Emergent Semiclassical Time in Quantum Gravity. Full Geometrodynamics and Minisuperspace Examples

TL;DR

This paper explores emergent semiclassical time in quantum gravity, comparing geometrodynamics and minisuperspace models, and connects various notions of time in cosmology and gravitational theories.

Contribution

It extends semiclassical treatment to geometrodynamics, analyzes differences with linear constraints, and compares emergent time schemes with existing approaches.

Findings

Quadratic constraints analogy between geometrodynamics and minisuperspace

Differences in linear constraints impact time emergence

Connections established between Newtonian, Machian, WKB, and cosmic times

Abstract

I apply the preceding paper's semiclassical treatment to geometrodynamics. The analogy between the two papers is quite useful at the level of the quadratic constraints, while I document the differences between the two due to the underlying differences in their linear constraints. I provide a specific minisuperspace example for my emergent semiclassical time scheme and compare it with the hidden York time scheme. Overall, interesting connections are shown between Newtonian, Leibniz--Mach--Barbour, WKB and cosmic times, while the Euler and York hidden dilational times are argued to be somewhat different from these.