Identification of a gravitational arrow of time

TL;DR

This paper demonstrates that a simple, time-symmetric Newtonian N-body system naturally develops an arrow of time through the growth of shape complexity, without requiring special initial conditions.

Contribution

It shows that the Newtonian N-body problem inherently produces a temporal arrow via complexity growth, challenging the need for special initial conditions in defining time's direction.

Findings

Solutions divide into two halves with increasing shape complexity

Structures acting as records are created as complexity grows

Each solution has a single past and two distinct futures

Abstract

It is widely believed that special initial conditions must be imposed on any time-symmetric law if its solutions are to exhibit behavior of any kind that defines an `arrow of time'. We show that this is not so. The simplest non-trivial time-symmetric law that can be used to model a dynamically closed universe is the Newtonian $N$-body problem with vanishing total energy and angular momentum. Because of special properties of this system (likely to be shared by any law of the Universe), its typical solutions all divide at a uniquely defined point into two halves. In each a well-defined measure of shape complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows and act as `records'. 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 the records of one branch and deduce a unique past and future direction from inspection of the available records.