[math-fun] Does entropy increase because the universe is expanding?
Read L.S. Schulman's book
--ok. I have not read Schulman's "Time's Arrows and Quantum Measurement" but I will try later. I had read some edition of "The Physical Basis of the Direction of Time" by HD and/or DH Zeh. There are many many books on those subjects, most of which I have not even seen, some of which are quite good, such as Roland Omnes: "The interpretation of Quantum Mechanics," and some of which are appallingly bad, such as Roger Penrose: "Emperor's new mind." There also was a good article on decoherence by W.Zurek in Physics Today 44,10 (Oct 1991). But in all the papers & books I saw, I never saw anything that convincingly resolved the issues associated with the quantum-classical transition, entropy, time-direction, etc using only the "standard model." If they tried, at some point they all had to rely on intuitive hopes/dreams "reasoning" which may or may not be valid, it became basically religion. Right now I'm not sure why, but the Everett school seems to be the most fashionable. Here's a random article about that from the web: http://plato.stanford.edu/entries/qm-manyworlds/ and if you think this solves everything rigorously and isn't religious hogwash, good luck to you. Now re
In general relativity the direction of time is not arbitrary.? The future is the direction in which black holes form.?
--I agree.
To continue the saga of this chemist in the contracting universe who observes the gas filling both vessels and the universe expanding, does he observe black holes or white holes?
--black.
In that contracting model, t is just a coordinate parameter. I collapses to a big crunch which is just a time-reversed big bang. Physical time has to correspond, at least locally, to increasing entropy so that one can form memories, etc. I think that for life to have evolved it has to have been in an expanding universe for a long time.
--the big crunch is a time-reverse big bang if all the microscopic details are ignored and we have a maximally symmetric universe filled with mythical uniform-density continuum-fluid matter & radiation, and in that model there is no such thing as entropy and indeed there is no statistical mechanics since no particles. --However in the real universe with things like stars, galaxies, etc, entropy exists and continues to increase with time including during & after turnaround and shrinkage toward a crunch. There is indeed a theorem (or pretty close to a theorem) in GR called "generalized second law" which includes both normal and black-hole entropy and says the sum cannot decrease. I think this stuff was treated in the excellent book by Hawking & Ellis "large scale structure" (but you have to know GR to read said book). --life certainly had to have been in expanding universe for long time, otherwise we'd be in unexpanded universe, which would not be friendly to life. However, if turnaround occurred, life presumably would continue until things got too hot, and life could certainly evolve on some planet where the first life there happened after the turnaround.
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Warren D Smith