A la recherche du temps perdu....in quantum gravity

Abstract

Causal set quantum gravity is based on the marriage between the concept of causality as an organising principle more basic even than space or time and fundamental atomicity. Causal sets suggest novel possibilities for "dynamical laws" in which spacetime grows by the accumulation of new spacetime atoms, potentially realising within physics C.D. Broad's concept of a growing block universe
in which the past is real and the future is not. To do justice to relativity and general covariance, the atoms must accumulate in a partial order, exactly the order that the atoms have physically amongst themselves. That this is possible is demonstrated by the Rideout-Sorkin Classical Stochastic Growth models. This proof of concept -- of the compatibility of relativity and ``becoming'' -- is, however, classical and is challenged by the global character of the physical world within a path integral framework for quantum theory. Out of the struggle to reconcile the global and local natures of the physical world may arise a quantal dynamics for causal sets.