Critique of the Wheeler-DeWitt equation

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.

13 pages LaTeX, one figure. It is stressed that the critique is not general, but only aimed at the use of the WDW equation for minisuperspaces

References in corpus (4)

• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Is General Relativity an 'Already Parametrized' Field Theory?
• A SCHRÖdinger Equation for Mini Universes
• Ehrenfest's Principle and the Problem of Time in Quantum Gravity

Cited by in corpus (7)

• Emergent discrete time and quantization: relativistic particle with extradimensions
• Stochastic Emergent Quantum Gravity
• Unitary and non-unitary evolution in quantum cosmology
• Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology
• We have time because we shall never know
• Space of events and the time observable
• Strings, Topological Change and Dark Matter