Time and the interpretation of canonical quantum gravity

Journal Article · Sun Oct 15 00:00:00 EDT 1989 · Physical Review (Section) D: Particles and Fields; (USA)

DOI:https://doi.org/10.1103/PhysRevD.40.2598· OSTI ID:5356514

Unruh, W G ^[1]; Wald, R M ^[2]

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1. Cosmology Program, Canadian Institute for Advanced Research, Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada V6T 2A6 (CA) Institute for Theoretical Physics, University of California, Santa Barbara, California 93106
2. Enrico Fermi Institute and Department of Physics, 5640 S. Ellis Avenue, University of Chicago, Chicago, Illinois 60637

The unsatisfactory status of the interpretation of the wave function of the Universe in canonical quantum gravity is reviewed. The naive interpretation'' obtained by straightforwardly applying the standard interpretive rules to the canonical quantization of general relativity is manifestly unacceptable; the WKB interpretation'' has only a limited domain of applicability; and the conditional probability interpretation'' requires one to pick out a preferred time variable'' (or preferred class of such variables) from among the dynamical variables. Evidence against the possibility of using a dynamical variable to play the role of time'' in the conditional probability interpretation is provided by the fact (proven here) that in ordinary Schroedinger quantum mechanics for a system with a Hamiltonian bounded from below, no dynamical variable can correlate monotonically with the Schroedinger time parameter {ital t}, and thus the role of {ital t} in the interpretation of Schroedinger quantum mechanics cannot be replaced by that of a dynamical variable. We also argue that the interpretive problems of quantum gravity are not alleviated by the incorporation of observers into the theory. Faced with these difficulties, we seek a formulation of canonical quantum gravity in which an appropriate nondynamical time parameter is present. By analogy with a parametrized form of ordinary Schroedinger quantum mechanics, we make a proposal for such a formulation. A specific proposal considered in detail yields a theory which corresponds at the classical level to general relativity with an arbitrary, unspecified cosmological constant. In minisuperspace models, this proposal yields a quantum theory with satisfactory interpretive properties, although it is unlikely that this theory will admit sufficiently many observables for general spacetimes.

• OSTI ID: 5356514
• Journal Information: Physical Review (Section) D: Particles and Fields; (USA), Vol. 40:8; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM GRAVITY
UNIVERSE
WAVE FUNCTIONS
COSMOLOGICAL MODELS
GENERAL RELATIVITY THEORY
HAMILTONIANS
PHASE SPACE
PROBABILITY
QUANTIZATION
QUANTUM MECHANICS
RENORMALIZATION
SPACE-TIME
VECTOR FIELDS
WKB APPROXIMATION
FIELD THEORIES
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SPACE
640106* - Astrophysics & Cosmology- Cosmology
657003 - Theoretical & Mathematical Physics- Relativity & Gravitation