THE THEORY OF RELATIVITY AND SUPER-LUMINAL SPEEDS (].3.) THE CATASTROPHE OF THE SPACE-TIME ON THE FINSLER METRIC

According to the different properties between the ds2 and the ds4, it is discussed that the space-time will have the catastrophe nature on the Finsler metric ds4 (see Cao, 1990, Paper II). The space-time transformations and the physical quantities will suddenly change at the catastrophe theory of the space-time. It will be supposed that only the dual velocity of the super-luminal-speed could be observed (see Cao, 1988). If so, a particle with the super-luminal-speed-nu > c, could be regarded as its anti-particle with the dual velocity-nu-1 = c2/nu < c.