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location New York City
age 41
visits member for 3 years, 11 months
seen 14 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.


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.
Mar
17
comment What happened to David John Candlin?
@Sofia: I didn't do it myself, I was blocked repeatedly due to user flags over my language. Regarding your case, the votes were relatively fair, voting is not a problem on these sites. Regarding your questions about whether the Euler Lagrange equation is always a minimum the answer is no--- after one period of the Harmonic oscillator, all solutions starting at q=0 with any initial velocity focus to q=0 again, and beyond this point, the solution to the EL eqn is a saddle point, some perturbations make the action go up, others make it go down. This is basic to Morse theory and Penrose's theorem.
Mar
15
awarded  Nice Answer
Mar
13
comment What fundamental principles or theories are required by modern physics?
@drake: Actually, there is a topological difference, in that there are two boundaries to time, past and future, but these are two boudaries to the light cone. I don't know whether this counts as a "difference between space and time", obviously there is a psychological difference, and there is an entropy difference, but I think you mean something else.
Mar
13
comment What fundamental principles or theories are required by modern physics?
@drake: S-matrix is both, because the asymptotic states go to infinity in space at infinity in time, they are simply asymptotic in both senses, and the asymptotic states are relativistically invariant, and the relativity transformations on plane waves don't have any strange singling out of time. exp(i(kx + w t)) is manifestly Lorentz invariant and treats time and space more or less equally (only the metric sign is different), with x,t vector and w,k covector, and these asymptotic states are the only "real" thing in an S-matrix point of view.
Mar
13
comment What fundamental principles or theories are required by modern physics?
... regarding measurement, that's a philosophical issue, I take many-worlds to avoid dealing with philosophy. The modern S-matrix ideas are holographic, so you imagine that all the dynamics is happening on a cosmological horizon, so that there is no real difference between space and time anymore, they can both be considered to be reconstructed from the boundary theory, but on the boundary, you can consider boundary time as distinguished, blah blah, it's mostly philosophy. It is possible to define boundary path integrals using space-boundary conditions at all time too, by the way.
Mar
13
comment What fundamental principles or theories are required by modern physics?
@drake: If you define the boundary conditions as Schwinger did, using space-like hypersurfaces and the precise values of fields, then you are right, and time is a little distinguished (although conceptually less than in other formalisms). But if you follow Wheeler and Feynman and define the boundary conditions through scattering states, they are plane waves, and these are asymptotic conceptions equally in both time and space. The S-matrix formulation treats both space and time equally, even in the boundary conditions. Causality in S-matrix is analyticity, which is not a space-time property.