Structures of Spacetime

Abstract

Simple geometric properties of spacetime and free particles underlie the theory of relativity just as Euclidean geometry follows from simple properties of points and straight lines. The vacuum, the empty four-dimensional curved spacetime, determines straight lines and light rays. In the absence of gravity, the vacuum is isotropic and homogeneous and does not allow to distinguish rest from uniform motion. Therefore, contrary to Newton’s opinion, the vacuum cannot contain the information about a universal time which could be attributed to events. Whether two different events are simultaneous depends on the observer—just as in Euclidean geometry it depends on a given direction whether two points lie on an orthogonal line.