Norman Samish wrote:
> Brent: ". . . It seems to me that an information theoretic analysis
> should be able to place a lower bound on how small a probability can be
> and not be zero."
> Norman: Doesn't a lower limit on probability repudiate the notion of
> Tegmark, Vilenkin, et al, that there are necessarily duplicate worlds to
> ours, if only we go out far enough?
> Brent: I don't see why these questions are related. There are only
> *necessarily* duplicate worlds if there is an infinity of worlds of a
> higher order than the information content of a world.
> Norman: I don't understand what "higher order than the information
> content of a world" means.
I mean greater cardinality, as the real numbers are of greater cardinality than
the integers. I actually don't know if this is a theorem, but if there are
countably many universes and spacetime is a continuum, then the infinity of
universes could just be distinguished by a single real parameter of spacetime
> Norman: If you repudiate duplicate worlds, do you also repudiate
> infinite space?
> Brent: Space could be infinite without there being duplicate worlds.
> "Repudiate" is too strong a word. I doubt they are relevant.
> Norman: I asked that because my understanding is that "In infinite time
> and space, whatever can happen must happen, not only once but an
> infinite number of times." Do you disagree?
> Brent: If one can originate, then any number can. But I don't see that
> such an infinity has any implications.
> Norman: To me, an initial infinity of high-energy false vacuum, without
> an origin, is not logical.
I don't think the theory says anything about the false vacua being "initial".
In Guth's form of the theory they are eternal, i.e. continually being created
a branching process.
If it's not logical, then you should be able to infer a contradiction from its
assumption. But I think you put too much faith in logic. ISTM that any theory
that gives a natural law account of the origin of the universe will imply that
there are arbitrarily many, because what is to prevent the process that
originated this universe from happening again? It's implicit in natural laws
that they apply at all times and places.
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