Are the notions of past, present and future compatible with the General Theory of Relativity?

TL;DR

This paper examines the compatibility of A- and B-theories of time with General Relativity, concluding that A-theory notions of past, present, and future are more fundamental and compatible with relativistic spacetimes.

Contribution

It formalizes A- and B-theories within General Relativity and demonstrates that A-theory aligns better with the structure of relativistic spacetimes, especially in time-orientable cases.

Findings

A-theory notions are more fundamental in relativistic spacetimes.

B-theory is incompatible with certain structures in globally hyperbolic spacetimes.

GR favors A-theory and the concepts of past, present, and future.

Abstract

The notions of time and causality are revisited, as well as the A- and B-theory of time, in order to determine which theory of time is most compatible with relativistic spacetimes. By considering orientable spacetimes and defining a time-orientation, we formalize the concepts of a time-series in relativistic spacetimes; A-theory and B-theory are given mathematical descriptions within the formalism of General Relativity. As a result, in time-orientable spacetimes, the notions of events being in the future and in the past, which are notions of A-theory, are found to be more fundamental than the notions of events being earlier than or later than other events, which are notions of B-theory. Furthermore, we find that B-theory notions are incompatible with some structures encountered in globally hyperbolic spacetimes, namely past and future inextendible curves. Hence, GR is favorable to A-theory and the notions of past, present and future.