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.
Highlights
The riddle of Time’s Arrow is an outstanding problem in modern physics
The riddle of time consists in the observation that this asymmetry disappears when we turn to the microlevel: here, the all processes seem to be possible in both directions of time
It should always be remembered that it is developed in classical thermodynamics, and is best understood in stationary or quasi-stationary situations. This is very far from what we meet in cosmology, where some of our ordinary physical concepts get a new twist
Summary
The riddle of Time’s Arrow is an outstanding problem in modern physics. How does it come that we can remember yesterday but not tomorrow? Why do we all grow older but never grow younger? We all know that what is possible in one direction of time may be quite impossible in the other. This is very far from what we meet in cosmology, where some of our ordinary physical concepts get a new twist Still, another specific problem with Time’s Arrow seems to be that our very human perspective tends to make us formulate the questions in the wrong way, and that many of our conclusions may already be unconsciously built into our assumptions (see Price [2]). This is related to the old discussion originating from Gold’s famous paper [3] and continued by Hawking, Page, LaFlamme and others (see [4] [5]), but from a rather different perspective. Some of the ideas in this paper have been discussed earlier in a more preliminary and technical form in [6], where some related ideas can be found
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