Stathis Papaioannou, <[EMAIL PROTECTED]>, writes:
> Let me add a postscript to this quicky: does the multiverse include perfect 
> duplications, or only arbitrarily close to perfect - and does it make a 
> difference?

It depends on what you mean by the multiverse, and on what the laws of
physics are locally.  I just happened to be reading a paper linked from
Max Tegmark's page which answers the question in the affirmative for the
level 1 and level 2 multiverse(s).  The paper is "Many worlds in one",
by Garriga and Vilenkin, http://arxiv.org/abs/gr-qc/0102010.

Tegmark's level 1 multiverse is our universe when it is taken to be
infinite in size.  There should be duplicates of each finite sized region.
The level 2 multiverse is the larger ensemble predicted by inflation
theory.  It contains an infinite number of level 1 multiverses, each
infinite in size.

The Garriga/Vilenkin paper explains more clearly than anything I had
previously read how we can fit an infinite number of infinite sized level
1 universes into the level 2 universe.  The answer is that inflation
occurs exponentially fast and lasts forever.  In relativity, time and
space are somewhat interchangeable.  From the level 2 perspective, new
space is constantly (and rapidly) being added to each level 1 universe.
Because this goes on forever, the "eventual" size of each level 1
region is infinitely large.  But because of the interchangeability,
when we look at it from the "inside view" of each level 1 universe,
it can be considered to have been born infinitely large.

The other main goal of this paper is to argue that the observable
finite-sized regions of the universe do have exact duplicates elsewhere
in the level 1 and level 2 ensemble.  The duplicates are not merely
approximate, but rather they are exact.  This is based on quantum theory
only allowing a finite amount of information to be present in a region
(the Bekenstein bound).  Therefore our whole observable universe bubble
has only a finite number of bits in it, and so there should be an infinite
number of other bubbles with exactly the same pattern of bits, and these
are exact duplicates.

Another interesting result of this paper concerned "daughter universes".
In some models, it may be possible to trigger the formation of new
inflating regions which would "bud off" from our own space time and
produce their own infinite-sized level 2 universes.  The authors of this
paper had proposed in an earlier one that this could be a mechanism for
civilizations to survive heat death, that they could create daughter
universes and somehow send information into them which could be taken
up and incorporated by civilizations evolving in the daughter universes.

However, in the context of the multiverse, this won't really work,
because any finite number of messages are insignificant in the context
of an infinitely-duplicated multiverse.  Only a finite number of regions
can receive the messages, compared to an infinite number of regions
that either don't receive them, or receive spontaneously-generated fake
messages (like our discussion earlier today of "magical" universes).
Therefore the messages can have only an infinitesimal impact on the
evolution of the daughter universes and cannot be considered a meaningful
form of survival.

Hal Finney

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