60,674 reputation
484206
bio website
location New York City
age 41
visits member for 3 years, 8 months
seen 12 hours ago

I do not participate on this site any longer, except to respond to comments regarding my own text, if that text is unavailable in another form. I do not accept the political moderation atmosphere here, it is not compatible with open science. Unfortunately, this seems to be a recurring pattern on such sites--- they grow with promises of open participation, and then shut down in a phase transition of censorious moderatorship. Hopefully physicsoverflow.org will be the first exception to this rule, as the policies there were crafted specifically to avoid this phenomenon.


4h
awarded  schroedinger-equation
14h
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.
14h
comment What's the interpretation of Feynman's picture proof of Noether's Theorem?
@LarryHarson: Thanks, I'm glad you got it. It's a really beautiful argument, and the implicit confusions really get all people to learn variational derivatives very well, and in such a way that they never get confused again, it's classic Feynman clarity. I didn't do the Wiki on that, this stuff is understood by the people who do functional derivatives, mathematicians and physicists both, I tried to stick only to controversial stuff, not waste energy on stuff that is already accepted.
1d
comment How do you start self-learning physics
@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.
2d
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.
2d
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.
2d
revised What is lepton number?
fix terminology
2d
comment What is lepton number?
@Tim: Oops, I meant helicity, sorry, will fix.
2d
comment What's the interpretation of Feynman's picture proof of Noether's Theorem?
@LarryHarson: Yes, I meant "variation in L" where I wrote "variation in S" (fixed it just now). It's not just "multiplied by dt", it's "integrated against t", and the result is what you say, except it's $\delta S/\epsilon = (P_1(t_1) + P_2 (t_1)) - (P_1(t_0)+P_2(t_0))$, i.e. the change in momentum. The point is that delta function variation gives a singular change in L which only makes sense under an integral, but it makes sense because it is a code for the local contribution of variations in response to a continuously varying change. This is the usual story in variational calculus.
2d
revised What's the interpretation of Feynman's picture proof of Noether's Theorem?
minor fix
2d
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
14
comment What's the interpretation of Feynman's picture proof of Noether's Theorem?
@LarryHarson: It's an infinitesimal delta function variation, which means that it's both infinite and infinitesimal at the same time. This is the confusion when you make an infinitesimal delta function variation, it's something you need to sort out, and I explained how to sort it out and make it rigorous in the answer. The variation is only "infinite" in the sense that delta-functions are infinite at the point they are nonzero, it turns into an infinitesimal variation if you smear the delta function, or else equivalently if you do all the variations continuously and integrate by parts.
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.