Physics in a general length space-time geometry: Call for experimental revision of the light speed anisotropy

We present a phenomenological model for the nature in the Finsler and Randers space-time geometries. We show that the parity-odd light speed anisotropy perpendicular to the gravitational equipotential surfaces encodes the deviation from the Riemann geometry toward the Randers geometry. We utilize an asymmetrical ring resonator and propose a setup in order to directly measure this deviation. We address the constraints that the current technology will impose on the deviation should the anisotropy be measured on the Earth surface and the orbits of artificial satellites.