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