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Cited by 59Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

Proposal for solving the ‘‘problem of time’’ in canonical quantum gravity

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Wald, Robert M.·1993·Physical Review D
DOI 10.1103/physrevd.48.r2377
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Abstract

The ``problem of time'' in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states, and local observables on this Hilbert space, for a theory in which the spacetime metric is treated as a quantum field, so no classical metrical or causal structure is present on spacetime. We describe an approach, much in the spirit of ideas proposed by Misner, Kucha\ifmmode \check{r}\else \v{r}\fi{}, and others, to defining states and local observables in quantum gravity which exploits the analogy between the Hamiltonian formulation of general relativity and that of a relativistic particle. In the case of minisuperspace models, a concrete theory is obtained which appears to be mathematically and physically viable, although it contains some radical features with regard to the presence of an ``arrow of time.'' The viability of this approach in the case of infinitely many degrees of freedom rests on a number of fairly well-defined issues, which, however, remain unresolved. As a by-product of our analysis, the theory of a relativistic particle in curved spacetime is developed.

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  • Procedures based on a Klein-Gordon type inner product instead describe the universe as expanding forever.

    “procedures based on a Klein-Gordon type inner product instead describe the universe as expanding 'forever' [4].”

    From Quantum observables and recollapsing dynamics (1995) · cites this paper as [4]

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Research works printed but not linked: 3

  1. [3][3] K. Kuchar, in Proceedings of the 4th Canadian Conference on Relativity and Relativistic Astrophysics ed. by G. Kunstatter, D. Vincent, and J. Williams, (World Scientific, Singapore, 1992). -
  2. [8][8] A. Ashtekar and A. Magnon, Proc. Roy. Soc. Lond. A346 , 375 (1975). B.S. Kay, Commun. Math. Phys. 62 , 55 (1978). -
  3. [18][18] The main issues involved in (1) and (5) are closely related to the issue of isolating the 'true dynamical degrees of freedom' of the classical gravitational field. If a suitable 'gauge fixing' and 'deparametrization' of classical general relativity could be accomplished, then it should be possible to resolve these issues in the manner described in A.O. Barvinsky, Phys. Rep. (in press). -

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Authors
Wald, R. M.
Affiliations
University of Chicago (US)
Corresponding author
Wald, Robert M.
ORCID
Wald, Robert M.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1993-09-15
Volume
48
Issue
6
Pages
R2377-R2381
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.48.r2377
OpenAlex
W2081097082
Cited by
59
References
15
Citations by year
2026: 1 · 2025: 5 · 2024: 1 · 2023: 3 · 2022: 4 · 2020: 2 · 2017: 3 · 2016: 2 · 2014: 1 · 2012: 5
FWCI
3.67
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
problem of time, canonical quantum gravity, Hilbert space structure, local observables, minisuperspace model, arrow of time, Hamiltonian formulation of general relativity, quantum spacetime

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