Rigidly connected accelerated clocks

Abstract

Standard clocks at rest in (i) a rigidly hyperbolically accelerated reference frame, (ii) on a rotating disk, and (iii) on the surface of the earth are considered. Special relativity is sufficient to predict the behavior of the clocks in cases (i) and (ii). In case (iii), however, gravitational effects are important, which is taken account of by use of the principle of equivalence. It is concluded that in cases (i) and (ii) clocks connected along a line in the direction of the acceleration do not maintain Einstein synchronization. As to the rate of standard clocks on the surface of the earth, the drifts caused by the rotating motion of the earth and the deviation of the earth’s surface from a sphere cancel each other. On the geoid this cancellation is exact. This means that the synchronization of clocks at every position at the mean sea level, no matter how far apart on the earth they are located, is not destroyed by these effects. Owing to tidal effects clocks on the earth at different positions in the solar gravitational field do not maintain their synchronization. This effect is several orders of magnitude less than the above ones.