On causal dynamics without metrisation: Part II

Abstract

An interpretation of an ordering relation as an operator is constructed by appeal to the notion of homotopy. A metric-free definition of a causal ordering is given, after carefully investigating, by means of the notion of ordered sets, what is crucial to the notion of causality. A metric-free condition is derived that a causal ordering operator must satisfy, and a concrete realisation is found to exist that embodies the paraphernalia of Minkowski space with Zeeman's fine topology. Moreover, it is seen that a coordinate space used to give a cartography to causally related events must have ‘at least’ a hyperbolic metric.