The Theory of Relativity and Superluminal Speeds - Part Three - the Catastrophe of the Spacetime on the Finsler Metric

According to the different properties between the ds ² and the ds ⁴, it is discussed that the space-time will have the catastrophe nature on the Finsler metric ds ⁴ (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-speedv>c, could be regarded as its anti-particle with the dual velocityv ₁=c ²/v<c.