Time and Evolution in Quantum and Classical Cosmology

TL;DR

This paper investigates how to define a meaningful notion of time in quantum cosmology, examining phase space variables, their Poisson brackets, and the implications for classical and quantum evolution.

Contribution

It demonstrates that the Poisson bracket condition for internal time variables is not strictly necessary or sufficient, and discusses switching between different internal times and the Montevideo interpretation.

Findings

Poisson bracket condition for time variables is not always required.

Switching between different internal times is feasible.

The Montevideo interpretation offers insights into quantum cosmology.

Abstract

We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators the classical evolution is reproduced. We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.