The static spacetime relative acceleration for general free fall and its possible experimental test

Abstract

Mishra has recently established, using a generic static metric, the relative local proper time 3-acceleration of a test particle in one-dimensional free fall relative to a static reference frame in any static spacetime. In this paper, on the grounds of gravitoelectromagnetism we establish, in a covariant spacetime form, the relative 4-acceleration for general free fall, indicating its canonical representation with its 3-space kinematic content. Then we obtain the relation between this representation and the very well known expression for relative free-fall acceleration in Fermi coordinates. Taking this into account, it is shown that an experiment with relativistic beams in a circular accelerator, modelled by Fermi coordinates, recently proposed by Moliner et al, can test the covariant result established here, and, therefore, can also verify Mishra’s formula. This possibility of experimental verification, besides its intrinsic importance, can answer a recent question by Vigier, related to his recent proposal of derivation of inertial forces.