The de Broglie Wave as Evidence of a Deeper Wave Structure

TL;DR

This paper proposes that the de Broglie wave is a modulation of an underlying carrier wave, offering a new physical interpretation that unifies matter and radiation and impacts quantum mechanics concepts.

Contribution

It introduces a novel interpretation of the de Broglie wave as a modulation of a carrier wave, providing a more natural physical ontology and implications for wave-particle duality.

Findings

De Broglie wave is a relativistically induced modulation of a carrier wave.

The carrier wave has a standing wave form in the particle's rest frame.

This interpretation impacts understanding of wave functions and particle trajectories.

Abstract

It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie also assumed the existence of this antecedent standing wave, but it would appear that he failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schr\"{o}dinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories.