Extend Special Relativity to the Superluminal Case

Abstract

First, we extend the special relativity into the superluminal case and put forward a superluminal theory of kinematics, in which we show that the temporal coordinate need exchanging with one of the spatial coordinates in a superluminal inertial frame, and that the coordinate transformations from any superluminal inertial frame to the rest frame (here rest just says in a relative sense) are the same as the Lorentz transformations from some normal inertial frame to the rest frame. Consequently, the causality can not be violated. Secondly, we investigate the superluminal theory of dynamics and find that the total energy of any object moving at a speed of $v$ (faster than the speed of light in vacuum $c$) is equal to the total energy of that object moving at a speed of $u (u<c)$ provided that the product of two speeds satisfy $uv=c^{2}$. Lastly, we conjecture that this superluminal theory can give a novel interpretation to the essence of matter waves put forward by de Broglie.