Abstract

Keeping the two fundamental postulates of the theory of special relativity (the invariance of the velocity of light and the principle of relativity in inertial frames of reference), and assuming the generalized Finslerian structures of gravity-free space and time in the usual inertial coordinate system without loss of their flatness, we form a new test theory of special relativity. In the new test theory, the localized Lorentz transformation stands between any two usual inertial coordinate systems, and gravity-free space and time match the Fock velocity-space. We produce a new velocity distribution that is different from the Maxwell velocity distribution for free particles. This new distribution approaches zero as velocity goes to the velocity of light. It is claimed that the deviation of the new distribution from its previous formula will provide experimental means of testing the structures in gravity-free space and time of special relativity.