Lie Theory Suffices to Resolve the Local Classical Problem of Time

Abstract

The problem of time - a foundational question in quantum gravity - is due to conceptual gaps between GR and physics' other observationally-confirmed theories. Its multiple facets originated with Wheeler-DeWitt-Dirac over 50~years ago. They were subsequently classified by Kucha\v{r}-Isham, who argued that most of the problem is facet interferences and posed the question of how to order the facets. We show the local classical level facets are two copies of Lie theory with a Wheelerian two-way route therebetween. This solves facet ordering and facet interference. Closure by a Lie algorithm generalization of Dirac's algorithm is central.