Local Lorentz Transformation and Mass-Energy Relation of Spinor

Abstract

In this paper, we strictly establish classical concepts and relations according to a Dirac equation with scalar, vector and nonlinear potentials. To calculate classical parameters for moving spinor, the local Lorentz transformations for parameters are derived. The calculation shows that different kinds of potentials result in different energy-speed relations, and the energy-speed relations for these potentials are derived in detail. The usual mass-energy relation $E = mc^2$ holds only for the linear spinor. The energy-speed relations can be used as fingerprints to identify the interactive potentials of a particle by elaborated experiments. The analysis and results of this paper can also provide some natural explanations for the foundation of quantum mechanics, and clarify some long-standing puzzles in the theory.