In this
paper, a simple model for a closed multiverse as a finite probability space is
analyzed. For each moment of time on a discrete time-scale, only a finite
number of states are possible and hence each possible universe can be viewed as
a path in a huge but finite graph. By considering very general statistical
assumptions, essentially originating from Boltzmann, we make the set of all such
paths (the multiverse) into a probability space, and argue that under certain
assumptions, the probability for a monotonic behavior of the entropy is
enormously much larger then for a behavior with low entropy at both ends. The
methods used are just very simple combinatorial ones, but the conclusion
suggests that we may live in a multiverse which from a global point of view is
completely time-symmetric in the sense that universes with Time’s Arrow
directed forwards and backwards are equally probable. However, for an observer
confined to just one universe, time will still be asymmetric.
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