Modification of special relativity and formulation of convergent and invariant quantum field theory

Abstract

Besides the two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the one-way velocity of light in all inertial frames of reference, the special theory of relativity employs another assumption. This assumption concerns the flat structures of gravity-free space and time in the usual inertial coordinate system. We introduce the primed inertial coordinate system, in addition to the usual inertial coordinate system, for each inertial frame of reference, and assume the flat structures of gravity-free space and time in the primed inertial coordinate system and their generalized Finslerian structures in the usual inertial coordinate system. Combining this alternative assumption with (i) and (ii), we modify the special theory of relativity. The modified theory involves two versions of the light speed, infinite speed c' in the primed inertial coordinate system and finite speed c in the usual inertial coordinate system. It involves the c'-type Galilean transformation between two primed inertial coordinate systems and the localized Lorentz transformation between two corresponding usual inertial coordinate systems. It also involves a new physical principle. This principle is applied to reform of mechanics, field theory and quantum field theory. The validity of relativistic mechanics in the usual inertial coordinate system remains, while field theory is freshened. Based on the establishment of a transformation law for the quantized field systems, we construct a convergent and invariant quantum field theory, in full agreement with experimental facts, founded on the modified special relativity theory and the quantum mechanics theory.