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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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/12/1424 |
| _version_ | 1797544362742120448 |
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| author | Marek Danielewski Lucjan Sapa |
| author_facet | Marek Danielewski Lucjan Sapa |
| author_sort | Marek Danielewski |
| collection | DOAJ |
| 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>i</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. |
| first_indexed | 2024-03-10T13:59:23Z |
| format | Article |
| id | doaj.art-b6b2f8de00fb44fd9d2635b96b605d7f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T13:59:23Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-b6b2f8de00fb44fd9d2635b96b605d7f2023-11-21T01:19:57ZengMDPI AGEntropy1099-43002020-12-012212142410.3390/e22121424Foundations of the Quaternion Quantum MechanicsMarek Danielewski0Lucjan Sapa1Faculty of Materials Science & Ceramics, AGH UST, Mickiewicza 30, 30-059 Kraków, PolandFaculty of Applied Mathematics, AGH UST, Mickiewicza 30, 30-059 Kraków, PolandWe 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>i</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.https://www.mdpi.com/1099-4300/22/12/1424relativistic quaternion quantum mechanicsCauchy-elastic solidSchrödinger and Poisson equationsquaternionsKlein–Gordon equation |
| spellingShingle | Marek Danielewski Lucjan Sapa Foundations of the Quaternion Quantum Mechanics Entropy relativistic quaternion quantum mechanics Cauchy-elastic solid Schrödinger and Poisson equations quaternions Klein–Gordon equation |
| 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 | relativistic quaternion quantum mechanics Cauchy-elastic solid Schrödinger and Poisson equations quaternions Klein–Gordon equation |
| url | https://www.mdpi.com/1099-4300/22/12/1424 |
| work_keys_str_mv | AT marekdanielewski foundationsofthequaternionquantummechanics AT lucjansapa foundationsofthequaternionquantummechanics |