Minisuperspace model of Machian Resolution of Problem of Time. I. Isotropic Case

TL;DR

This paper extends a Machian approach to resolving the Problem of Time in quantum cosmology, demonstrating its applicability to a closed isotropic minisuperspace model with scalar matter, and sets the stage for future inhomogeneity analysis.

Contribution

It adapts and applies a Machian resolution framework to a widely studied quantum cosmological model, integrating classical, semiclassical, and histories approaches.

Findings

Machian resolution works for isotropic minisuperspace models

Combines classical, semiclassical, and histories approaches successfully

Provides groundwork for inhomogeneity and structure analysis

Abstract

A local resolution to the Problem of Time that is Machian and was previously demonstrated for various relational mechanics models is here shown to work for a more widely studied quantum cosmological model. Namely, closed isotropic minisuperspace GR with minimally-coupled scalar field matter. This uses work firstly along the lines of Barbour's at the classical level. Secondly, it uses a Machianized version of the Semiclassical Approach to Quantum Cosmology. Finally, it uses a combined Machianized version of a combined Semiclassical Histories Timeless Records scheme along the lines of Halliwell's work. This program's goal is the treatment of inhomogeneous perturbations about the present paper's model, drawing also qualitatively from the relational mechanics examples since these have nontrivial notions of inhomogeneity/structure (clumping) as well as nontrivial linear constraints.