Recently, there has been a lot of talk in the media about the "Big Rip". It most certainly resulted from the paper by Marcelo M. Disconzi and Thomas W. Kephart where they have figured out a mathematical system that allows the state parameter of the vacuum energy to drop below -1. Obviously this means the big rip is a possibility (perhaps a certainty?) and they have calculated the time frame to be 22 billion years. My question is what happens to the Poincaré recurrence theorem in a big rip universe? Is it still a possibility? And if yes then does the big rip lead us back to the classic Boltzmann brain situation?

  • $\begingroup$ The Poincare recurrence theorem doesn't have much meaning in classical mechanics, either, and it gets completely eliminated by quantum mechanics. For one thing it requires a constant phase space and for perfect recurrence that space would have to be both finite dimensional and discrete (classical mechanics doesn't provide that). In quantum mechanics the outcome of a future measurement is uncertain, even if the phase space is countable and has a discrete spectrum... which means that the future trajectory has a much larger number of choices than the past. $\endgroup$ – CuriousOne Jul 3 '15 at 15:15
  • $\begingroup$ Sorry, I am unable to understand how the existence of a set of states impacts Poincare recurrence. Maybe you could explain a bit. Also, have a look here physics.stackexchange.com/q/94122 $\endgroup$ – Gibtardo Jul 3 '15 at 15:38
  • $\begingroup$ Poincare recurrence depends on the topology of the phase space. It does, for instance, not occur at all in an open phase spaces, i.e. it wouldn't happen in the 19th century version of an infinite classical universe. Imagine a ball on a hill surrounded by an infinite flat plane. The ball rolls down the hill... and keeps rolling forever. No recurrence is possible in this trivial mechanical example. $\endgroup$ – CuriousOne Jul 3 '15 at 15:45
  • $\begingroup$ That I agree with. I understand that it requires constant phase space and is at odds with classical mechanics. But I don't understand the quantum mechanics issue with it. Anyway why would we even consider classical mechanics here? $\endgroup$ – Gibtardo Jul 3 '15 at 15:55
  • $\begingroup$ The Poincare recurrence theorem is a classical result. Quantum mechanics, on the other hand, clearly states that one can't predict the future outcome of measurements, so even if the entire universe could recreate the physicist and his measurement device, the next measurement would be just as much a coin toss as the one in the universe before. Nature does not know any more than the observer what the next macroscopic state will be. This leaves every possible future (within conservation laws, if they happen to be exact) completely open, even to nature. To me that's not recurrence. $\endgroup$ – CuriousOne Jul 3 '15 at 16:02

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