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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.
Apr
7
comment Landau poles in dimension <4?
@AbdelmalekAbdesselam: Whoops! The correlation function goes as $1/|x-y|^{1.5}$, not the J! The J powerlaw is fixed by demanding that the equation of motion gives this correlation function as a solution, I'll fix it now. For the $\alpha$, the range of allowed $\alpha$ which produce unitary field theories is precisely the ones for which the Schwinger representation is a sum over Levy flights with a sensible probability exponent, which is why I like to call these "Levy field theories". Generalizing traditional particle Brownian paths to Levy Flights was my path to these, not Speer.
Apr
6
comment Why does a gas get hot when suddenly compressed? What is happening at the molecular level?
@user462437: Each ball would get a smaller increase in speed, and the process of moving the wall in would take longer, the net result is the same (obviously, but work it out if it is confusing).
Apr
6
comment Why does a gas get hot when suddenly compressed? What is happening at the molecular level?
@user4624937: Slow or fast, the gain in energy from the collisions is the same, it is the total work done against the pressure. I was assuming it is adiabatic already.
Apr
4
comment Quantum Mechanics by Dirac
@physicslover: Disclaimer: I learned from Dirac. I made up my own exercises by scrounging undergrad books, writing simple programs, and trying to understand chemistry and so on. Dirac was very good for showing how to use formal methods to guide physical intuition, because Dirac's arguments are extremely formal, guided by mathematical identities, e.g. his clever but nearly physically meaningless derivation of the canonical commutation relations in the early intro chapters. The perturbation theory there is excellent, and you can make up your own exercises easily by perturbing the HO.
Apr
4
comment Quantum Mechanics by Dirac
@physicslover: Young Feynman had issues due to his philosophy that one must rediscover everything (true, but he overdoes it). He eventually redid QM, via the path integral. Dirac's book is best read in parallel with Feynman and Heisenberg's original papers (Dreimannarbeit too). The physical picture can be lost if you don't know the old quantum theory and the stuff that's now on Wikipedia under "Matrix Mechanics". But given this stuff, Feynman's vol III, Wikipedia, Dirac is a very good intro to canonical QM. The only part that is not so great is the QED, but even that covers Dirac gauge well.
Apr
2
awarded  Nice Answer
Mar
27
comment How can it be that the beginning universe had a high temperature and a low entropy at the same time?
@Sklivvz: The post starts with the rejection of the position, so what you say is clear, I think.
Mar
26
comment Which physics quantities are real and which just a tool in the Newtonian apporach?
For a closed system where momentum is conserved, the total KE change before and after is frame independent. For an individual particle it is not, that should fix your confusion.
Mar
26
comment How can it be that the beginning universe had a high temperature and a low entropy at the same time?
@Sklivvz: No, no. People disagree with obvious things all the time, simply because other people claim to disagree with them. The reason I say it is obvious is because of the holographic physics of the 1990s told you how to treat horizons, you are supposed to consider them physically as boundaries and define your quantum theory by patches with "complementarity" between patchs. This confirms that his picture is certainly a consistent way to treat the cosmological horizon, and it should not be rejected. The rejection is people saying it is demonstrably wrong, and this is obviously false.
Mar
26
comment Is it safe to study from MIT and Berkeley course series, or they contain wrong information?
@Ooker: I guess that's what happens when you die, and you don't specify the unit choice in your will. People should respect his decision when he was alive.