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Open AccessArticle

Foundations of the Quaternion Quantum Mechanics

1
Faculty of Materials Science & Ceramics, AGH UST, Mickiewicza 30, 30-059 Kraków, Poland
2
Faculty of Applied Mathematics, AGH UST, Mickiewicza 30, 30-059 Kraków, Poland
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(12), 1424; https://doi.org/10.3390/e22121424
Received: 7 November 2020 / Revised: 3 December 2020 / Accepted: 14 December 2020 / Published: 17 December 2020
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations)
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. View Full-Text
Keywords: relativistic quaternion quantum mechanics; Cauchy-elastic solid; Schrödinger and Poisson equations; quaternions; Klein–Gordon equation relativistic quaternion quantum mechanics; Cauchy-elastic solid; Schrödinger and Poisson equations; quaternions; Klein–Gordon equation
MDPI and ACS Style

Danielewski, M.; Sapa, L. Foundations of the Quaternion Quantum Mechanics. Entropy 2020, 22, 1424. https://doi.org/10.3390/e22121424

AMA Style

Danielewski M, Sapa L. Foundations of the Quaternion Quantum Mechanics. Entropy. 2020; 22(12):1424. https://doi.org/10.3390/e22121424

Chicago/Turabian Style

Danielewski, Marek; Sapa, Lucjan. 2020. "Foundations of the Quaternion Quantum Mechanics" Entropy 22, no. 12: 1424. https://doi.org/10.3390/e22121424

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