Stathis Papaioannou writes:
> On 18 July 2004 Hal Finney wrote:
> > We had some discussion a while back about a paper which proposed some
> > similar ideas, http://xxx.lanl.gov/abs/hep-th/0208013, Disturbing
> > implications of a cosmological constant.  If you want to look in the
> > archives, the thread was called "Doomsday-like argument in cosmology"
> > and was in August 2002...
>
> Yes, I know there are all sorts of twists on the standard models in 
> cosmology out there, most of them controversial. But what I am looking at is 
> the "worst case scenario" for many world theories: no "Big Crunch", no 
> Tipler Omega Point, no daughter universes from black holes, no God, just a 
> finite universe expanding and cooling forever.

Right, that's the same thing as that paper assumed.  And it should be noted
that this is basically the standard model of cosmology at present.

> In a zillion years from now, 
> the universe will be a zillion light years across, almost all the "stable" 
> matter will have decayed, and the temperature will be extremely close to 
> absolute zero. My understanding is that even in this bleak scenario, 
> standard, non-controversial physics does not exclude the possibility that 
> new matter/energy will arise out of the vacuum. In the MWI of QM, this 
> possibility MUST be realised in some parallel universe, albeit one of very 
> low measure if the new matter is something like the event "P" I defined in 
> my original post, an exact copy of our solar system complete with conscious 
> inhabitants. In a non-MW interpretation of QM, P is possible but 
> fantastically unlikely. If the probability of P occuring in a unit time 
> period remains constant, or increases, with time, then - remember, we still 
> have eternity ahead even though a zillion years have already passed - P will 
> certainly occur. If this probability falls with time, P may or may not 
> occur, depending on the equation. Can anyone write down the equation showing 
> how Pr(P) evolves as a function of time in the above situation?

The paper did in fact deal implicitly with this question.  As I wrote, in
effect they seemed to take as given that the probability was constant.
As you have noted, this implies that all possible universes would
appear eventually.  This is what produced the "disturbing implications"
of their title.

Hal

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