THE STATIC SPACETIME RELATIVE ACCELERATION FOR GENERAL FREE-FALL AND ITS POSSIBLE EXPERIMENTAL TEST

Mishra has recently established, using a generic static metric, the re lative local proper time 3-acceleration of a test particle in one-dime nsional free fall relative to static reference frame in any static spa cetime. In this paper, on the grounds of gravito-electromagnetism we e stablish, in a covariant spacetime form, the relative 4-acceleration f or general free fall, indicating its canonical representation with its 3-space kinematic content. Then we obtain the relation between this r epresentation and the very well known expression for relative free-fal l acceleration in Fermi coordinates. Taking this into account, it is s hown that an experiment with relativistic beams in a circular accelera tor, 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 verific ation, besides its intrinsic importance, can answer a recent question by Vigier, related to his recent proposal of derivation of inertial fo rces.