Essence of Special Relativity, Reduced Dirac Equation and Antigravity

TL;DR

This paper explores the fundamental symmetries of special relativity, introduces a reduced Dirac equation, and predicts antigravity effects between matter and antimatter based on negative mass considerations.

Contribution

It presents a novel perspective on special relativity's symmetries, derives a reduced Dirac equation for hydrogen-like atoms, and predicts antigravity between matter and antimatter.

Findings

Invariance under space-time and mass inversion reflects particle-antiparticle symmetry.

A reduced Dirac equation is formulated for hydrogen-like atoms.

Negative mass paradox suggests antigravity between matter and antimatter.

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