[Paper Review] What is rest mass in the wave-particle duality? A proposed model

Donald C. Chang|arXiv (Cornell University)|Apr 8, 2004

Relativity and Gravitational Theory8 references3 citations

TL;DR

This paper proposes that rest mass in wave-particle duality arises from a transverse wave number characterizing radial wave function variation in the transverse plane, treating mass analogously to energy and momentum. By modeling matter waves like photons, the approach derives the mass-energy relation and naturally leads to the Klein-Gordon equation, unifying relativistic wave behavior with wave-particle duality.

ABSTRACT

In the wave-particle duality, a free particle can be considered as a wave packet. Is there a wave property that corresponds to the rest mass of the particle? This is an interesting question that has not been extensively explored before. We suggest that this problem may be approached by treating the rest mass on the same footing as energy and momentum. Here we demonstrate that, by assuming that the matter wave of a particle behaves like a photon, one could derive the mass-energy relation from the solution of a simplified wave equation. This solution suggests that the rest mass of a particle is associated with a "transverse wave number", which characterizes the radial variation of the wave function in the transverse plane. This finding has several appealing features. For example, it shows a consistent geometrical relationship between mass, energy and momentum in both the wave and particle perspectives. Also, it predicts that a massless particle must travel at the constant speed of light. Furthermore, from a philosophical point of view, this model suggests that the mass-energy relation attributed to the special theory of relativity may have a root in the wave-particle duality. Indeed, it is shown that the Klein-Gordon equation can be derived naturally based on this model.

Motivation & Objective

• To explore whether rest mass has a corresponding wave property in wave-particle duality, a question largely unaddressed in prior research.
• To establish a consistent geometrical relationship between mass, energy, and momentum across both wave and particle descriptions of matter.
• To investigate whether the mass-energy equivalence relation (E=mc²) emerges from wave dynamics rather than postulating it as a separate principle.
• To derive the Klein-Gordon equation from a wave-based model of rest mass, thereby connecting quantum field theory with wave-particle duality.

Proposed method

• Model the matter wave of a free particle as a wave packet analogous to a photon, assuming wave behavior governed by a simplified wave equation.
• Introduce a transverse wave number as the wave property corresponding to rest mass, describing radial variation of the wave function in the transverse plane.
• Apply wave mechanics principles to derive the energy-mass relation by treating mass as a wave parameter analogous to energy and momentum.
• Use the derived wave model to reconstruct the Klein-Gordon equation, showing its natural emergence from the wave-based framework.
• Demonstrate that the model predicts massless particles must travel at the speed of light, consistent with relativity.
• Establish a unified geometric interpretation of mass, energy, and momentum by treating them as interrelated wave parameters.

Experimental results

Research questions

• RQ1 Can rest mass be associated with a specific wave property in the wave-particle duality framework?
• RQ2 How does the wave model of matter lead to the derivation of the mass-energy equivalence relation?
• RQ3 What is the role of the transverse wave number in characterizing the rest mass of a particle?
• RQ4 Does the proposed wave model naturally lead to the Klein-Gordon equation?
• RQ5 Can the constancy of the speed of light for massless particles be derived from wave dynamics in this model?

Key findings

• Rest mass is proposed to correspond to a transverse wave number that describes the radial variation of the wave function in the transverse plane.
• The model derives the mass-energy relation (E=mc²) from a simplified wave equation, showing it arises from wave dynamics.
• The model predicts that massless particles must travel at the speed of light, consistent with special relativity.
• The Klein-Gordon equation is shown to emerge naturally from the proposed wave-based framework, linking it to quantum field theory.
• A consistent geometrical relationship between mass, energy, and momentum is established across both wave and particle perspectives.
• The model suggests that the mass-energy equivalence relation may originate from wave-particle duality rather than being an independent postulate.