Time in quantum gravity: An hypothesis

Carlo Rovelli
Phys. Rev. D 43, 442 – Published 15 January 1991
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Abstract

A solution to the issue of time in quantum gravity is proposed. The hypothesis that time is not defined at the fundamental level (at the Planck scale) is considered. A natural extension of canonical Heisenberg-picture quantum mechanics is defined. It is shown that this extension is well defined and can be used to describe the "non-Schrödinger regime," in which a fundamental time variable is not defined. This conclusion rests on a detailed analysis of which quantities are the physical observables of the theory; a main technical result of the paper is the identification of a class of gauge-invariant observables that can describe the (observable) evolution in the absence of a fundamental definition of time. The choice of the scalar product and the interpretation of the wave function are carefully discussed. The physical interpretation of the extreme "no time" quantum gravitational physics is considered.

  • Received 27 September 1990

DOI:https://doi.org/10.1103/PhysRevD.43.442

©1991 American Physical Society

Authors & Affiliations

Carlo Rovelli

  • Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 and Dipartimento di Fisica, Universita' di Trento, Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Italy

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Vol. 43, Iss. 2 — 15 January 1991

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