Simultaneity and test-theories of relativity

Abstract

Two intertwined issues in special relativity-clock synchronisation and the experimental verification of special relativity-are investigated, and novel results are given in both areas. The validity of the conventionality of distant simultaneity is supported, and the special theory of relativity is recast in a general synchrony "gauge" to reveal the operational significance of synchronisation in measurement and prediction within special relativity. For similar reasons, the Mansouri-Sexl test-theory is extended to allow arbitrary synchrony to be properly taken into account in the verification of relativistic theories. The generalised test-theory is used to analyse recent experiments and to demonstrate that there is no basis to claims that simultaneity relations are empirically definable. Synchrony considerations are extended to the case of a non-inertial observer exhibiting arbitrary motion within the context of any metric theory: a local co-ordinate system is developed using differential geometric techniques and a generalisation of the Frenet frame. The analysis used for the accelerated observer is adapted to produce a test-theory of local Lorentz invariance in a space of arbitrary curvature. The test-theory incorporates the conventionality of distant simultaneity which, combined with the geometric approach, illuminates the role of synchrony in test-theories. The Sagnac effect is investigated within this new test-theory, enabling the use of a precision ring laser, such as the Canterbury Ring Laser, to bound parameters of the theory and thus to test local Lorentz invariance.