A de Broglie-Bohm Model of Pure Shape Dynamics: $N$-body system

TL;DR

This paper develops a de Broglie-Bohm model for N-body systems within Pure Shape Dynamics, analyzing the shape space dynamics and numerically exploring the 3-body case to understand complexity and time's arrow.

Contribution

It introduces a novel de Broglie-Bohm model for N-body systems in Pure Shape Dynamics and provides numerical analysis of the 3-body case.

Findings

Numerical simulations show attractor-driven complexity behavior.

The shape space dynamics align with classical complexity patterns.

Evidence supports the link between complexity and the arrow of time.

Abstract

We provide the construction of a de Broglie-Bohm model of the $N$-body system within the framework of Pure Shape Dynamics. The equation of state of the curve in shape space is worked out, with the instantaneous shape being guided by a wave function. In order to get a better understanding of the dynamical system, we also give some numerical analysis of the 3-body case. Remarkably enough, our simulations typically show the attractor-driven behaviour of complexity, well known in the classical case, thereby providing further evidence for the claim that the arrow of complexity is the ultimate cause of the experienced arrow of time.