Time’s Arrow in a Finite Universe

Martin Tamm^*

Department of Mathematics, University of Stockholm, Stockholm, Sweden.

DOI: 10.4236/ijaa.2015.52010                

Abstract

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.

Keywords

Multiverse, Time’s Arrow, Cosmology, Entropy

Conflicts of Interest

The authors declare no conflicts of interest.

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