Essence of Special Relativity, Reduced Dirac Equation and Antigravity

Abstract: The essence of special relativity is hiding in the equal existence of particle and antiparticle, which can be expressed by two discrete symmetries within one inertial frame --- the invariance under the (newly defined) space-time inversion (${\bf x}\to -{\bf x},t\to -t$), or equivalently, the invariance under a mass inversion ($m\to -m$). The problems discussed are: the evolution of the $CPT$ invariance into a basic postulate, an unique solution to the original puzzle in Einstein-Podolsky-Rosen paradox, the reduced Dirac equation for hydrogenlike atoms, and the negative mass paradox leading to the prediction of antigravity between matter and antimatter. {\bf Keywords}: Special relativity, Reduced Dirac Equation, Antiparticle, Antigravity