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Dear Bob (if I may?)
Thanks for your comments.
With regard to your first point, I didn’t mean to put the consistent histories approach in the Everettian camp. I see them as two separate interpretations of the formalism of quantum mechanics. My point is, rather, that many Everettians make use of some of the concepts and formalism from the consistent histories approach.
With regard to the second point, I agree that an anthropic argument for temporal asymmetry is possible in a classical world in which entropy is increasing. Indeed this is the approach that Boltzmann took. His idea was that given enough time we should expect low entropy regions of the universe to form purely through random fluctuation away from equilibrium. We can then employee anthropic reasoning to explain why we find ourselves on the upward entropy slope of one of these low entropy regions. As is well known, however, this anthropic explanation fails: entropy fluctuations down to a minimum equal to the entropy of the world we see around us now are overwhelmingly more likely than entropy fluctuations whose minimum entropy is anything like what we believe to have been the case in the distant past. The anthropic reasoning above, then, leads to the conclusion that it is overwhelmingly likely that the entropy fluctuation in which we exist bottomed out just moments ago, and all the records we appear to have of a lower entropy past are false. This conclusion is not only unwelcome, it is self-undermining since it takes away any justification for believing the theories we used to reach the conclusion.
The general lesson we can take away from this is that when providing an anthropic explanation it is not enough to show that some property X should be expected in some part of the cosmos and then use anthropic reasoning to explain why we find ourselves in such a place. The distribution of X must also be appropriate in some sense. In Boltzmann’s case the problem was that regions of sufficient low entropy were more likely to have false records of a lower entropy past than true. The anthropic explanation I am suggesting in the Everettian case does not appear to have this problem. While I still have trouble getting my head around the meaning of probabilities in EQM, there does not seem to be any suggestion that one set of consistent histories is “more probable” than another.