Critique of the Wheeler-DeWitt equation

TL;DR

This paper critiques the Wheeler-DeWitt equation, highlighting its inconsistencies and the problem of time, and proposes a Hamilton-Jacobi approach to construct a dynamical internal clock for consistent quantization.

Contribution

It introduces a Hamilton-Jacobi formalism to construct a dynamical internal clock, enabling consistent canonical quantization with a proper classical limit.

Findings

Constructed a dynamical time using Hamilton-Jacobi formalism

Achieved a consistent canonical quantization method

Resolved issues related to the classical limit and problem of time

Abstract

The Wheeler-DeWitt equation is based on the use of canonical quantization rules that may be inconsistent for constrained dynamical systems, such as minisuperspaces subject to Einstein's equations. The resulting quantum dynamics has no classical limit and it suffers from the infamous ``problem of time.'' In this article, it is shown how a dynamical time (an internal clock) can be constructed by means of a Hamilton-Jacobi formalism, and then used for a consistent canonical quantization, with the correct classical limit.