The arrow of time and a-priori probabilities

TL;DR

This paper investigates whether the observed time asymmetry of entropy increase can be explained by different a-priori probability assignments to past and future events, challenging the assumption of a low-entropy beginning of the universe.

Contribution

It proposes a novel perspective that the arrow of time may arise from asymmetrical a-priori probabilities rather than initial low entropy conditions.

Findings

Highlights the role of probability assignment in the emergence of time asymmetry

Questions the necessity of a low-entropy initial state for the universe

Suggests alternative explanations for the thermodynamic arrow of time

Abstract

The second law of thermodynamics is asymmetric with respect to time as it says that the entropy of the universe must have been lower in the past and will be higher in the future. How this time-asymmetric law arises from the time-symmetric equations of motion has been the subject of extensive discussion in the scientific literature. The currently accepted resolution of the problem is to assume that the universe began in a low entropy state for an unknown reason. But the probability of this happening by chance is exceedingly small, if all microstates are assigned equal a-priori probabilities. In this paper, I explore another possible explanation, which is that our observations of the time-asymmetric increase of entropy could simply be the result of the way we assign a-priori probabilities differently to past and future events.