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Entangled Electron for New Quantum Mechanics Part 2

Lino Zamboni

Published Mar 21, 2026• 0 citations
Publisher

Abstract

This work integrates and completes the previous studies (viXra 2411.0050 and 2412.0092 Quantum Physics) . The attractive and repulsive potentials are defined, where the magnetic moment and spin play an essential role in ensuring the stationarity of the electron and the orbitals that constitute it .A hypothesis is proposed regarding a source of the electrostatic field , determined by the extreme polarization of the quantum vacuum , which exists at very short distances corresponding to very high energy densities . The effect of such polarization creates a void , induced by the surrounding charges of opposite sign , whose attractive effects are balanced by spin , which generates a local centrifugal force . The application of this concept provides an innovative solution to the unresolved problem of the "Poincaré stress" . Following the framework of traditional quantum mechanics , the Hamiltonians and Schrödinger equations are defined for each orbital . The resulting wave functions , which are entangled like the orbitals they refer to , are combined with appropriate normalized coefficients to form the global electron wave function .

DOI
10.5281/zenodo.19145145

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This work integrates and completes the previous studies (viXra 2411.0050 and 2412.0092 Quantum Physics) . The attractive and repulsive potentials are defined, where the magnetic moment and spin play an essential role in ensuring the stationarity of the electron and the orbitals that constitute it .A hypothesis is proposed regarding a source of the electrostatic field , determined by the extreme polarization of the quantum vacuum , which exists at very short distances corresponding to very high energy densities . The effect of such polarization creates a void , induced by the surrounding charges of opposite sign , whose attractive effects are balanced by spin , which generates a local centrifugal force . The application of this concept provides an innovative solution to the unresolved problem of the "Poincaré stress" . Following the framework of traditional quantum mechanics , the Hamiltonians and Schrödinger equations are defined for each orbital . The resulting wave functions , which are entangled like the orbitals they refer to , are combined with appropriate normalized coefficients to form the global electron wave function .
This work advances the theoretical framework of the electron model introduced in a previous paper (viXra: 2411.0050 -Quantum Physics) , which describes the electron as composed of entangled mass elements . This model proposes an extension of the de Broglie-Bohm (dBB) paradigm , achieving compatibility with Special Relativity . Explicit expressions for 𝑍 and 𝑍𝐶 are derived , describing the sequence of orbitals and their associated masses , along with a detailed analysis of their physical significance . An innovative interpretation of spin and magnetic moment is presented , viewing them as invariant properties across orbitals , despite variations in the associated parameters . This perspective provides a potential explanation for the experimentally observed phenomenon of spatial spin separation from its particle . Additionally , the Appendix includes applications of the 𝑀𝑍 matrix—a conceptual tool integral to the proposed formalism—for estimating particle masses, specifically those of the muon and tauon, with notable accuracy. This work represents the second part of a trilogy. A forthcoming extension will focus on the characteristics of orbitals, with particular emphasis on the definition of attractive and repulsive potentials and the associated Hamiltonian, thereby completing the theoretical framework.
Replacing the potential energy of electromagnetic interactions in the original Schrödinger equation with the potential energy of gravitational interactions can lead to the Schr ö dinger equation of gravitational potential energy. It is a product of the combination of classical mechanics and quantum mechanics, suitable for describing macroscopic and microscopic systems. A quantum chemistry method that combines classical mechanics and quantum mechanics can be established. Multiple computational examples have been provided for applying this method. The established basic particle structure configuration of wave elements can explain the source of electron spin magnetic moments. These three facts constitute a new quantum mechanics theoretical system — a localized realism quantum mechanics system that combines classical mechanics with quantum forces. This has a positive impact on promoting the development of material structure theory and quantum theory
Abstract 1. In a recent paper Dirac* has brilliantly removed the defects before existing in the mechanics of the electron, and has shown how the phenomena usually called the “ spinning electron ” fit into place in the complete theory. He applies to he problem the method of q-numbers and, using non-commutative algebra, exhibits the properties of a free electron, and of an electron in a central field of electric force. In a second paper † he also discusses the rules of combination and the Zeeman effect. There are probably readers who will share the present writer’s feeling that the methods of non-commutative algebra are harder to follow, and certainly much more difficult to invent, than are operations of types long familiar to analysis. Wherever it is possible to do so, it is surely better to present the theory in a mathematical form that dates from the time of Laplace and Legendre, if only because the details of the calculus have been so much more thoroughly explored. So the object of the present work is to take Dirac’s system and treat it by the ordinary methods of wave calculus. The chief point of interest is perhaps the solution of the problem of the central field, which can be carried out exactly and leads to Sommerfeld’s original formula for the hydrogen levels. But it is also of some interest to exhibit the relationship of the new theory to the previous equations which were derived empirically by the present writer.* It appears that those equations were an approximation to the new ones, derived by an approximate elimination of two of Dirac’s four wave functions. We shall also review a few other points connected with the free electron, the emission of radiation from an atom and its magnetic moment, and shall outline a discussion of the Zeeman effect.
Even after nine decades of successful run of the Quantum Mechanics (QM), different viewpoints on foundational problems of Quantum Physics are still being actively debated. That is because mathematical logic of QM often defies the physical intuition which constitutes the main spirit of Physics. De Broglie’s hypothesis of matter waves implied that the dynamic characteristics of a micro particle in motion, can be ascribed to the wave characteristics of the wavelet accompanying the particle. The Schrödinger equation models the matter-wave interactions through wavefunction ψ and effectively serves as the foundation of QM. Even though mathematical structure of the Schrödinger equation is sound and elegant, here we show a conceptual mistake in the development of this equation wherein the physical situation has not been correctly modeled in the equation. The Coulomb potential energy of the proton electron pair in Hydrogen atom is essentially the negative interaction energy between their superposed electrostatic fields which is inversely proportional to their instantaneous separation distance. Assuming the proton to be relatively fixed at the origin of an appropriate coordinate system, the potential energy of the orbiting electron will be a function of instantaneous position coordinates of the electron. This has not been properly modeled in the Schrödinger equation. The resulting errors in the solution have been quantitatively demonstrated in this paper. We have stressed the necessity of incorporating a specific correction in the potential energy term of the Schrödinger equation, after which it may facilitate the adoption of Bohmian QM.
This paper introduces a new theoretical paradigm for elementary particles, specifically the electron, proposing an internal structure composed of entangled mass elements. The model extends Bohm’s quantum potential theory ,redefining the quantum potential as an emergent property of intra-particle entanglement, rather than as a purely mathematical non-local function. This framework offers a novel resolution to the problems of wave function collapse and non-locality, while ensuring compatibility with special relativity. Additionally, the model incorporates concentric "s"-type orbitals to describe the spatial arrangement of mass elements, providing a framework that aligns with the principles of quantum mechanics while allowing for a stationary and symmetric configuration of the electron. Though detailed electrostatic and relativistic derivations are beyond the scope of this work, this paradigm suggests a unified and physically grounded interpretation of quantum phenomena that bridges the gap between quantum mechanics and classical physics. Further developments and mathematical formalism will be discussed in subsequent work .
Chapter 14 is entirely devoted to the electron spin and an introduction to quantum entanglement. The first part deals with the groundbreaking discovery of spin, its introduction into quantum formalism, and some of its most important effects on atomic spectra, notably the anomalous Zeeman effect. Historically, spin has been considered as an angular momentum that particles can have by the mere fact of their existence, which is called "intrinsic" and does not require any explanation. To address this shortcoming, Section 4 presents a possible explanation for the origin of electron spin as a result of its interaction with the vacuum field. Section 5 introduces the entangled system of two particles with spin, which provides an opportunity to discuss, necessarily schematically, the Schrödinger cat and the Einstein-Podolsky-Rosen thought experiment, as well as the Bell inequalities.