Time in Quantum Geometrodynamics

TL;DR

This paper proposes a new quantization method in quantum geometrodynamics that addresses the problem of time by focusing on true dynamic variables and allowing off-shell states, leading to a unified emergence of time and covariance.

Contribution

It introduces a quantization procedure that separates the constraints from the dynamics, enabling a consistent treatment of time in quantum gravity.

Findings

Addresses the problem of time in quantum gravity

Allows off-shell states in the quantum theory

Provides a unified view of time and covariance

Abstract

We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general covariance symmetries. The resulting theory, unlike the standard approach, takes into account the states that are off shell with respect to the constraints, and thus avoids the problems of time. In this approach, quantum geometrodynamics, general covariance, and the interpretation of time emerge together as parts of the solution of the total problem of geometrodynamic evolution.