Relational Particle Models. I. Reconciliation with standard classical and quantum theory

TL;DR

This paper explores relational particle models as a way to reconcile classical and quantum physics, showing they can model various phenomena and serve as toy models for quantum cosmology, challenging traditional absolute frameworks.

Contribution

It introduces direct relational formulations of classical mechanics and demonstrates how quantized relational models can avoid semiclassical issues, providing new insights into quantum cosmology.

Findings

Relational models can reproduce classical physics phenomena.

Small universe models exhibit spectral gaps and energy interlocking.

Relational quantum models can bypass semiclassicality problems.

Abstract

This paper concerns the absolute versus relative motion debate. The Barbour and Bertotti 1982 work may be viewed as an indirectly set up relational formulation of a portion of Newtonian mechanics. I consider further direct formulations of this and argue that the portion in question -- universes with zero total angular momentum, that are conservative and with kinetic terms that are (homogeneous) quadratic in their velocities -- is capable of accommodating a wide range of classical physics phenomena. Furthermore, as I develop in Paper II, this relational particle model is a useful toy model for canonical general relativity. I consider what happens if one quantizes relational rather than absolute mechanics, indeed whether the latter is misleading. By exploiting Jacobi coordinates, I show how to access many examples of quantized relational particle models and then interpret these from a relational perspective. By these means, previous suggestions of bad semiclassicality for such models can be eluded. I show how small (particle number) universe relational particle model examples display eigenspectrum truncation, gaps, energy interlocking and counterbalanced total angular momentum. These features mean that these small universe models make interesting toy models for some aspects of closed universe quantum cosmology. While, these features do not compromise the recovery of reality as regards the practicalities of experimentation in a large universe such as our own.