scholarly journals Foundations of the Quaternion Quantum Mechanics

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1424
Author(s):  
Marek Danielewski ◽  
Lucjan Sapa
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Bohmian Mechanics ◽  
Physical Reality ◽  
French Mathematician ◽  
Elastic Continuum ◽  
The Family ◽  
General Kind ◽  
Quaternion Representation ◽  
Straightforward Consequence

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.

scholarly journals Foundations of the Quaternion Quantum Mechanics

2020 ◽  
Author(s):  
Marek Danielewski ◽  
Lucjan Sapa
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Bohmian Mechanics ◽  
Physical Reality ◽  
French Mathematician ◽  
Elastic Continuum ◽  
The Family ◽  
General Kind ◽  
Quaternion Representation ◽  
Straightforward Consequence

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

scholarly journals Quaternions and Cauchy Classical Theory of Elasticity

2020 ◽  
Vol 44 (2) ◽  
pp. 67-70
Author(s):  
Marek Danielewski ◽  
Lucjan Sapa
Keyword(s):  
Classical Theory ◽  
Wave Equations ◽  
Elastic Solid ◽  
Physical Reality ◽  
Theory Of Elasticity ◽  
Multiple Wave ◽  
French Mathematician ◽  
Starting Point ◽  
Quaternion Representation ◽  
Straightforward Consequence

AbstractDeveloped by French mathematician Augustin-Louis Cauchy, the classical theory of elasticity is the starting point to show the value and the physical reality of quaternions. The classical balance equations for the isotropic, elastic crystal, demonstrate the usefulness of quaternions. The family of wave equations and the diffusion equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic solid. Using the quaternion algebra, we present the derivation of the quaternion form of the multiple wave equations. The fundamental consequences of all derived equations and relations for physics, chemistry, and future prospects are presented.

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

scholarly journals Quantum Mechanics and Physical Reality

Nature ◽  
1935 ◽  
Vol 136 (3428) ◽  
pp. 65-65 ◽  
Author(s):  
N. BOHR
Keyword(s):  
Quantum Mechanics ◽  
Physical Reality

scholarly journals Local Theories and Bohmian Mechanics

2020 ◽  
Vol 4 ◽  
pp. 196
Author(s):  
C. Syros
Keyword(s):  
Quantum Theory ◽  
Bohmian Mechanics ◽  
Physical Reality ◽  
The Self ◽  
Self Consistency

One of the last develoonents in the research for extending the scope of the quantum theory is the recently appearing work on the Bohmian Mechanics. The motivation for an extension is provided by the conclusions of the EPR paradoxon and the famous alternative concerning the physical reality. Discussed are some properties of Bohmian Mechanics concerning the self-consistency of the theory.

scholarly journals Quantum Trajectories in Entropic Dynamics

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 25
Author(s):  
Nicholas Carrara
Keyword(s):  
Quantum Mechanics ◽  
Stochastic Equation ◽  
Bohmian Mechanics ◽  
Quantum Trajectories ◽  
Stochastic Mechanics ◽  
Scalar Particles ◽  
Double Slit ◽  
The Continuum ◽  
Entropic Dynamics

Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson’s stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously transition between fluctuating particles and the smooth trajectories assumed in Bohmian mechanics. In this work we explore the consequences of the ED framework by studying the trajectories of particles in the continuum between stochastic and Bohmian limits in the context of a few physical examples, which include the double slit and Stern-Gerlach experiments.

scholarly journals Did bohr succeed in defending the completeness of quantum mechanics?

2020 ◽  
Vol 24 (1) ◽  
pp. 51-63
Author(s):  
Kunihisa Morita
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Recent Trend ◽  
Physical Reality ◽  
Current Paper ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Completeness Of Quantum Mechanics

This study posits that Bohr failed to defend the completeness of the quantum mechanical description of physical reality against Einstein–Podolsky–Rosen’s (EPR) paper. Although there are many papers in the literature that focus on Bohr’s argument in his reply to the EPR paper, the purpose of the current paper is not to clarify Bohr’s argument. Instead, I contend that regardless of which interpretation of Bohr’s argument is correct, his defense of the quantum mechanical description of physical reality remained incomplete. For example, a recent trend in studies of Bohr’s work is to suggest he considered the wave-function description to be epistemic. However, such an interpretation cannot be used to defend the completeness of the quantum mechanical description.

scholarly journals Nonlocality in Bell’s Theorem, in Bohm’s Theory, and in Many Interacting Worlds Theorising

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 567 ◽  
Author(s):  
Mojtaba Ghadimi ◽  
Michael Hall ◽  
Howard Wiseman
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Bohmian Mechanics ◽  
Bell’S Theorem ◽  
Bell's Theorem ◽  
Significant Progress ◽  
Technical Problems ◽  
New Approach ◽  
Weak Notion ◽  
Bohm’S Theory

“Locality” is a fraught word, even within the restricted context of Bell’s theorem. As one of us has argued elsewhere, that is partly because Bell himself used the word with different meanings at different stages in his career. The original, weaker, meaning for locality was in his 1964 theorem: that the choice of setting by one party could never affect the outcome of a measurement performed by a distant second party. The epitome of a quantum theory violating this weak notion of locality (and hence exhibiting a strong form of nonlocality) is Bohmian mechanics. Recently, a new approach to quantum mechanics, inspired by Bohmian mechanics, has been proposed: Many Interacting Worlds. While it is conceptually clear how the interaction between worlds can enable this strong nonlocality, technical problems in the theory have thus far prevented a proof by simulation. Here we report significant progress in tackling one of the most basic difficulties that needs to be overcome: correctly modelling wavefunctions with nodes.

scholarly journals Classical Logic in the Quantum Context

2020 ◽  
Vol 2 (4) ◽  
pp. 600-616
Author(s):  
Andrea Oldofredi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Logic ◽  
Classical Logic ◽  
Theory Of Measurement ◽  
Propositional Calculus ◽  
Bohmian Mechanics ◽  
Physical Content ◽  
Present Essay ◽  
Classical Propositional Calculus

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay, we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions by virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be shown that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact that is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.

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