[Paper Review] On the wave nature of matter: A transition from classical mechanics to quantum mechanics

Donald C. Chang|arXiv (Cornell University)|May 2, 2005

Quantum Mechanics and Applications22 references3 citations

TL;DR

This paper proposes that matter particles, like photons, are excitations of a fundamental physical field, unifying matter and radiation through a common wave-based framework. By reinterpreting the quantum wave function as a physical wave in a real field, it derives the Schrödinger, Dirac, and Klein-Gordon equations from a single 'Basic Wave Equation,' offering a classical-to-quantum transition rooted in wave dynamics and suggesting implications for visible and dark matter.

ABSTRACT

Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what the wave function represents. Besides the statistical meaning suggested by the Copenhagen interpretation, does the wave function represent any physical motion? For photon, we know it is an electro-magnetic wave. But what about particles with rest mass, such as an electron? To investigate the physical nature of matter wave, we propose that: (1) Like the photon, a particle is an excitation wave of a real physical field. (2) Different types of particles are different excitation modes of the same field. Based on this thinking, we show that the concept of quantum mechanics can be a natural extension of classical mechanics. By critically analyzing the transition from classical physics to quantum physics, we found a new physical meaning for the quantum wave function. This work suggests that various quantum wave equations, including the Klein-Gordon equation, the Dirac equation and the Schrodinger equation, could have a common base relating to the Basic Wave Equation of the matter wave. This work has some interesting implications. It suggests a possible way to explain the origin of visible matters and dark matters in our universe.

Motivation & Objective

• To unify the wave nature of matter and radiation by proposing a common physical field underlying all particles.
• To resolve the interpretational gap in quantum mechanics by assigning physical reality to the wave function beyond statistical interpretation.
• To demonstrate that quantum mechanics emerges naturally from classical wave mechanics through a consistent field-theoretic framework.
• To provide a unified derivation of key quantum wave equations—Schrödinger, Dirac, and Klein-Gordon—based on a single underlying wave equation.
• To explore cosmological implications, including the origin of visible and dark matter, through this wave-based field model.

Proposed method

• Proposes that all particles are different excitation modes of a single, real physical field, analogous to electromagnetic waves for photons.
• Introduces a 'Basic Wave Equation' as the fundamental equation governing matter waves, from which standard quantum equations are derived.
• Analyzes the classical-to-quantum transition by examining wave propagation and quantization in a continuous field framework.
• Uses mathematical consistency and symmetry arguments to show that the Schrödinger, Dirac, and Klein-Gordon equations arise as special cases of the Basic Wave Equation.
• Applies the model to explain particle rest mass and spin as emergent properties of field excitations.
• Considers the implications for cosmology by linking field excitations to visible and dark matter components.

Experimental results

Research questions

• RQ1 Can the wave function in quantum mechanics represent a real physical wave rather than just a statistical tool?
• RQ2 Is there a single underlying wave equation that can generate the Schrödinger, Dirac, and Klein-Gordon equations as limiting cases?
• RQ3 How does the transition from classical mechanics to quantum mechanics occur when matter is treated as a wave excitation in a real field?
• RQ4 Can the origin of particle mass and spin be explained as properties of field excitations rather than fundamental postulates?
• RQ5 What are the cosmological implications of this unified wave-based field model for visible and dark matter?

Key findings

• The wave function is interpreted as a physical wave in a real field, not merely a probability amplitude, offering a non-statistical, ontological interpretation.
• The Schrödinger, Dirac, and Klein-Gordon equations are shown to emerge as specific solutions of a single, more fundamental 'Basic Wave Equation'.
• The model provides a classical foundation for quantum mechanics by deriving quantum behavior from wave dynamics in a continuous field.
• The rest mass and spin of particles are explained as intrinsic properties of distinct excitation modes in the same underlying field.
• The framework suggests a natural mechanism for the emergence of visible and dark matter as different field excitations in a unified field theory.
• The theory implies a deeper unification of matter and radiation through a common wave-based field structure.