Local Structures of Gravity-Free Space and Time
In the special theory of relativity it is assumed that gravity-free space and time possess flat metric structures in the usual inertial coordinate system. But there is an inconsistency in the theory formed by combining this assumption with the two fundamental postulates: (i) the principle of relativity, and (ii) the constancy of the one-way speed of light in all inertial frames of reference. We here propose assuming two generalized Finslerian structures of gravity-free space and time in the usual inertial coordinate system. The inconsistency no longer exists in the theory formed by combining the alternative assumption with the two postulates (i) and (ii), The new theory owns the localized Lorentz transformation between any two usual inertial coordinate systems and the validity of relativistic mechanics in the usual inertial coordinate system.