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Applied Physics Research

Relativistic Completion of Schrodinger’s Quantum Mechanics by the Ether Theory

David Zareski

Published Jul 15, 2019• 0 citations
Publisher

Abstract

One recalls that we have shown in our precedent publications that the ether is an elastic isotropic medium. One presents the exact equation and its non-relativistic approximation that govern the ether in presence of a Schwarzschild-Coulomb field to which is submitted a Par(m,e) (particle of mass m and of electric charge e ). We present the exact relativistic solution of this exact equation in the circular case. We prove that the Schrödinger equation is such a non-relativistic approximation, that is, is a particular case of the ether elasticity theory. One recalls that the Schrödinger equation was obtained by the use of operators and not from the theory of elasticity. It follows that this manner of obtaining this equation from operators is arbitrary and does not permit to obtain its complete relativistic form, but permits to reach absurd conclusions as, e.g., the cat that, at the same moment, is alive and dead. One shows then that other results ensuing from the Schrödinger equation are particular cases of the non-relativistic equation that governs the elastic ether, like for example: the Bohr-Sommerfeld condition, and the eigenstates function equation.

DOI
10.5539/apr.v11n4p52

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One recalls that we have shown in our precedent publications that the ether is an elastic isotropic medium. One presents the exact equation and its non-relativistic approximation that govern the ether in presence of a Schwarzschild-Coulomb field to which is submitted a Par(m,e) (particle of mass m and of electric charge e ). We present the exact relativistic solution of this exact equation in the circular case. We prove that the Schrödinger equation is such a non-relativistic approximation, that is, is a particular case of the ether elasticity theory. One recalls that the Schrödinger equation was obtained by the use of operators and not from the theory of elasticity. It follows that this manner of obtaining this equation from operators is arbitrary and does not permit to obtain its complete relativistic form, but permits to reach absurd conclusions as, e.g., the cat that, at the same moment, is alive and dead. One shows then that other results ensuing from the Schrödinger equation are particular cases of the non-relativistic equation that governs the elastic ether, like for example: the Bohr-Sommerfeld condition, and the eigenstates function equation.
The Schrödinger equation ensues from the following axiom: in Cartesian coordinates and in absence of gravitation, to the component , (), of the momentum tensor is associated the operator . We show here this equation is a particular case of the equation that governs, even in presence of gravitation, the oscillatory displacements of the points of the ether shown to be a specific elastic medium. That is to say that the Schrödinger equation of which the solutions are the scalar state functions is a particular case of the equation of the vectorial waves propagated in the ether. As shown in previous publications, a mobile particle is a superposition of these waves that form a globule moving like this particle; here we show, in particular that, in a bound state, it is the interferences of these waves that creates the so called “quantum states”. The ether elasticity theory therefore do not only generalizes the quantum mechanics, but also gives the physical signification of the quantum phenomena.
Abstract We discuss the discovery of the relativistic wave equation for a spin-zero charged particle in the Coulomb field by Erwin Schrödinger (presumably during the Christmas holidays of 1925–1926). However, in this new approach, an essential discrepancy was found with the fine structure formula for energy levels already obtained by Sommerfeld in the framework of the ‘old’ quantum mechanics. As a result, Schrödinger had to withdraw the original ‘relativistically framed’ article, a draft of which has never been found, from a journal and start all over with his centennial article on the nonrelativistic stationary Schrödinger equation. Our goal here is to follow the original ‘relativistic idea’ from a modern mathematical viewpoint and elaborate on why Schrödinger did not publish it. We hope that this consideration will encourage readers to study quantum physics starting from one of the crucial moments of its creation.
The major problem in quantum physics is to find the wave function of a given physical system and to understand (predict) how the wave function of the system evolves in time, or how it changes under external influences. In 1926, Erwin Schrodinger predicted that the wave function of a given physical system might be completely determined if the total energy of the system was known. Since the equation represents a real physical system, it must satisfy the following conditions: the equation must be linear and coefficients appearing in this equation should only depend on the parameters characteristic of the particle. This chapter focuses on to the non-relativistic case only. It considers the case of a free particle moving in one dimension. The chapter shows that the Schrodinger equation can be obtained from the energy of the free particle. It shows that the Schrodinger equation guarantees the conservation of normalization of the wave function.
The energy-momentum tensor T μ ν for the scalar field configurations of the relativistic Schrodinger theory is constructed. Its time component Too is identified with the energy functional E[Ψ] for the stationary solutionsΨ. The confidence into the proposed functional is supported by the fact that it reproduces exactly the relativistic mass eigenvalues of the one-particle systems. For many-particle systems, the non-relativistic limit of relativistic Schrodinger theory is found to coincide exactly with the Hartree-Fock approach.
We describe here the coherent formulation of electromagnetism in the nonrelativistic quantummechanical many-body theory. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because of the manifold of misinterpretations emerging from the hystorical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions inspired from the classical electromagnetic theory of point-like charges. However, this later is known to be inconsistent due to the self-interaction. This way could not be continued further to include properly the magnetic forces between the charged particles and lead to a lot of confusion about the interpretation of the magnetic field in the Hamiltonian, as well as about the gauge invariance. We emphasize the importance of the distinction between the applied (external fields) and the field in the matter. All these problems are length properly solved within the non-relativistic QED, nevertheless the confusion dominates in all the problems related to the magnetic properties of the solid state.
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.