Dear Bruno and Friends,
It looks like Srednicki and Hartle have been thinking of issues similar to
ours about the notion of a measure. Please see the following paper.
http://arxiv.org/abs/1004.3816
The Xerographic Distribution: Scientific Reasoning in a Large Universe
Authors: Mark Srednicki, James Hartle
(Submitted on 21 Apr 2010)
Abstract: As observers of the universe we are physical systems within it. If
the universe is very large in space and/or time, the probability becomes
significant that the data on which we base predictions is replicated at other
locations in spacetime. Predictions of our future observations therefore
require an assumed probability distribution---the xerographic
distribution---for our location among the possible ones. It is the combination
of basic theory plus the xerographic distribution that can be predictive and
testable by further observations. This is illustrated by examining a toy model
of a classical deterministic universe with a fixed flat metric.
I strongly believe that we are very close to resolving many of the problems
that we have wrestled with.
Onward!
Stephen
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