s . ge n - ph ] 1 6 Ju l 2 00 1 The Development of Special Relativity in the Superluminal Case

We extend the special relativity into the superluminal case and firstly put forward a new 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 discuss the superluminal theory of dynamics and then lead to a conclusion 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), and the product of two speeds satisfies uv = c 2. Lastly, we conjecture that this superluminal theory can give another novel interpretation to the essence of matter waves put forward by de Broglie.