[math-fun] Does entropy increase because the universe is expanding? Quantum, Schulman
My earlier recommendation of book by Roland Omnes on quantum interpretation may have been wrong -- I might have meant the book by Max Jammer instead. I took a look at L.S.Schulman: Times arrows & quantum measurement, Cambridge UP 1997. His first page (xv) says "idea first suggested by Thomas Gold 1958: the local thermodynamic arrow of time is a consequence of the expansion of the universe." Page 2 he says this is "stark power of a great - nearly obvious - truth... but others consider Gold's thesis neither obvious nor true. Moreover despite my admiration, I find Gold's argument flawed. It is a subtle flaw..." By the way, I do not recall Zeh's book even broaching this whole subject, presumably because Zeh considered it to be garbage. Zeh's book strikes me as far superior to Schulman's but unlike Schulman does not attempt to take a stance. LSS claims he is going in ch4 to explain/elaborate Gold to deduce that the cosmo-expansion and 2nd law time arrows both must be aligned. He also claims ch6 is the "other heart of his book" and it presents his own quantum measurement theory. ch11 overviews. Turning to ch4 he explicitly says "Coffee cools because the quasar 3C273 grows more distant." Well, I have to congratulate LSS on his courage -- he certainly is up front with his outrageous garbage. LSS says he is going to impose "two time boundary conditions" which is something that physicists almost never do and already seems extremely suspect. In 4.1 he says "the issue is not whether systems move from uncommon to common states but why uncommon came first." Well, no. In my picture, there is an observable and unobservable part of the universe, and we must average over the states of the latter when observing the former, and the whole ball of wax is always in one state (and that one state cannot be said to be "common" or not, that word has no meaning). So LSS here does not understand the picture. (Also in my picture it is no paradox if the universe "must have begun in a low entropy state," I still am ok with high entropy in the sense that in my picture that does not prevent entropy increase. Entropy increase is about information transfer/swapping between the unobservable and observable parts of the universe.) Then LSS says Gold observed that what is key is that "the expansion allows photons to get away." Photons that get away form part of the unobservable part of the universe and thus can "measure" our part and thus cause decoherence. Correct idea, but missing my picture which notes for "gravitons," not photons, gravitons always "get away" even in a contracting universe. I basically agree with the Gold idea that photons by "getting away" can cause decoherence, though... but if we live in a "turnaround to crunch" universe, photons actually never really get away. Gold then considers a star inside a magic insulating box. Note I too had considered that,but making the point gravitons would pass thru the box walls and could not be stopped even in principle. Incidentally S.Weinberg in his GR book estimates our sun outputs about 1 megawatt of graviton radiation continually. Gold ignores gravitons, and claims after a long time the star in the box would lose "time's arrow." Meaning what? It would reach thermodynamic equilibrium? This would involve the gas of photons surrounding the star acquiring so great entropy that the star, by emitting photons via nuclear reactions, would no longer be raising the entropy of the whole system. So, I agree that would happen if there were no gravitons, but SO WHAT? This is not losing time's arrow, this is proceeding according to the entropy arrow until a state of maximum entropy was reached. Perfectly normal. And incidentally in order for this to happen the photon gas surrounding the star would need to reach a temperature exceeding MeV certainly. In the real universe with gravitons I suspect the star would continue burning inside Gold's magic box until essentially every single hydrogen was fused, rendering the whole argument garbage. In 4.2 Schulman says a bunch of stuff about entropy wholy unsupported by any numerical calculation. For example, do black holes have a lot of entropy or a little? You need to do a numerical calculation to find out. He does not. That makes everything he says in this section unsupported garbage. It is easy to do the calculations, in fact I once did as an undergraduate... he just does not. The fact is black holes are the main numerical contributor to the entropy of the universe today, contrary to LSS's false claim they are "minor." So his whole picture of the universe is just wrong. Anyhow, I've now got to the end of LSS's core chapter 4 and I find it basically incoherent. This cannot be taken seriously.
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Warren D Smith