Clocks and gravity

Abstract

We consider the assumption that clocks measure proper time-that is, in a gravitational field ideal clocks are governed by the equationds2=g ij dxi dxj-and give some theoretical and experimental constraints on clock measurements. In particular, we find that if we assume that clocks are governed by an equation of the formds4=c ijkl dxi dxj dxk dxl, then this equation must reduce to the quadratic equation in a weak, spherically symmetric, static gravitational field (at least to first order in the Newtonian gravitational potentialU), otherwise “additional” contributions to the time-delay effect of radar propagation (that are not observed) are predicted.