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Applied Physics Research

Establishment of New Fundamental Theory in Diffusion Phenomena

Takahisa Okino

Published Jan 29, 2019• 2 citations
Publisher

Abstract

Investigating the elementary process of diffusion revealed that the De Broglie hypothesis is really valid in a material and further that the Schrödinger equation is reasonably derived from the diffusion equation. The diffusion equation is thus one of the fundamental equations in physics. The problem between a moving coordinate system and a fixed coordinate system for the diffusion equation had never been discussed until recently in the history of diffusion theory. In that situation, it is revealed that investigating the problem between those coordinate systems is indispensable for understanding the diffusion phenomena. The new findings obtained here, which are revolutionary in the existing diffusion theory, will be not only dominant but also indispensable for further advance in the diffusion study.

DOI
10.5539/apr.v11n1p82

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Investigating the elementary process of diffusion revealed that the De Broglie hypothesis is really valid in a material and further that the Schrödinger equation is reasonably derived from the diffusion equation. The diffusion equation is thus one of the fundamental equations in physics. The problem between a moving coordinate system and a fixed coordinate system for the diffusion equation had never been discussed until recently in the history of diffusion theory. In that situation, it is revealed that investigating the problem between those coordinate systems is indispensable for understanding the diffusion phenomena. The new findings obtained here, which are revolutionary in the existing diffusion theory, will be not only dominant but also indispensable for further advance in the diffusion study.
Since a material is composed of micro particles, investigating behavior of those particles is essentially dominant for materials science. The diffusivity of diffusion equation is relevant to not only a collective motion of micro particles but also a motion of single particle. An elementary process of diffusion was thus theoretically investigated in a local space and time. As a result, the investigation concluded that the wave nature of micro particle results from denying the mathematical density theorem of a real time in the Newton mechanics. In other words, the basic theory of quantum mechanics is established in accordance with the cause-and-effect relationship in the Newton mechanics, for the first time, regardless of the de Broglie hypothesis. In relation to the collective motion of micro particles, the new diffusion theory was also reasonably established using the universal expression of diffusivity obtained here. In the present paper, the new findings indispensable for the fundamental knowledge in physics are thus systematically discussed in accordance with the theoretical frame in physics.
The evidence that the probability interpretation is indispensable for the wave function has not been reasonably revealed since the early stages of quantum theory like the topic of Schrödinger’s cat has been discussed from various viewpoints. Recently the Schrödinger equation has reasonably derived from the diffusion equation in accordance with the causality for the Newton mechanics, regardless of the de Broglie’s hypothesis. In the derivation process, the problem of probability interpretation has been reasonably solved in relation to a wave function collapse, and moreover not only the evidence for a micro particle having a wave nature but also the evidence for validity of the de Broglie’s hypothesis itself has been theoretically revealed. Further, the other fundamental problems having been unsolved for a long time are also reasonably solved. For example, it is theoretically revealed that such a single composite particle as a cluster molecule has a wave nature when it is composed of atoms smaller than about 770 numbers.
Investigating the elementary process of diffusion yielded the universal expression of diffusivity relevant to the angular momentum of each microparticle in a material. Using the diffusivity obtained then for the diffusion equation, the wave equation of Schrödinger was theoretically derived from the physical concept in Newton mechanics. The derivation itself reveals that any moving microparticle has the wave image as an intrinsic nature. It was theoretically revealed that the relation having been accepted as a hypothesis proposed by De Broglie is valid for any moving microparticle and that another relation of matter-wave is possible. The new diffusion theory based on the matter-wave will be useful for further development of the nanotechnology in materials science.
The correlation between the Schrödinger equation and the diffusion equation revealed that the relation of material wave is not a hypothesis but an actual one valid in a material regardless of the photon energy. Using the relations of material wave and uncertain principle, the quantum effect on elementary process of diffusion is discussed. As a result, the diffusivity is obtained as a universal expression applicable to any problem of diffusion phenomena. The Gauss theorem in theory and the Kirkendall effect in experimentation reveal the necessity of the coordinate transformation for a diffusion equation. The mathematical method for solving an interdiffusion problem of many elements system is established. The phase shift of the obtained analytical solution indicates the correlation between the solutions of each diffusion equation expressed by a fixed coordinate system and by a moving coordinate system. Based on the coordinate transformation theory, some unsolved problems of diffusion theory are reasonably solved and also some new important findings are discussed in relation to matters in the existing diffusion theory.
Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.