Events in Space and Time

Abstract

Our understanding of physical space has its historical origin in the system of geometry developed by Euclid. This was based on a collection of axioms and postulates, most of them rather directly related to our primitive perception of physical space. On the basis of the axioms and postulates, a rich variety of theorems could be deduced which could then be confirmed, at least in some approximation, by direct measurement. Only one of the postulates, Euclid’s fifth postulate, was by no means obvious in its application to physical space. This stated that, given a straight line in a plane, one and only one straight line could be found in the same plane which passed through some point not on the line but did not meet the given line at any finite distance, i.e., was parallel to the given line. The fifth postulate was needed to prove Pythagoras’ theorem, and all the relations based on it connecting the distances between points in two or three dimensions.