Tim May writes:
> OK, let us assume for the sake of argument that we should be
> overwhelmingly likely to be living in one of these "time-reversed
> cycles" (which I distinguish from "bounces" back to a Big Bang state,
> the more common view of cycles).
> By the same Bayesian reasoning, it is overwhelmingly likely that any
> observer would find himself in a TRC in which other parts of the
> universe eventually visible to him (with telescopes) are "incompletely
> reversed." Let me give a scenario to make the point clearer.
> [Example elided]
Yes, that's a good point, it seems completely correct. It is consistent
with the basic argument in the paper, a better example than the one they
gave about the microwave background being too hot.
These kinds of considerations were summed up by Wei Dai in his original
> This is a variant on the Doomsday argument. The core argument of the paper
> is this:
> If we live in a world with a true cosmological constant, then the
> observers whose observable universe is macroscopically indistinguishable
> from ours are a tiny fraction of all observers. Therefore "the only
> reasonable conclusion is that we do not live in a world with a true
> cosmological constant."
When Wei writes about universes "macroscopically indistinguishable from
ours", I believe he means ones that don't suffer from the kinds of flaws
that Tim describes. Clearly the vast majority of observers spawned in
time-reversed universes would have the smallest possible time-reversed
region sufficient to generate life, and the rest of the universe would
still be chaotic. The fact that we observe a huge, complete universe,
rich in structure, which appears to have a consistent history, means that
we are very special and unusual in a universe dominated by recurrences.
I think I see Wei's point that this is similar in flavor to the Doomsday
argument. The paper's cosmological theory predicts that the vast majority
of observers would see a universe more like Tim describes, and not what
we see. Therefore, either we are very special, or the theory is wrong.
In the Doomsday argument, the theory that life will go on far into the
future predicts that the vast majority of observers would see a history
very different from what we see. Again we can conclude that either we
are very special, or the theory is wrong.
I haven't yet tried to understand Wei's use of the Self Indication Axiom
and how there can be a universe model which is supported by the Doomsday
type argument but not contradicted by the SIA.