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A general description of energy propagation: Matter and wave

Hyunhwan Choi

Published Jan 5, 2026• 0 citations
Publisher

Abstract

A study was carried out to explain a wave propagation of the relativistic energy that comes in the squared form. What looks physically incompatible concept of wave and particle was combined into a general wave of the complex energy. From the fact that the energy of matter is expressed by the squared form, a wave of the massless and massive energies was presented, which plays a role in the formation of matter wave. This study revealed that the energy is separated into the complex value with a imaginary mass that makes the wave different from the plane wave. The wave propagation is described by plugging the complex energy into the wavefunction, in which a modified mass-energy equivalence from the special relativity was used. From the fact that the energy of matter is consist of a complex value, it is also explained that the space around a rest-mass is a space with a imaginary mass. As a result, a general expression of matter and wave is described by the complex wave including an imaginary mass and a real momentum, by which a reasonable explanation is given for the radiation of mass energy, and explains the role of imaginary mass in the propagation of energy.

DOI
10.5281/zenodo.18149391

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A study was carried out to explain a wave propagation of the relativistic energy that comes in the squared form. What looks physically incompatible concept of wave and particle was combined into a general wave of the complex energy. From the fact that the energy of matter is expressed by the squared form, a wave of the massless and massive energies was presented, which plays a role in the formation of matter wave. This study revealed that the energy is separated into the complex value with a imaginary mass that makes the wave different from the plane wave. The wave propagation is described by plugging the complex energy into the wavefunction, in which a modified mass-energy equivalence from the special relativity was used. From the fact that the energy of matter is consist of a complex value, it is also explained that the space around a rest-mass is a space with a imaginary mass. As a result, a general expression of matter and wave is described by the complex wave including an imaginary mass and a real momentum, by which a reasonable explanation is given for the radiation of mass energy, and explains the role of imaginary mass in the propagation of energy.
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Abstract Various attempts at a thoroughly wave-theoretic explanation of matter have taken as their fundamental ingredient the de Broglie or matter wave. But that wave is superluminal, whereas it is implicit in the Lorentz transformation that influences propagate ultimately at the velocity c of light. It is shown that if the de Broglie wave is understood, not as a wave in its own right, but as the relativistically induced modulation of an underlying standing wave comprising counter-propagating ináuences of velocity c, the energy, momentum, mass and inertia of a massive particle can be explained from the manner in which the modulated wave structure must adapt to a change of inertial frame. With those properties of the particle explained entirely from wave structure, nothing remains to be apportioned to anything discrete or ìsolidîwithin the wave. Consideration may thus be given to the possibility of wave-theoretic explanations of particle trajectories, and to a deeper understanding of the Klein-Gordon, Schrˆdinger and Dirac equations, all of which were conceived as equations for the de Broglie wave.
It was predicted by Einstein that energy and mass can be converted between each other. But why? Energy and mass are two very different physical concepts. How can they be exchanged with each other? We think the key to answer this question is to recall that a particle can behave like a wave. Particle properties like energy and momentum are known to be related to their corresponding wave properties (frequency and wave vector). Mass is clearly a particle property; is it also related to a wave property? This study suggests that it is. We found that mass and energy appear to share similar physical nature in the wave perspective. Both of them are related to the curvature of bending the vacuum medium during the propagation of the excitation wave. This similarity explains why they are convertible.
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.
We will here show that there is one more relativistic wave equation rooted in the relativistic energy Compton moment relation, which should not be confused with the standard relativistic energy momentum relation. The standard momentum is, from a quantum perspective, rooted in the de Broglie wave. The de Broglie wave is not mathematically defined for rest-mass particles and has strange properties such as converging to infinity when the particle is almost at rest. As mentioned in the previous paper, the de Broglie wave is likely just a mathematical derivative of the true matter wave, which we have good reasons to think is the Compton wave. A wave equation that satisfies the relativistic energy Compton momentum relation will, in addition automatically satisfy the standard relativistic energy momentum relation, so there is no conflict between these two relations. The new one related to Compton is just the deeper reality and help explain why it gives simpler and more elegant relativistic wave equations, which are likely easier to interpret in terms of the physical reality.
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.