Role of time in the sum-over-histories framework for gravity

Abstract

I sketch a self-contained framework for quantum mechanics based on its path-integral or “sum-over-histories” formulation. The framework is very close to that for classical stochastic processes like Brownian motion, and its interpretation requires neither “measurement” nor “state-vector” as a basic notion. The rules for forming probabilities are nonclassical in two ways: they use complex amplitudes, and they (apparently unavoidably) require one to truncate the histories at a “collapse time,” which can be chosen arbitrarily far into the future. Adapting this framework to gravity yields a formulation of quantum gravity with a fully “spacetime” character, thereby overcoming the “frozen nature” of the canonical formalism. Within the proposed adaptation, the value of the “collapse time” is identified with total “elapsed” spacetime four-volume. Interestingly, this turns the cosmological constant into an essentially classical constant of integration, removing the need for microscopic “fine tuning” to obtain an experimentally viable value for it. Some implications of the “V = T” rule for quantum cosmology are also discussed.