Branching in Relativistic Space-Times

Abstract

Abstract The chapter shows how local indeterminism underlying BST combines with relativistic space-times. First it defines particular BST structures in which histories are isomorphic to Minkowski space-times. It further argues that many general relativistic space-times are one-history structures of BST. It introduces the notion of non-Hausdorff differential manifolds and investigates if they can be interpreted modally, as structures of BST with multiple histories. It investigates bifurcating curves in non-Hausdorff manifolds, which are natural representations of alternative evolutions of point-like objects. As the required bifurcating curves are unlikely in General Relativity, whereas there are cases of indeterministic general relativistic space-times, the chapter concludes that General Relativity is globally indeterministic, but locally deterministic.