is projected from.


title: Electric potential energy and speed

text: If we have electric field and we put electron there , the electron will move in the opposite direction as the electric field. My question is electron in that direction will speed up or slows down ? And what happens to Electric potential energy of that electron, it will increase or decrease?


title: State space of strings: Spin-1 particles in the conformal gauge?

text: I obviously have a problem with basics of group theory. consider an open string in flat spacetime. there are usually two common gauge to solve the classical problem and quantize the strings:   1. lightcone gauge    2. conformal gauge.  After quantization, you study the state space, and here I have a problem with probably the representations of the $SO(24)$ (I focus on bosonic strings). I explain my problem explicitly below: 1-in lightcone gauge: for the second excited state, $N=2$ : the mass is $M^2=1/\alpha'$ and the bases for this subspace are : $a^\mu_2 |0\rangle $ and $a^\mu_1a^\nu_1|0\rangle $ 2- in the conformal gauge: for the second excited state, $N=2$ : $M^2=1/\alpha'$ and the bases for this subspace are: $a^\mu_1a^\nu_1|0\rangle$ and, not $a^\mu_2|0\rangle$. (see Polchinski problem 4.1) Now the problem is: Do we have a spin one particle with the mass :$M^2=1/\alpha'$ ? in lightcone gauge's state space we have it but, in conformal gauge we have only spin 2 particles with this mass. Is it really a problem?! or just a paradox comes from two different representations of the $SO(24)$ ? I hope you got my question. thank you very much


title: Cauchy Problem for Boltzmann Equations

text: One of the first profound analysis about the solutions of the Boltzmann Equation was given by DiPerna and Lions in the late 1980s. You can find one of their main papers here: http://www.jstor.org/discover/10.2307/1971423?uid=3737528&uid=2&uid=4&sid=21102076873573 If you do not have access to the paper then use this link: http://www.4shared.com/office/eeIqgvxB/MathematicsOn_the_Cauchy_Probl.html I was reading through this and similar papers and one of the things I do not understand is the _interpretation_ of the solution. The paper delivers more or less a proof for the existence of a global solution of the Boltzmann Equation, but what can we do with it? If you have an idea how to interpret it I would be very thankful. P.S: I put a question about the proof of one of the Lemmas on http://mathoverflow.net/questions/132871/cauchy-problem-for-boltzmann- equations


title: What is the deepest cause of the such high specific heat capacity of water?

text: Yes, I know about the hydrogen bridges. But I think, it isn't the deepest cause. Anyway, they are only second-order bindings, although quite strong. I think, somehow should have the water a significant number of "hidden degrees of freedom", or some like internal structure with a lot of degrees of freedom. But it is only my naive intuition. So, what is the deepest cause?


title: Calculating Riemann Tensor Using Tetrad Formalism

text: I was trying to calculate the Riemann Tensor for a spherically symmetric metric: $ds^2=e^{2a(r)}dt^2-[e^{2b(r)}dr^2+r^2d\Omega^2]$ I chose the to use the tetrad basis: $u^t=e^{a(r)}dt;\, u^r=e^{b(r)}dr;\, u^\phi=r\sin\theta d\phi; \, u^\theta=rd\theta$ Using the torsion free condition with the spin connection $\omega^a{}_{b}\wedge u^b=-du^a$ I was able to find the non-zero spin connections. In class my teacher presented the formula: $\Omega^i{}_{j}=d\omega^i{}_j+\omega^i{}_k\wedge \omega^k{}_j=\frac{1}{2}R^i{}_j{}_k{}_l\,u^k\wedge u^l$ But this can't be right since I calculate with this: $\Omega^t{}_\phi=-\frac{1}{r}a_r \,e^{-2b}u^t\wedge u^\phi \implies R^t{}_\phi{}_\phi{}_t=-\frac{1}{r}a'e^{-2b}$ The real answer involves a factor of $e^a$, $\sin \theta$ and no $\frac{1}{r}$ term. Any help is appreciated. **Edit** : Here is some of my work: $du^t=-a_re^{-b}u^t\wedge u^r$ $du^\phi=-\frac{1}{r}[e^{-b}u^\phi\wedge u^r+\cot \theta u^\phi\wedge u^\theta]$ (I will not show the calculations for the rest) From no-torsion equation, we get 2 out of 4 spin connections (the rest require the two missing exterior derivatives that I have not shown in this post): $\omega^t{}_r=a_re^{-b}u^t$ $\omega^\phi{}_r=\frac{1}{r}e^{-b}u^\phi$ Then $\Omega^t{}_\phi$ is as shown above. Explicitly: $\Omega^t{}_\phi=d\omega^t{}_\phi+\omega^t{}_r\wedge \omega^r{}_\phi+\omega^t{}_\theta\wedge \omega^\theta{}_\phi$ where the first and last terms are 0 since $\omega^t{}_\phi$ and $\omega^t_\theta$ are 0.


title: Why can't we use entanglement to defy Heisenberg's Uncertainty Principle?

text: In principle, it is possible to entangle any property of two particles, including speed and momentum. Surely then, this could be used to defy the Uncertainty Principle, which states that the momentum and position of a particle cannot be together measured with accuracy, but the more accurate one gets, the less accurate the other becomes: $\Delta x\Delta p=\dfrac{\hbar}{2}$. If one was to set up an experiment where two particles are entangled, one could then measure the position of one particle with great accurary at the same time as measuring the momentum of the other particle with great accuracy, which would mean that, as the two particles are entangled, one would then know the momentum of the particle they measured the position of. Therefore, the Uncertainty Principle would have been defied, as both momentum and position have been measured with a high accuracy. However, this can't be true, as someone would have thought of this before. So why wouldn't this work?


title: Is there a more scientific term for "obstruction of EM waves"?

text: When EM waves pass through things like rain and hail, they can be "obstructed" and bounced back or absorbed, rather than passing through. I'm conducting an experiment on this effect, and wondered if there is a more scientific/nerdy way of saying this? I thing obstruction sounds somewhat unprofessional. Looking in a thesaurus I see interference. I like that better, but it seems very vague. Is there a word that just means absorption or scattering, such that the detector can't detect them?


title: Variation of the purely covariant Riemann tensor

text: I need to find the variation of the purely covariant Riemann tensor with respect to the metric $g^{\mu \nu}$, i.e. $\delta R_{\rho \sigma \mu \nu}$. I know that, $R_{\rho \sigma \mu \nu} = g_{\rho \eta} R^\eta_{\sigma \mu \nu}$ and $\delta R^\eta_{\sigma \mu \nu} = \nabla_\mu (\delta \Gamma^\eta_{\nu \sigma})- \nabla_\nu (\delta \Gamma^{\eta}_{\mu \sigma}).$ So do I need to use the product rule like so, $\delta R_{\rho \sigma \mu \nu} = \delta (g_{\rho \eta} R^\eta_{\sigma \mu \nu}) = \delta (g_{\rho \eta}) R^\eta_{\sigma \mu \nu} + g_{\rho \eta} \delta( R^\eta_{\sigma \mu \nu})$, which gives me a relatively messy answer. Is there another way to approach this?


title: Drag on a spinning ball in fluid

text: I am a physics newbie (high school level) and I am wondering what happens when a spherical object is spinning on the spot in a bunch of gas (no gravity here, just an imaginary physics sandbox). Am I right to assume there will be some _frictional drag_ which adds torque in the direction opposite to the spin? How would I go about computing such a torque? Would it be proportional to the angular velocity of the ball (On the assumption air particles would be hitting the sphere in a way like how rain hits you more when you're running)? If the drag is proportional to the angular velocity, then I would assume there would be a terminal angular velocity if the ball was subject to a constant external torque much like how an object falling under a constant force (gravity) would reach terminal velocity due to air resistance.


title: Does the Earth help stabilize changes in the moon's obliquity as well?

text: We know that the moon helps stabilize changes in Earth's obliquity. But what about Earth and the moon? Are some of the obliquity-stabilizing effects (of the moon on the Earth) communicated through tidal dissipation (the friction which is presumably isotropic) - effects that would otherwise change the Earth's obliquity if it didn't experience that tidal dissipation from the moon?


title: What would happen if the polar ice caps of Mars melted?

text: My dad told me that Mars' polar ice caps are made of H2O and CO2. If they melt, would it add an atmosphere to Mars and allow life?


title: Can electromagnetic waves be interpreted as a collection of infinite coupled oscillators?

text: I recently learned, for the first time, that the behavior of waves can be derived by treating them as an infinite set of coupled oscillators. This makes sense for waves whose medium is matter; it's easy to see how water waves, for instance, can be seen as the individual water molecules tugging on their neighbors as they oscillate. At the same time, however, I've only ever seen electromagnetic waves treated continuously, and again this makes the most sense, since electromagnetic waves are just oscillations in a continuous field. But I wonder, is there an interpretation of EM waves as a set of discrete coupled oscillators? Would such a treatment be useful in any way?


title: Why does hot oil explode when pouring water on it?

text: I am puzzled to know, What is the reason of hot oil make sound and explode when we pouring water on it?


title: What is fundamentally physically impossible?

text: Mathematical logic defines quite clearly what is true or false in math, and also that some theorems are impossible to prove. This resulted in some clear definitions of axioms set like Peano, ZF or ZFC, which are proved (or strongly believed) to be consistent, i.e do not allow to demonstrate both a theorem and its negation. In physics, the distinction between axioms, postulates, principles and laws isn't clear at all. Some laws are linked to others, however not by simple derivation. For example the first law of thermodynamics is related to conservation of energy, which in turn is equivalent to the invariance by time translation by by Noether's theorem, which means (to me) it depends on the (perfect) cosmological principle. We consider as "impossible" anything that violates any of those laws or principles, but are some violations "more impossible" than others because some laws are "stronger"? For example thermodynamics or energy conservation are definitely unquestionable at our scale, but since they're connected to the cosmological principle at large scale (which can be criticized), are we sure they're "absolutely true"? Are we sure the principles of physics are consistent, or might we end up with contradictions between, say, Einstein's principles and quantum mechanics? And do we have something approaching Gödel's theorem in physics to assert that some things that we observe (dark matter?) are impossible to describe with our current laws, but that we need some more? Well, I realize my question is actually several. Please answer with just a link or book reference if you think I should just read more.


title: Quantum Cryptography

text: First question was a little bit ambiguous. Photons are passed through a linear polarizer that is oriented $\theta$ degrees again the photon passes through another linear polarizer that also have a $\theta$ degree orientation. Now my question is that why the second polarizer will effect the spin axis angle of the photon. Actually I am not from a physics background and new to Quantum Cryptography.Please. help.


title: Psychorometric equation : calculation of dew point

text: I would like to calculate a dew-point temperature having wet and dry bulb temperatures and atmospheric pressure. I have the equation, but this equation uses following coefficients:   * A: 6.116441   * K: 0.000662 ( Psychrometer constant )   * m: 7.591386   * Tn: 240.7263 (Triple point temperature ) To calculate water vapor saturation pressure I use simplified formula: $$ \mathrm{Pws} = A\times\cfrac{m \cdot T}{T+Tn} $$ T is temperature The given values are good for temperatures around 20 Celsius, but they fail around -5 or even lower. The accuracy around -20 degree ( wet bulb temperature) are terrible ( error around 3 : 5 degree ). What are the names of m and A coefficients? Where can I find these values for low temperatures?


title: Does decreasing the length of the line between a harness and zip wire increase the velocity at which you travel?

text: My friend is an instructor at an outdoor adventure centre which has lots of zip wires. The instructor's harness has a shorter line that attaches to the zip wire than the normal harness does and she claims that you go much faster with it. Is this true? I can't think of any reason as to why it would be MUCH faster but apparently their speed gun proved it. **Edit:** Diagram for clarity ![enter image description here](http://i.stack.imgur.com/iBLdm.png)


title: How exactly do I calculate this correlation function?

text: I found a research paper (from 1977) that has a particular equation I need to reproduce. The paper essential calculates dynamic light scattering correlation functions. The full equations I need to work out is this: $$ f(q,\tau) = \frac{\int_{-1}^{+1}(1-2w^2\nu^2) \exp(-w^2\nu^2)\ d\nu \times \int_{0}^{2\pi} A[q,\mu(t)]A^*[q,\mu(0)]\ d\psi}{\int_{0}^{2\pi} |A[q,\mu(0)]|^2\ d\psi} $$ Essentially I need to calculate this for values of the delay time $t$. The bit I am not sure how to do is the $\int_{0}^{2\pi} A[q,\mu(t)]A^*[q,\mu(0)]\ d\psi$. The actual functional form of A isn't that important, but it consists of spherical Bessel functions and the term $\psi$ which is to be numerically integrated over. Now, where I am stuck is what do I actually do to calculate that function for the delay times. I have tried a lot of things but I just cant get it looking like they have in the paper. Here is what I have tried:   * Calculate $\int_{0}^{2\pi} A[q,\mu(t)]$ for all delay times, and then use a built in autocorrelation function to obtain the results.   * Take my first $t$ value (say 0.01 sec), and my second $t$ value (say 0.02 sec) and then calculate $\int_{0}^{2\pi} A[q,\mu(0.02)]A^*[q,\mu(0.01)]\ d\psi$... etc for all t values (so $t0$ lags 1 behind t.   * A few other things. As you can see I am a bit confused, if anyone has any insight as to how I would calculate this by hand that would be extremely helpful. * * * ### Edit: The full functional form of $A(q,\mu(t))$ is $$ A(q,\mu(t))\propto \frac{3j_1(u)}{u} + F^3 \frac{m_2-m_1}{m_1-1}\frac{3j_1(f u)}{fu} %Old version: \frac{F^3 (m_2-m_1) (3 j_1(F \mu(t)))}{(m_1-1) (F \mu(t))}+\frac{3 j_1(\mu(t))}{\mu(t)} $$ where $j_1$ is a spherical Bessel function of the first kind, $u=q\sqrt{a^2\mu^2(t)+b^2(1-\mu^2(t))}$, $F=1-\frac ta$, and $\mu(t)=\cos(\psi)\sin(\theta)\sin(\alpha(t))+\cos(\theta)\cos(\alpha(t))$, for $\nu=\cos(\theta)$ and $\alpha(t)=\omega t+\phi$. Yes, I am after $f$ vs $t$ for a $q$ of my choice. I am just not sure I am computing the integral properly for the values of $t$. For example, lets say my $t$ of interest was $0.1, 0.2,0.4, 0.8, 1.6$ (just an example). For the very first $t$, would I simply do, $$ \int_{0}^{2\pi}A[q,\mu(0.2)]\times A[q,\mu(0.1)] $$ Then for the next $t$ $$ \int_{0}^{2\pi}A[q,\mu(0.4)]\times A[q,\mu(0.1)] $$ or $$ \int_{0}^{2\pi}A[q,\mu(0.4)]\times A[q,\mu(0.2)] $$ And dont I need to average over the same delay time $\tau$? So for $\tau 1$ its $$ \int_{0}^{2\pi}A[q,\mu(0.2)]\times A[q,\mu(0.1)]\\\ \int_{0}^{2\pi}A[q,\mu(0.4)]\times A[q,\mu(0.2)]\\\ \int_{0}^{2\pi}A[q,\mu(0.8)]\times A[q,\mu(0.4)]\\\ \int_{0}^{2\pi}A[q,\mu(1.6)]\times A[q,\mu(0.8)] $$. I am using Mathematica to evaluate these functions. As you can see I am rather confused. Thanks so much for your help. The paper I am referencing is: > Rotational—translational models for interpretation of quasi-elastic light > scattering spectra of motile bacteria. Michael Holz and Sow-Hsin Chen. > _Appl. Optics_ **17** no. 20, pp. 3197-3204 (1978).


title: Do black holes exert an infinite amount of energy at the event horizon?

text: An interesting thought crossed my mind when reading about Hawkings' apparent horizon theory. If we assume that event horizons _do_ actually exist, it would seem that black holes violate basic laws of physics. My (limited) understanding is that in traditional black holes, the event horizon is the place at which nothing, not even light, can escape falling into the singularity. I also believe that I have learned that for something other than light to travel at the speed of light, an infinite amount of energy would be required. Therefore, since a traditional event horizon is defined as the so-called "point of no return," wouldn't an infinite amount of energy be exerted at the event horizon? If light itself cannot escape, that would seem to mean that the gravitational force would be at least equal to the speed of light, and wouldn't that require infinite energy?


title: Calculate exact time of Solar midnight

text: I want to calculate real time of midnight (Solar midnight), but I am unable to find any formula or algorithm for that. I have times of sunrises and sunsets for every day of year. How can I get Solar midnight times from them? Thank you all.


title: Does General Relativity require that Spacetime must be a orientable?

text: > **Possible Duplicate:**   >  Can spacetime be non-orientable? Apart from the constraints put on the topology of spacetime by QFT (Parity For example), if the global topology of a universe is that of a Mobius band and at one point there is a gravitational field pointing towards a star and a passenger travels along the band and returns to the same point. Then he will find the gravitational field pointing away from the star causing an anti- gravity effect. Does this mean that space-time must be orientable?


title: Linear sigma models for F-Theory

text: Is it possible to describe the Local F-theory models which seems to be relevant for particle physics phenomenology using Gauged Linear Sigma Models (GLSM), this includes describing the decoupling limit using the parameters of the GLSM? Actually, I am not sure if my question makes sense. Another related question is: Can elliptically fibered Calabi-Yau 4-folds be described as the IR limit of GLSM while also producing the global constraint of F-Theory compactifications, and also producing the Weierstrass form of the elliptic fibre. Thanks in advance.


title: What possible science could we do during the 2012 Venus transit?

text: I had previously asked about how useful everyday solar physics data is to other astronomers ... But about a year from now, we will have another Venus transit, where Venus will pass between the sun and the earth ... I was just in a meeting with some EPO (education and public outreach) folks about trying to prepare something for the event, and we can do the basic 'make a pinhole camera' kids activities, and use it for awareness of our field ... But is there any novel science that we could use the event for? We're especially interested in trying to find something 'Citizen Science', where we could try to organize people to contribute some data from across the world that might help advance our knowledge of _something_. (it doesn't even have to be astronomy ... We had an idea of trying to get people to take pictures of the transit, and send the images, and we could try to use it to estimate how the quality of seeing varies, but we weren't sure if there were liability issues if someone managed to ruin a camera or their eyes in the process)


title: Does phase lead or lag in a plasma?

text: Plasmas have an index of refraction less than 1. So say you sent one beam of light through a plasma and another one along a path just as long but in free space. Is the plasma beam's phase lead or lag the free space beam's phase?


title: Derivation of Weyl tensor

text: I want to derive the Weyl tensor along the lines of this derivation, but I am unable to complete it. (I am only interested in $4$ dimension for now.) Every contraction I perform gives either $0=R + 3 \lambda L$ or $0=0$ but not an additional equation to calculate $L$ and $\lambda$. Does anyone know a source where I can find this derivation in detail or point me to the crucial point I am missing? Thank you!


title: Do all known planets and moons have magnetic field?

text: In this Wikipedia article it is stated, that magnetic field of Earth is caused by currents in her core. The same origin is for Jupiter magnetic field. For Moon (article) there is a magnetic field, but having other origin than the Earth's one, perhaps Uranus too. Are there any other planets that we know for sure they have no magnetic field (or perhaps it should be considered as none) or are we sure that all such bodies must have magnetic field (why then)?


title: Expanding universe

text: If we know the universe is expanding in whatever direction we look, can't we reasonably estimate where the 'center' of the Universe is? Is the rate of expansions in all directions the same?


title: Is 'color' characteristics of a body or characteristics of light?

text: 1. In situation when body exposed by light, is 'color' characteristics of a body or characteristics of light? Is there any difference on macro/micro levels?   2. Will exist such term as 'color' in parallel universe where electro-magnetic waves doesn't exists?


title: Single-channel vs multi-channel scattering

text: I am studying quantum scattering and stumbled upon the "scattering channel" and "single- and multi-channel scattering" terms. However, I didn't manage to find any sufficiently formal definitions of these, could someone please explain me them?


title: Meaning of Eigenvalues/Eigenvectors of a linear system of equations

text: I have a 41x41 system of linear equations (inhomogen) which I derived with Eureqa by describing the timecourse of fMRI haemodynamic data from a brain area as a function of the timecourses of 40 other brain areas (from Brodmann areas). The person who was measured had to do some specific task and had seen some pictures. So the timecourse data is a function of the stimuli and my equations somehow also describe the stimuli. e.g. brainarea1= f(brainarea2,...,brainarea41) brainarea2= f(brainarea1,...,brainarea41) ... brainarea41=f(brainarea1,...,brainarea40) (See this link here for the equations) So..now I can solve this linear system, can compute the eigensystem for example.. but my question is..   1. What would a physicist do with such a system. What is the straightforward way to analyze such a linear system of equations? Also, which Eigenvalues and Eigenvectors are of interest?  What would they mean is this case, when I for example take the Eigenvector of the biggest Eigenvalue? In other words: What does the Eigenvector tell me about the system?   2. Is it possible to extract the timings when the person saw some stimuli from the system or somehow extract more information about the stimuli, when I know the exact time a stimuli occurred (which I do know)? Since the data of the timecourses is a function of what stimuli the person saw, one can see the frequency of the stimuli in the frequency domain if Fourier transform is applied. But is there something else one can do with this system?    3. What would change if my system is a nonlinear system of equations? Would there be some fundamental constrictions or limits in my possibilities to analyze the system? I'm not hoping for some specific solutions to that matter, but maybe for some helpful hints and tips how to go deeper into it, maybe what I could read up on and so on.


title: What Does it Mean for an Extra Dimension to Have Size?

text: Recently I watched this presentation by Brian Greene on string theory. In it he describes how the reason we don't observe the extra dimensions required by string theory could be because they are very small and "hidden" from us. He uses an analogy of looking across a parking lot at a telephone wire. From our vantage point the wire seems flat. However, to an ant crawling on the wire, it would not seem flat at all. The ant can see this clearly, though the fact is "hidden" from us in our vantage point. I can see how this crude analogy can provide a conceptualization of why possible other dimensions cannot be seen, but I don't see how this can in any way hint toward the extra dimension being "small." It seems to me that it is the object (telephone wire) that seems small to us because we are so far away. This creates the illusion that the wire exists in two dimensions and not three. This does not mean that the third dimension itself is small. My question is, what does it mean to call a dimension "small?" Is this a physical size or is this a mathematical quantity/expression that is associated with size for the benefit of the layman? Also, if a dimension can indeed have a physical size, then can we assign a size to the three dimensions that we can see? I found a similar Phys.SE question here. However, the answers on this question deal more with how dimensions can be experimentally measured, and did not completely answer my question.


title: Is thermal/heat energy the same thing as internal energy?

text: I learned that internal energy of an object is the sum of the kinetic energy and potential energy of the molecules of the object. Is this energy the same thing as the heat energy the object contains?


title: One-loop $\phi^4$ theory in $d = 3$

text: I'm trying to calculate the 1 loop correction to the propagator in massless $\phi^4$ theory, in $d = 3$, just for fun. The diagram just looks like a straight line with a circle touching tangently to it. I'm not sure whether to take $ m = 0$ straightaway or to compute it for $m > 0$ before taking $m \to 0$, because the two methods give different answers. The diagram is $\sim \int d^3k \frac{1}{k^2 - m^2}$. If I set $m = 0$ straightaway, then I get $\sim \int k^2 dk \frac{1}{k^2} \sim \Lambda$, where $\Lambda$ is the cutoff. On the other hand, if I do the integral, using the results in the appendix from Peskin and Schroeder \begin{align} \int d^dk \frac{1}{k^2 - m^2} \sim \frac{\Gamma(1-d/2)}{(m^2)^{1-d/2}} =\Gamma(-1/2)(m^2)^{1/2}. \end{align} $\Gamma(-1/2)$ is finite, so taking $m \to 0$ this diagram is $0$. So one one hand it's UV divergent, on the other hand it's 0. Which method should I be using? Are the theories where $m=0$ and $m \to 0$ not the same? I also seem to have missed out the $i \varepsilon$ prescription in the propagator in the first case - if I include that in and evaluate the diagram before sending $\varepsilon \to 0$, then the diagram is $0$ too. Or perhaps it does not matter too much because the mass renormalization term can take care of either divergence and such discrepancies will not show up in calculations of any observables anyway? Thanks.


title: Show that the Laplace-Runge-Lenz vector is conserved using poisson brackets

text: (I realise similar Phys.SE questions already exist but there is no answer with the Poisson bracket notation, I'll take this down if someone lets me know I should have commented in the existing question.) I am trying to show that the Poisson bracket between the Hamiltonian and the Laplace-Runge-Lenz vector vanishes, i.e. $$\left\\{H,A\right\\}_{PB}=0$$ where $\vec{A} = \left(p \times L\right) - m k\cdot \hat{r}$, and the Hamiltonian is for an orbit is given by, $$H = \frac{m}{2}\left(\frac{dr}{dt}\right)^2 + \frac{k}{r}$$ I have been trying to use tensor notation to write out the cross product term and the fundamental Poisson brackets but am not having any luck.


title: Writing equation for amplitude of driven harmonic oscillator in Lorentzian form

text: This harmonic oscillator is driven and damped, with the form: $$\ddot{x} + \lambda \dot{x} + \omega_0^2 x = A \cos(\omega_d t)$$ Now, I have used the ansatz (guess): $x(t) = B \cos(\omega_d t + \phi)$, and have written B in the form: $$B = \frac{A} {\sqrt{(\omega_o^2-\omega_d^2)^2+\lambda\omega_d^2}}$$ Next, I am required to " _approximate B using the Lorentzian form_ " $$B = \frac{C}{(\omega_d - \Omega)^2+\biggl(\frac{\Gamma}{2}\biggr)^2}$$ However, this is where I am stuck. I know that because it says "approximate" I will somehow have to drop out terms from my first expression to B, but I don't know where to start. How can I write B in this form? **EDIT:** I have found a wikipedia article on resonance which show a form very similiar to what I seek, however, I can't seem to find a derivation http://en.wikipedia.org/wiki/Resonance


title: Electricity production

text: Are there alternate means to produce electricity than magnetic induction? I observe that all places this method is used .Do other methods exist even if this being the most profitable way.


title: Why Microchannel Plates can be operated only in vacuum?

text: Why it is said that the Microchannel Plates can be operated in vacuum? What is the maximum pressure in which it can be operated? Also, while it is not operating, should it be kept in vacuum? Is this because the semiconducting property of the channels can be affected by the atmospheric pressure? Or while operating the gas molecules can be ionized and burn the detector?


title: Is there a mathematical relationship here or am I looking for relations when there are none?

text: ![Left: Shows two balls of equal mass suspended from a ceiling with string, Right: Shows to large orbiting bodies in outer space](http://i.stack.imgur.com/uNqiq.png) When I was taking classical mechanics, we dealt a lot with pendulums, and orbiting bodies problems. This lead me to think about the two situations depicted above. Left: Shows two balls of equal mass suspended from a ceiling with string, Right: Shows to large orbiting bodies in outer space. For some reason, my intuition is begging that there these two cases are somehow mathematically related. However, I need help finding this relationship. It seems that the as the string twists and the balls get closer and closer to each other, its awfully similar to the case when two bodies in space orbit each other until they collide too! (Or am I just crazy and thinking too much?) What relevant equations / geometric relationships are needed here to establish a relationship between these two cases? (Kepler's Laws, what else?) ![enter image description here](http://i.stack.imgur.com/R9BP6.png) **Going further:** Given that the strings magically "go through each other" at every rotation, can't this be related to the case in which the two orbiting masses orbit a third body, say a star, located at the center of the axis of rotation? (Picture not provided here, but I hope you understand my further question) Again, What relevant equations are needed here to establish a relationship between these two cases? ![enter image description here](http://i.stack.imgur.com/LExIK.png) **Going _even_ further:** This is getting pretty hand wavy, but I was thinking that perhaps this could be a new way of looking at the 3-body problem or multi-body problem using the string and ball model? Would Knot theory come into play?


title: What's an "Action" and what does the Lagrangian equation mean exactly?

text: How and why would a particle take the shortest path? $L=KE-PE$? What's the $KE-PE$ mean in English? I understand the 'mechanics' but not the idea itself. Please explain simply, I do know Calculus but the simpler the better. Please don't say because that's how nature is, because I get that a lot.


title: Explicit form of the entropy production in hydrodynamics

text: I'm trying to understand how hydrodynamics arise from a precise, mathematical formulation of thermodynamics, learning mostly from Landau's "Hydrodynamics". So Landau starts from formulating the dynamical equations for the non viscous fluid, 5 equations, because there are 5 variables (pressure, density and a 3-component velocity field). The equations are: the mass continuity equation, the Euler equation (momentum continuity equation) and a statement of the fact, that there is no dissipation of energy, i.e. entropy is constant ($\frac{ds}{dt} = 0$). Now, when describing a viscous flow we add dissipation through stress $-$ the Euler equation becomes the Navier-Stokes equation. My problem concerns the last equation, which should account for entropy production. You see Landau doesn't say anything about entropy per se, but just finds an equation for energy transfer analogous to the other continuity equations, and finds a way of describing a lost in kinetic energy of a flow caused by viscosity. My question is: how to state this equation as a direct generalization of the non viscous case, i.e. in terms of entropy? How to even approach this in terms of thermodynamics? What (thermodynamically speaking) is the process of dissipation? we need to know that, to calculate the $DQ = dE_{kin}$, don't we? Assuming we know the rate of change of the kinetic energy. Trusting Landau on that one, it has the form: $$ \frac{dE_{kin} }{dt} = -\frac{\eta}{2} \int \left( \frac{\partial v_i}{\partial x_k}+ \frac{\partial v_k}{\partial x_i}\right)^2 dV $$ To get the $\frac{ds}{dt}$, do we just need to divide this by temperature? I'm trying to explain everything here in terms of thermodynamics, because I only know typical, very basic examples of thermodynamics processes and I have a difficulty in interpreting what is truly happening here (in terms of entropy).


Who should I contact if I see an unknown object in the sky? Should I contact the nearest observatory? Or is there some official place run by, say, NASA or ESA that take in observations in their member countries? (Of course, the unknown object can be anything from a weather balloon reflecting the sun behind the horizon to a supernova.)


title: What is a spectrometer, and why are they so useful in science?

text: I've heard reference to many telescope and spacecraft that have a device known as a spectrometer, and I'm curious, what is the purpose of these device? What's the working principal behind them and what do we use them for?


title: Ways of verifying the origin of a meteorite?

text: Assume you have a small sliver of a lunar or martian meteorite (or an object asserted to be so). Without using any special scientific equipment, is it possible to verify (or give a high probability) that it is indeed of lunar or martian origin? Are there any visual or other tests one can do to confirm the source? _(If this question is off-topic or not quite right, feel free to close.)_


title: Alternative symmetries for the Maxwell Lagrangian?

text: I'm wondering about how to show that $A_a\rightarrow A_a+\alpha\partial_0A_a$, with $\alpha$ infinitesimal, is an infinitesimal symmetry of $\mathcal L=-\frac14F_{ab}F^{ab}$. \begin{equation} F_{ab}\rightarrow F_{ab}+\partial_a(\alpha\partial_0A_b)-\partial_b(\alpha\partial_0A_a)=F_{ab}+\partial_0(\alpha F_{ab}). \end{equation} \begin{equation} \Rightarrow \mathcal L\rightarrow\mathcal L-\frac12F_{ab}\partial_0(\alpha F^{ab})=\mathcal L-\frac14\partial_0(\alpha F_{ab}F^{ab}). \end{equation} We require $\delta\mathcal L=0$ for it to be called "a symmetry of $\mathcal L$", right? Or do we only require $\delta\mathcal L=$ a total derivative? Either way, I don't seem to get what we want.


title: Phase factor for nearest neighbor hopping in the Haldane Model

text: In Haldane's model, he imagines a staggered magnetic field in graphene where the net flux through a unit cell is zero. To model this, he has a phase factor in next nearest neighbor hopping on the honeycomb lattice. Why does he not consider a phase factor for hopping between nearest neighbors as well?


title: electron in the nucleus

text: In the event that the electron is in nucleus of the atom ( ~~via tunneling effects and other things I don't understand~~ ), How does QED deal with this situation?


title: Where does the requirement of prime number dimension figure in generating mutually unbiased bases (MUB)?

text: I have been studying this paper by S. Bandyopadhyay et al. - "A new proof for the existence of mutually unbiased bases". Here is the link. They explicitly construct MUB using generalized Pauli matrices. The statement of the theorem goes as follows: "For any prime d, the set of the bases each consisting of the eigenvectors of $Z_d, X_d, X_dZ_d, X_dZ_d^2,...,X_d(Z_d)^{d-1}$ form a set of $d+1$ mutually unbiased bases" Where $X_d$ and $Z_d$ are generalizations of Pauli matrices in $d$ dimensions and they satisfy $X_d|j> = |j+1>$ and $Z_d|j>=\omega^j|j>$ with $|d+1>=|1>$ (i.e. it is a cyclic system) The proof doesn't seem to use the requirement of $d$ being prime. It would really appreciate any help in figuring this out.


title: Does the metal foam "whiffleball" orbital reentry idea make any sense?

text: Planetary Resources is a company speaking publicly about mining near Earth asteroids for resources. I'm interested the physicality of a claim they make in a video here: http://www.youtube.com/watch?v=dVzR0kzklRE&t=27m55s They would like a method to reenter resources into the Earth's atmosphere that is more economic than conventional approaches, and they propose making a metal foam that is super low average density. In particular, they propose turning 100kg of Platinum into a 2m diameter ball. They mention that the terminal velocity of this (presumably at sea level) is <60 mph. Then this would ideally avoid the problems that:   * low masses get burned up in the atmosphere on reentry   * high masses slam into the Earth's surface This doesn't make intuitive sense to me. Sure, the drag coefficient is high and the mass is low, but that doesn't change the fact that you have to dissipate orbital kinetic energy over a finite distance. How would this avoid the problem of melting due to the heat and thus breaking up in the atmosphere? If a higher drag to mass ratio was a panacea, then wouldn't we just use parachutes for reentry, even in the initial stages? _meta note: if it proceeds to beta, I may request to migrate this question to_ http://area51.stackexchange.com/proposals/43283/space-exploration-and- technology


title: What is the height of the electron orbits of an atom?

text: What are the heights of the electron orbits of an atom? (How far apart are the energy levels of the electron relative to the center of the atomic nucleus?) How fast do electrons move in their orbits?


title: Determine the maximum capillary rise

text: The problem I have is this: > A capillary tube is immersed vertically in water. Knowing that water starts > to evaporate below 2kPa, determine the maximum capillary rise and tube > diameter. Assume the contact angle is 6 degrees and surface tension is 1 > N/m. The only equation I know of to use for this would be: $h = \frac{2\sigma_s cos(\theta)}{ \rho gR}$ where h is the capillary rise, $\sigma_s$ is the surface tension, $\rho$ is the density of water, g is 9.8 m/s ^2 and R is the radius. However I have 2 unknowns and only 1 equation and this relationship does not include pressure. My question is what other equation can I use in solving this problem, or is there a different equation that I should be using to solve this problem. The correct answer to this problem should be h=10.2 m, and R = 20 micro m.


title: How much work is done when pushing against a brick wall?

text: So this is one of the questions on my physics assessment and I would like to know how to calculate how much work is done when pushing against a brick wall. My teacher has told me the calculation is: weight(kg)x10 (this gives me the force)x distance. But what is the weight of and the distance of? As when you push against a brick wall the wall doesn't move and you can stop yourself from moving. Please answer as soon as possible, also I'm kind of younger so could you explain clearly(sorry) Emsee


title: Center of mass coordinates in Lagrangians and Laplacians

text: Is there a quick nice and easy way to write Lagrangian's and the classical/quantum Laplacian operator in terms of center of mass coordinates? The algebra is so involved and it has me confused about the entire process, I really really hope there is a quick way to instantly see why the entities should take the forms they do in C.o.M. coordinates without having to re- derive them every time. I have to start by drawing this picture http://upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Jacobi_coordinates.svg/500px- Jacobi_coordinates.svg.png and it only gets worse from there, I do not understand the intuition behind expressing the position vectors in terms of the center of mass $\vec{R}$ and the relative position vector $\vec{r}$ as done here http://www.worldforge.org/project/newsletters/July2002/LagrangianP3 it seems like it should be automatic, but to me it's algebra I mess up.


title: What happens to electrons when they are detected?

text: I know photons are absorbed and annihilated when they are detected but a) when electrons are detected, are they absorbed and annihilated? and b) if electrons are ever absorbed, what happens when they are? Are photons omitted?


title: Velocity measurement in relativistic perspectives

text: I understand the precepts of relativistic time dilation, but I'm looking to nail down the local perception of velocity in each frame. My question is threefold:   1. Given two observers $A$ (rest frame) and $B$, if $A$ observes $B$ traveling away from starting point $A$ at $V=2c/5$, does $B$ perceive a different value for $V$ based on dilation, or the same, based on it's local frame?   2. If it is the same (which is my assumption), how does this integrate with the predicted experience of $B$ from the point of view of $A$ (which I also assume would seem to act as a multiplier on perceived velocity due to dilation)?   3. As a further silly notion, does it change if at some point $B$ stops and proceeds to return to $A$ at the same previous velocity? My assumption is it does not.


title: Why in 2+1 spacetime dimensions electromagnetic wave (light) cannot be distinguished with acoustic wave (mechanical wave)?

text: I have heard a saying that in 2+1 spacetime dimensions electromagnetic wave cannot be distinguished with acoustic wave. Or maybe they want to say in 2+1 spacetime dimensions photon and phonon cannot be distinguished from each other. Is it true? Why?


title: Any examples of negative ADM energy solutions with WEC but not DEC satisfied?

text: Any examples of negative ADM energy solutions with weak energy condition (WEC) but not dominant energy condition (DEC) satisfied? Witten's proof of the positive energy theorem requires the dominant energy condition. Is there any counterexample of a metric satisfying the weak energy condition, but not the dominant energy theorem, with negative ADM energy?


title: Burning VS Melting: What is the relation in the atomic/molecular structure?

text: This has never been asked before on this site, so I thought I would ask this to help future searchers, passerbys, or others understand this better. What are the key differences between burning something and melting something? For example, you can burn cake before it melts in an oven, but you can't burn water in a solid state at the same temperature(it will separate the molecules and flow into space; you can't burn H20 either). So basically, why do some things burn then melt, and some things melt and burn, or do not burn at all? What does "burn" mean atomically, and what is its relation to melting? They are sometimes used interchangeably to express "burning something", or "melting it" as a greater extreme, despite the fact that ice will melt into water and will never burn, and cake will burn way before melting.


title: Condition for circular orbit

text: I am a little confused about the condition for circular orbit. Goldstein's Classical Mechanics has the condition for circular orbit as $$f'=0\tag1$$ where $f'$ is the effective force. I understand that the reason for this requirement is that the corresponding $V'$is at an extremum. However, setting $f'=0$ yields $$f(r)=-\frac{l^2}{mr^3}\tag2$$ and the one of the equations of motion becomes $$m\ddot r=0\tag3$$ This can't be right as it is saying that the net force on the object is zero, and yet the object is supposedly in a circular orbit. Am I interpreting equation (3) wrong?


title: Momentum in quantum mechanics

text: In quantum mechanics, we can have some superposition of matter waves that have different wavelengths. If then, can't momentum of a particle change every time measurement takes place? Or should I regard the momentum of a particle as the momentum of the wave packet which has single wavelength and frequence? If then, isn't the momentum of a particle always fixed? Then why do we need uncertainty principle? I think I am somehow messed up with uncertainty principle, but I am unsure what it is...


title: Modeling linear spring deformation in time

text: Suppose I had a spring (at equilibrium) and applied a certain force $F$, causing it to undergo elastic deformation. I know that by applying this specific force, hooke's law tells me that the spring will contract by a total distance $\Delta x=F/k$, where $k$ is hooke's constant. I want to be able to model this deformation in time. Assuming the force is constant in time, I want to be able to predict the length of the spring at any given time $t$. The standard differential equations are given as: $$mx'' + \mu x' + kx = F$$ However, I'm having difficulty adusting this equation to the situation I have described above. Certainly, if the spring was at equilibrium at first, there is an acceleration induced. Hence, I believe the $x'$ term should remain. However, if the force is applied constantly, the spring should deform continuously to its steady state position without oscillation (if I'm wrong about this, please correct me!). Hence, I also think there is an argument against including the acceleration term. Also, my spring system doesn't really have a dampening agent, so I'm not sure if it's feasible to include the velocity term either. However, I predict that the length of the spring to decay to its resting steady state length exponentially; indicating that the velocity term might be important to keep. I'm just not sure which assumptions are correct for my system. Any help with this would be greatly appreciated! :)


title: electrons in an atom and uncertainty principle

text: Electrons in an atom have quantized energy quantity. Can uncertainty principle be applied in this case, then? How does this work? As energy is fixed, this seems to disobey $\Delta E \Delta t \geq \hbar/2$...


title: Gravitational effect of charged masses held apart by a rod?

text: Imagine two oppositely electrically charged masses held apart by a rigid rod of negligible mass. At some distance the gravitational field due to this system is proportional to the sum of the masses + the pressure in the rod - the pressure due to the electrical attraction of the opposite charges. The pressures cancel so that the gravitational field just depends on the masses. Is this right? If the charged masses slip off the ends of the rod would the gravitational field due to the system decrease as there is no longer any positive pressure in the rod to balance the negative pressure of the electrical attraction?


title: Quantum Mechanics: Momentum operator questions

text: I'm asked to determine $\hat{P}|\Psi_0\rangle$, $\langle{\hat{P}}\rangle$, and $\langle\hat{P}^2\rangle$ for $$\Psi_0(u) = \psi_0 + 2\psi_1$$ I understand how to make the matrix for $P$ in regards to the original $\psi_0$ and $\psi_1$ functions, but I'm clueless for the $\Psi $ function that contains the two.


title: If light is a constant and can be slowed down, can it be sped up?

text: Can light be sped up, say for instance, when it enters into a black hole?


title: Monte carlo simulation for continuous spin model (e.g. XY or Heisenberg model)

text: Unlike the Ising model, the XY model and the Heisenberg model have a continuous spectrum. So one need discretize them for a numerical simulation. But how to make sure the discretization procedure reliable? For example, for the XY model with variables $\theta_i$, if $\theta_i$ is discretized by choosing a unit $\frac{2\pi}{N}$, how to make sure the $N$ is large enough?


title: Frequency modulation using visible light

text: Currently I am doing research into visible light communication from an Embedded Systems background (MSc), but I am struggling to relate the concepts of modulation of radio to visible light. I already apply modulation to a working VLC system, but the underlying system still puzzles me. My goal of this post is to create an understanding of the underlying fundamental concepts, so if there are flaws in my assumptions below please point me to it. **Radio** In RF communication, two modulation techniques are used: amplitude modulation and frequency modulation. All other modulation techniques are variations on these types. These modulation techniques change the electromagnetic field in terms of coherent photons with a specific frequency and amplitude (source). **Visible light communication** In VLC, amplitude modulation is the most common technique (changing the intensity), but frequency modulation is also used. As frequency relates to color, some research uses RGB LEDs to do this in combination with color filtered photodiodes. **(1)** However, and this is where the problem is, some research applies frequency and phase modulation using a single white LED. They use a photodiode as a receiver which is sensitive to intensity but not to color variations, so how is frequency modulation then possible? **(2)** It seems that VLC has a third kind of main modulation technique in comparison with RF, is this correct? **(3)** If so, what makes light so different from RF then, as it also is electromagnetic radiation? And can this third type be applied to RF?


title: Launch roll program for the Saturn five rocket

text: I have seen many questions answered about the roll program with relation to the shuttle launch and reducing stresses on the launch vehicle and various other reasons, but why was the roll program needed for the Saturn five rocket being a circular vehicle. Having watched films of other launch's in different countries using circular rockets, they do not appear to go through a roll program or is it carried out at a different part of the launch procedure.


title: Time dilation and the speed of light in the twin paradox

text: Suppose we look at the twin paradox where the twin traveling at high speed relative to an observer on earth has a clock which counts time by sending photons of light across a distance within the spaceship (perpendicular to the direction of motion) to a detector which counts off 'time' as the interval between photon detections. If the speed of light is constant in both frames, and the distance the photon travels is equal in both frames (no length contraction in the perpendicular direction), won't both observers say the same amount of time has passed in both frames at a later time (suppose the observer on earth uses an identical clock)? Wouldn't a difference in observed time intervals imply differences in the speed of light?


title: Energy-Momentum Tensor in QFT vs. GR

text: What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu f_i - \eta^{\mu\nu}\mathcal{L}$$ (the four conserved Noether currents corresponding to four possible spacetime translations) where $\\{f_i\\}_{i=1}^N$ are the $N$ matter fields in the theory, and we assume $f_i\mapsto\alpha^\nu\partial_\nu f_i$ for translations, and stress-energy tensor from the Einstein-Hilbert action, which is: $$ T_{\mu\nu}\equiv-\frac{2}{\sqrt{-g}}\frac{\delta\mathcal{L}_{Matter}}{\delta g^{\mu\nu}} $$ In particular, how do you get that the two are equal (are they?) for Minkowski space, for which there is no variation in the metric?


title: What is the cause of the large damage by atomic bomb?

text: I recently read in the Feynman Lectures that when the nuclei like that of uranium which are at the crucial level of balance between strong nuclear forces and electrical repulsive forces are taped lightly, they become unbalanced and are broken into pieces. Subsequently, these pieces are very strongly repelled by each other and the energy released by this method is so- called nuclear energy but is actually electrical energy. So I want to ask: is this the cause of large damage caused by atomic bombs or a major portion of the energy released in these explosions are the electromagnetic waves' energy which is due to mass decay?


title: Why not drop $\hbar\omega/2$ from the quantum harmonic oscillator energy?

text: Since energy can always be shifted by a constant value without changing anything, why do books on quantum mechanics bother carrying the term $\hbar\omega/2$ around? To be precise, why do we write $H = \hbar\omega(n + \frac{1}{2})$ instead of simply $H = \hbar\omega n$. Is there any motivation for not immediately dropping the term?


title: Why are popcorn seeds soft after popping?

text: When a seed of popcorn is heated up in oil, it pops like this: ![Slow-mo Popcorn](http://i.stack.imgur.com/r9wd1.gif) You can take one of these popped pieces and eat it with little to no problem. However, if you get an un-popped seed and sink your teeth in, it is noticeably harder. Why is this?


title: Fermi statistics and Berry phase

text: When the positions of two fermions are exchanged adiabatically in three- dimensional space, we know that the wave function gains a factor of $-1$. Is this related to Berry's phase?


title: Producing photons with same frequency, different amplitude wave

text: I don't understand how two photons of the same _frequency_ can have different _amplitudes_ , neither how to produce them. I know that classically the square of the amplitude is proportional to the energy, but photons aren't classical particles. My understanding is that a photon's energy is $h\nu$ - what does the square of its amplitude represent, then? Are there bounds to the amplitude of an EM wave? Take two waves of amplitudes $A_1$ and $A_2$ and frequency $f_0$. If $A_2 = 2A_1$, can the wave with amplitude $A_2$ be said to carry/be two $A_1$ photons of frequency $f_0$?


title: How to deterministically distinguish the following quantum states?

text: (1) How to deterministically distinguish the following quantum states: $$\frac{1}{\sqrt{2}}[|+0\rangle|0\rangle+|-1\rangle|1\rangle$$, $$\frac{1}{\sqrt{2}}|-0\rangle|0\rangle+|+1\rangle|1\rangle$$, $$\frac{1}{\sqrt{2}}|-0\rangle|0\rangle-|+1\rangle|1\rangle$$, $$\frac{1}{\sqrt{2}}|+0\rangle|0\rangle-|-1\rangle|1\rangle$$ where $$|\pm\rangle=\frac{1}{\sqrt{2}}[|0\rangle\pm|1\rangle$$ Here the first two particles are with Alice and the third with Bob.


title: Polyakov action as broken symmetry effective action

text: I would like to ask if it is possible to regard the Polyakov action as an effective action that describes the broken symmetric phase of a more general model. Could someone draw an analogy with O(N) Non-linear sigma model that describes the broken symmetric phase of a O(N) phi^4? What would be that model in the stringy case?


title: How to calculate a ballistic trajectory for a suborbital flight?

text: I'm trying to calculate the initial launch angles and velocity of a projectile (atmosphere's effects can be neglected), assuming that I know the lat/lon coordinates of both the launch and the destination points. Can you recommend any software libraries or reading materials that could help? Thank you.


title: Is Dr Quantum's Double Slit Experiment video scientifically accurate?

text: I'm fascinated by the fundamental questions raised by the Double Slit Experiment at the quantum level. I found this "Dr Quantum" video clip which seems like a great explanation. But is it scientifically accurate?


title: How does a synchroton work?

text: I know that a linear accelerator (linac) works by having terminals that get longer progressively and changes polarity due to AC current. And I also know that a cyclotron works by having two semi-circles that are connected to an AC source and magnetic field perpendicular to keep the particle moving in circles. But in a synchrotron, I understand that variable magnets are used to control the radius of the accelerating particle, however how is the particle accelerated?


title: Einstein equation $E=mc^2$: Does it mean an object without mass does not have energy?

text: Einstein equation $E=mc^2$ where $E$ is energy, $m$ mass, and $c$ the speed of light in vacuum. So does it mean objects without any mass does not posses energy for eg lights photons does not have mass but how can they posses energy


title: Explanation of homogeneity of space and time by giving examples?

text: while reading landau lifshitz i came across these three terms:-   1. homogeneity of space.   2. homogeneity of time.   3. isotropy of time. it will be a great help for me if someone can explain it to me by giving examples .


title: Dark matter and SO(10) grand unification

text: $SO(10)$ grand unified theories nicely accommodate a massive $\sim 10^{14-15}\; GeV$ sterile neutrino. Would this be a viable dark matter candidate? I haven't found any _specific_ material regarding this possibility and I was wondering if there is some simple reason to exclude it. GUT's based on $SU(5)$ have mostly been refuted, so the next candidate according the Occam's razor would be $SO(10)$. I know the energy range to test it is not accessible (and won't be for a long time) but I find it odd that $SO(10)$ GUT's don't feature much in people explanations regarding beyond the Standard Model physics. On a related note, would the absence of any proton decay in the Hyper- Kamiokande refute $SO(10)$? If proton decay is detected would this mean GUT's are the right way to go or do other classes of theories better incorporate proton decay?


title: Energy of the electron-muon reaction

text: Lets see the reaction: $e^- \mu^- \to e^- \pi^- \nu_\mu \;\;\;\;\;\;\;\;\;\;\; {(1)}$ I suppose, that this reaction occurs as follows $e^- \mu^- \to e^- \mu^- \pi^+ \pi^- \to e^- \pi^- \nu_\mu$ Is it possible at energy less than 2*140 MeV? The same is for the analogous proton-muon reaction $p^+ \mu^+ \to p^+ \pi^+ \bar{\nu}_\mu \;\;\;\;\;\;\;\;\;\;\;{(2)}$ Once more reaction: $p^+ p^+ \to p^+ p^+ \pi^- \pi^+ \to p^+ n \pi^+ \;\;\;\;\;\;\;\;\;\;\;{(3)}$ What are the experimental data? * * * **P.S.** This question is important enough. The main solar reaction is $p^+ p^+ \to d^+ e^+ \nu_e $ If this reaction occurs as follows $p^+ p^+ \to p^+ p^+ e^- e^+ \to p^+ n \nu_e e^+ \to d^+ e^+ \nu_e$ then it would require the energy of more than 2*0.511 MeV to take place. Cross section of this reaction will be much less, so the main solar reaction should be $p^+ p^+ e^- \to d^+ \nu_e $ * * * * * * **Update 20.02.11** Why I think so? I suppose that new particles are created in pairs particle- antiparticle. So the reaction $e^- e^- \to e^- e^- \pi^- \pi^+ $ requires the energy of more than 2*140 MeV to take place As well as the reaction $e^- e^- \to e^- e^- \pi^- e^+ \nu_e $ from symmetry considerations, since there is a decay $\pi^+ \to e^+ \nu_e$ And the result is $e^- e^- \to e^- e^- \pi^- e^+ \nu_e \to e^- \pi^- \nu_e $ contrary to $e^- e^- \to e^- \nu_e W^- \to e^- \pi^- \nu_e$ with the minimum reaction energy of 140 MeV The same is valid for the reactions (1) (2) (3) So what is the **experimental data** on minimum energy of these reactions?


Given a central field $U(r)$ satisfies $U(r) \rightarrow -\infty$ when $r \rightarrow 0$, then What if a particle falls into the center of a central field? Can you help me analysis this question in classical mechanics, relativistic mechanics and quantum mechanics? And, what will happen actually in experiments? Any help or suggestions will be appreciated!


title: Where do the photons mediating the electromagnetic force come from?

text: The electromagnetic field is mediated by photons (energy quanta). Its range is infinite, the interaction only weakens quadratically with distance due to the area of an expanding virtual sphere. Where do these photons come from? If they are virtual photons emitted by the charged particles, it does not make sense for them to have infinite range (uncertainty theorem). If they are energy packets radiated by the charged particle, where does this energy come from and why is it not depleted? In particular a stationary particle would not radiate Bremsstrahlung.


title: What is the term $t$, in the expression $E=t^{0}m^{1}c^{2}$?

text: $E=(t)^{0}(m)^{1}(c)^{2}$. Here, $m$ = mass of the body. $c$ = velocity of light. Is $t$ the time?


title: How to derive Fermi-Dirac and Bose-Einstein distribution using canonical ensemble?

text: My textbook says that microcanonical ensemble, canonical ensemble and grand canonical ensemble are essentially equivalent under thermodynamic limit. It also derives Fermi-Dirac and Bose-Einstein distribution from grand canonical ensemble. My question is then: How to derive Fermi-Dirac and Bose-Einstein distribution using canonical ensemble. The expression of canonical ensemble $$\rho\propto e^{-\beta E}$$ seems to imply Boltzmann distribution only.


title: How do you properly define a line in a Feynman diagram?

text: I've been reading Tony Zee's "Quantum Field Theory" and I'm really enjoying it. However, on p. 45 I came across what I think is an inconsistency. The sentences in question are: > The rules go something like this: > > (1) diagrams are made of lines and vertices at which four lines meet; > > ... > > (3) for each line assign 1/m2; Here's the thing: if a vertex is a point at which four lines meet, then most of his figures are wrong. Here are a few examples:   * Fig. 1.7.1b is listed as having four lines and one vertex, but if a vertex is a point where four lines meet then it has five lines.   * Fig. 1.7.1c is listed as having four lines and one vertex, but if a vertex is a point where four lines meet then it has six lines.   * Fig. 1.7.2b is listed as having six lines and two vertices, but if a vertex is a point where four lines meet then it has seven lines.   * Fig. 1.7.2c is listed as having six lines and two vertices, but if a vertex is a point where four lines meet then it has eight lines.   * Fig. 1.7.3b is listed as having seven lines and two vertices, but if a vertex is a point where four lines meet then it has eight lines. The problems I noted disappear if you consider the loops I examined to count as one line when assigning the mass terms. However, this is _not_ what Zee says. Is he wrong or am I missing something?


title: Topological quantum computation: abelian vs. non-abelian anyons

text: We need non-abelian fractional hall states because of the ground state degeneracy http://rmp.aps.org/abstract/RMP/v80/i3/p1083_1 (arXiv version for free). But we can also have degeneracy even in case of abelian fractional quantum hall states on topologcally non-trivial surfaces http://prb.aps.org/abstract/PRB/v41/i13/p9377_1. Could anyone tell me the reason (conceptual) for not using abelian state for quantum computation?


title: Near-field around parabolic antenna?

text: Having a discussion at work about the $H$-field around a big parabolic antenna. All of the safety tests done around the antenna only mention $E$-Field. They state in the radiating near-field the $E$ and $H$ are related so no need to measure them both. On the other hand all of the wire antenna have $H$-field included in their measurments. I would have thought this was the wrong way around. Simple wire antenna have near-fields extending only a couple of wavelength but paraboic near-field can extend to a few $km$. Only thing I can think of is that the near-field definition only applies to the front of the antenna - the back and surrounds are shielded by the parabola. > Is there a $H$-field, independent of the $E$-field in the immediate vicinity > of a parabolic antenna?


title: Should angular momentum change or it should not.?

text: Let us consider a body with an arbitrary shape. Let its center of mass be assigned coordinates (o,o,z) with respect to an origin.Now let us consider two equal and opposite forces acting on the body in such a way that they do not share their line of action and their lines of action do not pass through the center of mass. Now I first propose that the net torque acting on a given system about any given point is simply equal to the net torque acting on its center of mass about that point. I attempted to prove it in the following manner; Let us consider a system of mass with the center of mass having a position vector R w.r.t the origin (the point about which I am considering the angular momentum and torque).Now the angular momentum ,L, of the whole system can be broken into two parts, i.e. it can be expressed as the vector sum of the angular momentum of the center of mass w.r.t to the origin, denotated by A, and the angular momentum of the system about the center of mass,denotated by Z. so L = A+Z. ..........(1) Now let an external force F act on the system. Now we can write that F= mA, Where A is the acceleration the center of mass and m is the total mass of the system. Now the torque acting on the center of mass about the point = R X F. .............(2) Now let us consider the torque acting on the system about the center of mass. As the center of mass is accelerating any mass in the mentioned system will experience a torque due to the pseudo force. Hence the net torque acting on the whole system about the center of mass = K=sigma (Ri X miA). where Ri denotes the position vector of a point mass about the center of mass and mi denotes its mass. Hence K = {sigma ( mi. Ri)} X A. Now sigma (mi.Ri) = position vector the center of mass w.r.t to the center of mass= zero vector. Hence K= Zero vector. Now by differentiating bothe sides of (1) w.r.t time T,and interpreting in terms of physics we have torque acting on the system about the origin= torque acting on center of mass about origin + torque acting on the system about the center of mass. = R X F + K = R X F , since K= zero vector. Hence I proved what I stated. Now let us come back to the original question. In that question as the center of mass is not accelerating owing to the action of balanced forces, hence no torque is acting on C.O .M and as such the angular momentum of the body should not change. But practically speaking these forces generate a couple and tend to change the angular momentum of the body. So Where was I wrong ?


title: How does thermal broadening of the Fermi Function cause electron coherence loss?

text: Generally, there are two ways for electrons to lose their wave-like properties in a solid material. One is by way of collisions that cause changes in the energy and momentum of the electron. The other way is by temperature effects on electron physics, expressed through the "smearing" of the Fermi Function. From Quantum Heterostructures by Mitin: > ...At high temperatures, when electrons with significantly different > energies take part in kinetic processes, the coherence in the system is > destroyed as a result of a large spreading of the wave function phases. I have not been able to find a relationship between the spreading of the Fermi Function and phase shifts in the constituent electrons in the system. Could somebody clarify this?


title: How can tunneling be one-way?

text: I was recently at a lecture given by Dr. Harry Gray, a biophysical chemist, where he talked about how proteins (specifically those involved in photosynthesis) are able to use various phenomena, like superexchange and tunneling, to move electrons through them, coupling redox reactions despite the extreme distances (~20 Å). By using tunneling/superexchange, various redox proteins are able to move 300-2000 electrons/second over this distance, while the reverse rate is effectively zero. I asked about why this barrier is one-way, but I don't have enough base knowledge to understand his reply; something about how the injected hole is chased through a series of several bonds (sigma and hydrogen)... In any case, I'm curious for a simpler case and explanation of this 'diode' effect about how electrons can be shuttled one way with ease but not the other


title: Basic question concerning pure energy

text: Inside the core of a star thermonuclear fusion reaction fuses hydrogen atom into helium releasing massive heat/light and energy.When a blackhole eats up enough stars and gases it devours itself by releasing leftover gases and radiation {nothing but energy} called Quasar. In both the cases there's massive amount of energy involved.I keep hearing the word "Pure Energy" instead of just "Energy".What is pure energy anyways?How is it different from just energy?


title: How does QFT help with entanglement?

text: I'm a bit confused. QFT is claimed to incorporate both Quantum Mechanics and Special Relativity. Therefore it should address the problem of non-locality caused by entanglement. However when I search for an answer on the Internet, I found nothing. I'm not complaining. But it seems that most people only use QFT to do some fancy particle stuff and forgot we should care more about the more fundamental stuff.


title: Trying to understand a step in deriving Maxwell-Boltzman statistics

text: In the Wikipedia article on Maxwell–Boltzmann statistics, there is a point in the derivation that stumps me. When I get to where $\displaystyle W=N!\prod\frac{g^{N_i}}{N_i!}$ is quoted as a count of the number of possible ways particles can be found in each state, I am told we want to pick the $N_i$ in such a way as to maximize $W$. Why is it important to maximize $W$?


title: Something I don't understand in Quantum Mechanics

text: I've just started on QM and I'm puzzled with a lot of new ideas in it. 1.On a recent lecture I've attended, there is an equation says: $\langle q'|\sum q|q\rangle \langle q|q' \rangle =\sum q \delta(q,q')$ I don't understand why $\langle q'|q\rangle \langle q|q' \rangle =\delta (q,q')$ Can you explain this equation for me? 2.Actually, I'm still not clear about the bra-ket notation. I've learnt the bra and the ket could be considered as vectors. Then what are the elements of the vectors? Thank you very much!


title: How does this problems are solved (modeling/simulation)?

text: Can somebody guide me in what to read and learn in order to be able to solve or understand how to solve the following types of problems:   1. The modeling/simulation of the bullet, shot into the water container, at the bottom of which there is a glass cup   2. Automobile crash into the wall/another automobile.  I want to be able to construct the correct mathematical models of such problems. And then to be able to solve them numerically and get the simulation. Of course depending on the problem I will need supercomputer's power, but that is another question.


title: Why would Klein-Gordon describe spin-0 scalar field while Dirac describe spin-1/2?

text: The derivation of both Klein-Gordon equation and Dirac equation is due the need of quantum mechanics (or to say more correctly, quantum field theory) to adhere to special relativity. However, excpet that Klein-Gordon has negative probability issue, I do not see difference between these two. What makes Klein-Gordon describe scalar field while Dirac describe spin-1/2 field? Edit: oops. Klein-Gordon does not have non-locality issue. Sorry for writing wrongly. Edit: Can anyone tell me in detail why $\psi$ field is scalar in Klein-Gordon while $\psi$ in Dirac is spin-1/2? I mean, if solution to Dirac is solution to Klein-Gordon, how does this make sense?


title: Question on inflation as a phase transition

text: I have just finished watching the following video http://www.youtube.com/watch?v=beQ9fZ0jVdE where Laughlin, Gross and some students discuss e.g. about inflation. The following question is risen: Is inflation a phase transition (e.g. of the geometry of space time)?


title: Mass dimension of coupling constants in various dimensions

text: Just a quick question: Suppose I want to consider QED or YM in 4 dimensions we always say that the coupling constants are dimensionless and that the field then has a specific mass dimension. What happens if we change the dimensions we are considering? Do the mass dimensions of the fields then change or do the coupling constants become dimensionful?


title: Lepton number conservation in standard model

text: 1. Why is it said that in standard model lepton number is conserved?    2. How do I know that Lepton number is an abelian charge?    3. Why is this conservation not as sacred as electric charge conservation.    4. How does one mathematically distinguish between lepton number and electric charge?