Emergent semiclassical time in quantum gravity: II. Full geometrodynamics and minisuperspace examples

Abstract

I apply the preceding paper's emergent semiclassical time approach to geometrodynamics. The analogy between the two papers is 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 find that the emergent time-dependent wave equation for the universe in general not a time-dependent Schrödinger equation but rather a more general equation containing second time derivatives, and estimate in which regime this becomes significant. 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, Wentzel–Kramers–Brillouin (WKB) and cosmic times, while the Euler and York hidden dilational times are argued to be somewhat different from these.