A Gravitational Origin of the Arrows of Time

TL;DR

This paper proposes that the arrows of time originate from the asymmetry of the universe's true degrees of freedom, demonstrated through the Newtonian N-body problem and extended to certain models in General Relativity, offering an alternative to the past hypothesis.

Contribution

It introduces a gravitational origin for the arrows of time based on shape space asymmetry, with proofs in Newtonian and certain relativistic models, challenging the traditional low-entropy initial state explanation.

Findings

Solutions divide into two halves with irreversible complexity growth.

Complexity fluctuations create structures storing dynamical information.

Arrows of complexity and information are proven in Newtonian and Bianchi IX models.

Abstract

The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the `past hypothesis': the Universe had a very special low-entropy initial state. We present the first evidence for an alternative conjecture: the arrows exist in all solutions of the gravitational law that governs the Universe and arise because the space of its true degrees of freedom (shape space) is asymmetric. We prove our conjecture for arrows of complexity and information in the Newtonian N-body problem. Except for a set of measure zero, all of its solutions for non-negative energy divide at a uniquely defined point into two halves. In each a well-defined measure of complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows. Recognition of the division is a key novelty of our approach. Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of one past and one future. The `paradox' of a time-symmetric law that leads to observationally irreversible behaviour is fully resolved. General Relativity shares enough architectonic structure with the N-body problem for us to prove the existence of analogous complexity arrows in the vacuum Bianchi IX model. In the absence of non-trivial solutions with matter we cannot prove that arrows of dynamical information will arise in GR, though they have in our Universe. Finally, we indicate how the other arrows of time could arise.