Time ordering and the Lorentz group

Abstract

A simplified definition of point local clocks and the relationship between an inertial reference frame and a class of such clocks, at rest with respect to each other, are used for an algebraic determination of the geometry of Minkowski's space-time on the set of point events. The group of all automorphisms that preserve the time ordering induced by the set of all equivalent local clocks is shown to be generated by the inhomogeneous orthochronous Lorentz group and dilatations, consistently with a well-known result of E. C. Zeeman. The existence of a universal limit velocity and of an invariant clock cone through any event is among the implications of our proof, thus effectively exploiting a suggestion due to F. Severi.