Arrow(s) of Time without a Past Hypothesis

TL;DR

This paper explores models explaining the arrow of time without assuming a special low-entropy initial state, comparing approaches by Carroll and others, and proposing a new entropy definition for gravitational systems.

Contribution

It analyzes Carroll's model for a typical arrow of time, introduces a Boltzmann entropy for gravitational systems, and clarifies differences between relational and absolute entropy concepts.

Findings

Carroll's model can predict and retrodict without a Past Hypothesis.

A new Boltzmann entropy for classical gravity systems is proposed.

Relational shape complexity differs from absolute spacetime entropy.

Abstract

The paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a Past Hypothesis, i.e., the assumption of a special (low-entropy) initial state of the universe. After discussing the role of the Past Hypothesis and the controversy about its status, we explain why Carroll's model - which establishes an arrow of time as typical - can ground sensible predictions and retrodictions without assuming something akin to a Past Hypothesis. We then propose a definition of a Boltzmann entropy for a classical $N$-particle system with gravity, suggesting that a Newtonian gravitating universe might provide a relevant example of Carroll's entropy model. This invites comparison with the work of Barbour, Koslowski, and Mercati that identifies typical arrows of time in a relational formulation of classical gravity on shape space. We clarify the difference between this gravitational arrow in terms of shape complexity and the entropic arrow in absolute spacetime and work out the key advantages of the relationalist theory. We end by pointing out why the entropy concept relies on absolute scales and is thus not relational.