Clock synchronization by accelerated observers: metric construction for arbitrary congruences of world lines

Abstract

This paper reviews the problem of synchronizing the clocks (locally orthogonalizing the three-space) of an arbitrarily accelerated observer congruence. A general solution is given that maintains the isotropy and coordinate independence of the one-way velocity of light, but various particular cases, such as the "rotating disc or ring" congruence, are also discussed in detail. The congruence-based space-time metric that is constructed by the Einstein synchronization procedure is given explicitly, and the Hamilton–Jacobi method is used to write a useful equation for the geodesics of this space-time.The formal theory is related to experimental efforts to establish synchronization to an accuracy of a few nanoseconds over the rotating earth (Costain et al. and Ashby and Allan). In particular, a formally correct derivation of the "Sagnac corrected time" is given, and the expected experimental consequences are reviewed and compared to current experimental results.The measurable "global Sagnac effect" is distinguished from the "local Sagnac effect", which is, in fact, indistinguishable from Einstein synchronization. This clarifies earlier discussion concerning an orbital experiment proposed by Cohen and Moses.A suggestion regarding the application of absolute phase, very long baseline, radio interferometry to the measurement of the Sagnac effect (and possibly higher order effects) is given briefly.