A Method for Deriving the Dirac Equation from the Relativistic Newton's Second Law

TL;DR

This paper introduces a novel formalism linking relativistic Newtonian mechanics with quantum mechanics, enabling the derivation of the Dirac equation from a velocity field approach.

Contribution

It presents a new method to derive the Dirac equation starting from relativistic Newton's second law using a velocity field formalism.

Findings

Derived the Dirac equation from relativistic Newton's law

Established a connection between relativistic mechanics and quantum wave nature

Proposed a velocity field formalism for quantum mechanics

Abstract

The derivation becomes possible when we find a new formalism which connects the relativistic mechanics with the quantum mechanics. In this paper, we explore the quantum wave nature from the Newtonian mechanics by using a concept: velocity field. At first, we rewrite the relativistic Newton's second law as a field equation in terms of the velocity field, which directly reveals a new relationship connecting to the quantum mechanics. Next, we show that the Dirac equation can be derived from the field equation in a rigorous and consistent manner.