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We present a phenomenological model for the nature in the Finsler and Randersspace-time geometries. We show that the parity-odd light speed anisotropyperpendicular to the gravitational equipotential surfaces encodes the deviationfrom the Riemann geometry toward the Randers geometry. We utilize anasymmetrical ring resonator and propose a setup in order to directly measurethis deviation. We address the constraints that the current technology willimpose on the deviation should the anisotropy be measured on the Earth surfaceand the orbits of artificial satellites.

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