  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.
