The Relativistic Phase of the Causal Theory of Time: The Axiomatic Systems of Robb and Carnap

Abstract

The year 1905 was a decisive one for the causal theory of time. Until then it was only a metaphysical speculation or an epistemological interpretation; in 1905 it directly rejoined science in its immediate consequences. The Special Theory of Relativity demonstrated that two events which appear to be simultaneous in one system of reference are, in general, not simultaneous in another. If one event precedes another in one system, it could very well follow it in another. There are many events which are simultaneous in every admissible system, but this invariant simultaneity presupposes the spatiotemporal coincidence of two events and cannot exist for events not meeting this condition. Nevertheless, there is an important difference between simultaneity and succession (of widely separated events): simultaneity is always relative, but there is, in a certain sense, an absolute succession; an event which precedes another in a given system of reference, and is its cause, precedes it in every admissible system. And vice versa: if an event precedes another in every admissible system, the causal relation between them becomes possible. Hence the invariant succession relation coincides with the causal relation. This consequence of relativity seems to have determined the entire recent phase of the causal theory of time.