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Ron Maimon
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 Apr 18 awarded schroedinger-equation Apr 17 comment Why the Principle of Least Action? @Self-MadeMan: When you don't know the initial conditions, you place a probability distribution $\rho$ on these, then you evolve $\rho$ by evolving the initial conditions according to Newton's laws. Then the information missing in the encoded ignorance of the probability distribution $\rho$, which up to an infinite log-divergent constant (depending on the phase space discretization), $\int \rho\log\rho dx dp$ over phase space, is constant. This is the 19th century law of conservation of entropy in classical reversible mechanics, basically uncovered by Boltzmann/Lorschmidt, Liouville's theorem. Apr 16 comment How do you start learning physics by yourself? @OmnipresentAbsence: The Einstein story is not a myth to make incompetent people feel better. It is a fact that Einstein was flunked by Hermann Minkowski in 1902 because he considered Einstein a lazy math student. Einstein was not studying Minkowskian things like rings and abstract algebra, but instead was beginning his revolutionary work on atomic theory. This led Einstein to not get recommendation letters, and he ended up in a patent office. The story is not telling people to be lazy, rather it is warning them that the social order can't appreciate radical work, and will punish them for it. Apr 15 comment What is lepton number? @Tim: The issue here is that the neutrino field $\psi$, the chiral field with a single chirality, is not the only field associated with the neutrino. There is also $\bar{\psi}$ of opposite chirality. When the fields are massless, $\psi$ produces neutrino of one helicity, and $\bar\psi$ produces antineutrinos of opposite helicity. When the neutrino is 2-component massive (like in nature), the mass term mixes up the two helicities to one massive particle of no definite helicity, and the massive particle is from a combination of $\psi$ and $\bar\psi$, often also represented as a majorana field. Apr 15 comment What is lepton number? @Tim: To explain more properly, the two-component Lagrangian mass term for a chiral field $\psi_i$ is $\psi_i \psi_j \epsilon^{ij} + \bar{\psi_\dot{i}}\bar{\psi_\dot{j}} \epsilon^{\dot{i}\dot{j}}$. The field $\psi$ has one chirality with one helicity when massless, the field $\bar\psi$ transforms as the conjugate of opposite chirality and has opposite helicity, and creates an antineutrino, and the mass term violates lepton number. By chasing a nearly massless neutrino, you reverse direction of motion, and you convert it to an antineutrino, violating Lepton number by boosting. Apr 15 revised What is lepton number? fix terminology Apr 15 comment What is lepton number? @Tim: Oops, I meant helicity, sorry, will fix. Apr 15 revised What's the interpretation of Feynman's picture proof of Noether's Theorem? minor fix Apr 15 comment What is lepton number? @Tim: Chirality is only Lorentz invariant for a massless neutrino, it's the spin in the direction of motion. Your comment is incorrect. There is no chirality for a stationary neutrino, there is only a spin. Depending on which way you boost to infinite momentum, you get opposite chirality. Apr 14 revised Is the EmDrive, or “Relativity Drive” possible? added 1383 characters in body Apr 14 comment Reading the Feynman lectures in 2012 I just did (3d) now, using the most idiotic method. 10 bodies is about right, maybe you can get 20 or 30, I never did it systematically. There are good approaches for blocking up the computation into regions so that you don't have to compute order N^2 forces, rather distant bodies in blocks. You need to deal with drift and the no-control when two bodies collide, you get too-large instantaneous force, and a spurious numerical explosion. You can fix using dynamical timestep that is small enough to ensure energy conservation, or with the two-body in constant+linear background method I described. Apr 14 comment Reading the Feynman lectures in 2012 @tom: On a recent computer, if you just write the most basic code in C, without fancy classes, just the simplest code, 1000 particles do 10 steps a second. I heard this from a layperson (father of a friend) who showed me his code for gravity clusters and noted that he found systems that stabilized to crazy but non-chaotic orbits long before they reached two particles. He wanted to publish this. There are simple tricks--- use a second order method, and when two particles are about to near-collide, use the exact solution two particle scattering in background field as the first approximation. Apr 9 comment What's the interpretation of Feynman's picture proof of Noether's Theorem? @Qmechanic: I expanded my answer to include the simplest formal equivalent of Feyman's argument, and now I see that I ended up unintentionally plagiarizing your answer a little bit. I think I emphasized sufficiently different things to make my answer useful, and since your answer also overlaps my answer in a similar way, I hope you are not annoyed at this. Apr 9 revised What's the interpretation of Feynman's picture proof of Noether's Theorem? added 7506 characters in body Apr 8 comment Is it possible to separate the poles of a magnet? @RetardedPotential: Will answer on physicsoverflow. Apr 7 comment Landau poles in dimension <4? @AbdelmalekAbdesselam: It's not a coincidence, but best to ask on physicsoverflow. Apr 7 comment What's the interpretation of Feynman's picture proof of Noether's Theorem? The "horizontal line" means perturbing the velocity from $\dot{x}$ to $\dot{x} + \epsilon \delta(t-t_0)$, where the perturbation is thought of as an infinitesimal kick at time $t_0$. This is not mathematically sensible by itself without thinking a bit about regulating the delta-function, but when you do regulate everything and cross the t's and dot the i's, Feynman's proof goes through and produces the shortest niftiest proof of Noether's theorem. It is nowadays standard to use a continuously varying kick $\dot{x} + \epsilon(t)$ instead, to avoid the limits-talk. See my answer. Apr 7 revised Landau poles in dimension <4? errors Apr 7 revised Landau poles in dimension <4? typo Apr 7 comment Landau poles in dimension <4? @AbdelmalekAbdesselam: yes, you are right, it's 4.5 not 1.5, of course, I am sorry for the lapse.