Relational Particle Models. II. Use as toy models for quantum geometrodynamics

TL;DR

This paper uses relational particle models as simplified analogues to explore the Problem of Time in quantum geometrodynamics, analyzing their geometry, quantization, and emergent time concepts.

Contribution

It introduces relational particle models as toy models for quantum gravity, resolving the thin sandwich problem and demonstrating internal time within these models.

Findings

Resolved the thin sandwich analogue in the models

Identified an internal time in scale-invariant models

Studied semiclassical and records approaches for emergent time

Abstract

Relational particle models are employed as toy models for the study of the Problem of Time in quantum geometrodynamics. These models' analogue of the thin sandwich is resolved. It is argued that the relative configuration space and shape space of these models are close analogues from various perspectives of superspace and conformal superspace respectively. The geometry of these spaces and quantization thereupon is presented. A quantity that is frozen in the scale invariant relational particle model is demonstrated to be an internal time in a certain portion of the relational particle reformulation of Newtonian mechanics. The semiclassical approach for these models is studied as an emergent time resolution for these models, as are consistent records approaches.