Exact uncertainty approach in quantum mechanics and quantum gravity

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.

arXiv commentLatex, 14 pages; plenary talk presented at the 4th Australasian Conference on General Relativity and Gravitation (Melbourne, January 7-9, 2004); Proceedings to appear in GRG

References in corpus (6)

• Schrodinger equation from an exact uncertainty principle
• Exact uncertainty relations: physical significance
• Operator ordering and consistency of the wavefunction of the Universe
• Bosonic field equations from an exact uncertainty principle
• Quantum mechanics from a Heisenberg-type equality
• Superselection from canonical constraints

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