On Fri, Aug 16, 2002 at 12:26:10AM +0200, Saibal Mitra wrote:
> I haven't read the paper in detail, so I could be wrong. Consider the two
> alternatives:
>
> 1) true cosmological constant
>
> 2) no true cosmological constant
>
> We also assume SIA. Is it the case that there are much fewer observers in
> case of 2) than in case of 1) ? I haven't seen such a statement in the paper
> (but again, I could have missed it).

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You're right, we need to look at the alternative hypothesis. But there's
not just one alternative, there are several.
1) True cosmological constant, therefore heat death and endless Poincare
recurrences.
2a) The universe ends soon.
2b) The universe runs for a while longer, then gets reset to a low entropy
state and starts over. This happens in an endless cycle.
2c) The universe never ends, and life become ever more complex and
intelligent.
2d) No true cosmological constant, but we get heat death and endless
Poincare recurrences for some other reason.
2e) The universe never ends, but the total number of observers is a
relatively small finite number.
I think these exhaust all of the possibilities. A huge problem with SIA is
that 1, 2b, 2c, and 2d all imply an infinite number of observers, which
makes SIA impossible to use. But for sake of argument let's say these
universes do eventually end, and they all have the same (very large)
number of observers. Applying just DA (Doomsday argument) favors 2a, 2b
and 2e. Applying both SIA and DA favors 2b. So I guess you're right,
whether or not you apply the SIA does not affect the the paper's
conclusion that a shift away from 1 is warranted.
This makes me realize that SIA doesn't perfectly counteract the Doomsday
argument. DA makes you shift to 2a, 2b, and 2e. SIA then makes you shift
to 2b, whereas what we really want is to shift back to the original
distribution so we don't have to rule out 2c.