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Foundations of the Quaternion Quantum Mechanics

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (class...

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Autores principales: Danielewski, Marek, Sapa, Lucjan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7766457/
https://www.ncbi.nlm.nih.gov/pubmed/33348816
http://dx.doi.org/10.3390/e22121424
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author Danielewski, Marek
Sapa, Lucjan
author_facet Danielewski, Marek
Sapa, Lucjan
author_sort Danielewski, Marek
collection PubMed
description We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.
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spelling pubmed-77664572021-02-24 Foundations of the Quaternion Quantum Mechanics Danielewski, Marek Sapa, Lucjan Entropy (Basel) Article We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity. MDPI 2020-12-17 /pmc/articles/PMC7766457/ /pubmed/33348816 http://dx.doi.org/10.3390/e22121424 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Danielewski, Marek
Sapa, Lucjan
Foundations of the Quaternion Quantum Mechanics
title Foundations of the Quaternion Quantum Mechanics
title_full Foundations of the Quaternion Quantum Mechanics
title_fullStr Foundations of the Quaternion Quantum Mechanics
title_full_unstemmed Foundations of the Quaternion Quantum Mechanics
title_short Foundations of the Quaternion Quantum Mechanics
title_sort foundations of the quaternion quantum mechanics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7766457/
https://www.ncbi.nlm.nih.gov/pubmed/33348816
http://dx.doi.org/10.3390/e22121424
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