t -> sin t

Geodesics in this universe (which I refer to as the “Periodic Minkowski universe”), are such that particles oscillate about a fixed position. This leads to recurrence via “Loschmidt’s velocity reversion”, however without the time reversal, i.e., the time parameter continues to increase monotonically. See my paper –

http://arxiv.org/abs/0907.3165
Title: Loschmidt’s paradox, entropy and the topology of spacetime

If one does mixing of two gases experiment, in periodic Minkowski, one will see the gases initially mixing, and then deterministically seperating. And this happens not as a probablistical process, but due to the causal structure of the space time, as encoded in the line element of the periodic Minkowski universe. However, one can still consider probablistic process within this spacetime background – and vacuum fluctuations forming Boltzmann brains. The periodicity constraint would require that any Boltzmann brains created in such a universe, would eventually be destroyed.

The probability of many brains may still be lower than the probability of none, so a low-entropy initial state is still needed. The Big Bang seems to provide it in spades.

-Carl

You can get a universe like ours that way, but you’re overwhelmingly more likely to get just a single galaxy, or a single planet, or even just a single brain — so the statistical-fluctuation idea seems to be ruled out by experiment. (With potentially profound consequences.)

This argument seems incredibly weak to me. Think of it this way: I roll a 10 sided die a hundred times and write down the string of resulting digits. You examine the string of digits and exclaim: “do you know how unlikely it is that you got that exact string? This can’t be a statistical fluctuation”. You can’t look at a situation after the fact and say it couldn’t have happened at random because it’s very unlikely.

The other argument I’ve heard here – that statistical fluctuations would mean that you couldn’t trust memories of the past – seems more powerful, but still strangely unsatisfying. Apparently the reason that can’t be true is that it would be unpleasant to believe that the universe faked all the evidence of our past. Which is a sentiment that I agree with, but it doesn’t say much about whether the universe actually DID fake all the evidence of our past. I guess I’m willing to write that possibility off on practical grounds – there would be no point in doing science at all if it were true – but it’s still sort of disturbing.