General Relativity, Time and Determinism

James Isenberg

Published 2016-10-20Version 1

Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational phenomena, both at the astrophysical and the cosmological levels. The collection of spacetime solutions of Einstein's equations which have been effectively used for modeling the physical universe is a very small subset of the full set of solutions. Among this larger set, there are many spacetimes in which strange phenomena related to time are present: There are solutions containing regions in which determinism and the predictability of experimental outcomes breaks down (the Taub-NUT spacetimes), and there others in which the breakdown of determinism occurs everywhere (the G\"odel universe). Should the existence of these strange solutions lead us to question the usefulness of Einstein's theory in modeling physical phenomena? Should it instead lead us to seriously search for strange time phenomena in physics? Or should we simply treat these solutions as anomalous (if embarrassing) distractions which we can ignore? In this essay, after introducing some basic ideas of special and general relativity and discussing what it means for a spacetime to be a solution of Einstein's equations, we explore the use of spacetime solutions for modeling astrophysical events and cosmology. We then examine some of the spacetime solutions in which determinism and causal relationships break down, we relate such phenomena to Penrose's "Strong Cosmic Censorship Conjecture", and finally we discuss the questions noted above.