Characterization of Standard Clocks by Means of Light Rays and Freely Falling Particles

TLDR: In this article, a mathematical characterization of standard clocks (i.e., clocks measuring proper time) is presented, which yields an experimental method to test whether or not a given clock is a standard clock.

Abstract: A mathematical characterization of standard clocks (i.e., clocks measuring proper time) is presented, which yields an experimental method to test whether or not a given clock is a standard clock. The only tools needed are light rays and freely falling particles. For this reason our method fits very well in the framework of the axiomatic approach to space-time theory given by Ehlers, Pirani, and Schild [1], where just light rays and freely falling particles are used as primitive concepts. As the underlying space-time model we use a Weyl manifold (instead of a Lorentz manifold, which is the usual model of general relativity); this generalization is motivated by [1].