Physics
Scientific paper
Jan 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..43..442r&link_type=abstract
Physical Review D (Particles and Fields), Volume 43, Issue 2, 15 January 1991, pp.442-456
Physics
153
Scientific paper
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.
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