Wave-particle duality and the zitterbewegung

TL;DR

This paper explores the connection between Hamilton-Jacobi equations, wave-particle duality, and the wave equation of electromagnetism, providing insights into zitterbewegung and proposing a universal internal parameter for particles.

Contribution

It develops a theory linking Hamilton-Jacobi formalism with wave-particle duality and electromagnetism, introducing a universal internal parameter for consistent momentum definition.

Findings

Free spinless particles obey the electromagnetic wave equation.

Implications for zitterbewegung and isotropy are discussed.

A universal internal parameter dt/m(t) is proposed for consistency.

Abstract

In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle duality. This theory is now further developed to show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy. Moreover, it is shown that for the theory to be consistent, the momentum defined by the Hamilton-Jacobi function presupposes the existence of a universal parameter internal to the system defined by dt/m(t) for particles with mass, where t has the units of time and m = m(t) has the units of mass.