Abstract

There is an inconsistency in the theory of special relativity. It is assumed in the theory of special relativity that space and time posses the flat metric structures, Sp² = S_rsdx^rdx^s, r,s = 1,2,3, and d1'2 = dt2, in the usual inertial coordinate system (x^r,t), r = 1,2,3. From this assumption one can find an equation, y² = S^rsy^ry^s, where Y = dp/dt is the velocity-length, 'y^r = dx^r/dt is the usual (Newtonian) velocity. The velocity-space embodied in the equation is boundless and subject to the Galilei addition law. On the other hand, the theory of special relativity owns the Lorentz transformation between any two usual inertial coordinate systems. That in fact indicates a finite velocity boundary-the speed of light c and the Einstein law governing velocity additions.

Experiments clearly support the finite velocity boundary c, the Einstein velocity addition law and the Lorentz or the local Lorentz invariance. The Fock velocity-space is characterized by the boundary c and the Einstein addition law. Recognition of the Fock velocity-space leads us, in resolving the inconsistency, to assume the non-flat generalized Finslerian structures of gravity-free space and time in the usual inertial coordinate system without loss of their flatness.