Geodesics as Equations of Motion

Abstract

The empirical description of the evolution of a physical system is the account of observed changes of state of the system in time, the measure of time being that of the Systeme International. To describe the Sun-Mercury system Einstein proposed a model based on the assumption that the evolution of the system, i.e. its relative space-time trajectory describes a geodesic on space-time endowed with the Schwartzschild metric. The evolution parameter of a geodesic is, however, an affine parameter or equivalently the proper time. What this could mean is the subject of this paper.