Exact uncertainty approach in quantum mechanics and quantum gravity

TL;DR

This paper extends the exact uncertainty approach from quantum mechanics to quantum gravity, deriving the Wheeler-DeWitt equation without assuming traditional quantum structures, thus clarifying foundational aspects.

Contribution

It generalizes the exact uncertainty method to gravitational fields, deriving quantum gravity equations without relying on wavefunctions or operator formalism.

Findings

Derives Wheeler-DeWitt equation from classical ensembles with nonclassical fluctuations.

Provides a transparent foundation for quantum gravity without traditional quantum assumptions.

Achieves unique operator ordering in quantum gravity equations.

Abstract

The assumption that an ensemble of classical particles is subject to nonclassical momentum fluctuations, with the fluctuation uncertainty fully determined by the position uncertainty, has been shown to lead from the classical equations of motion to the Schroedinger equation. This 'exact uncertainty' approach may be generalised to ensembles of gravitational fields, where nonclassical fluctuations are added to the field momentum densities, of a magnitude determined by the uncertainty in the metric tensor components. In this way one obtains the Wheeler-DeWitt equation of quantum gravity, with the added bonus of a uniquely specified operator ordering. No a priori assumptions are required concerning the existence of wavefunctions, Hilbert spaces, Planck's constant, linear operators, etc. Thus this approach has greater transparency than the usual canonical approach, particularly in regard to the connections between quantum and classical ensembles. Conceptual foundations and advantages are emphasised.