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.
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.
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 .
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 .
It is shown that, within the frame of relativistic quan- tum (wave) mechanics, massive elementary spin 1 and spin 0 parti- cles can be regarded as extended entities of characteristic size~=mc that are described by pertinent non-local operators, among these correct energy and momentum operators, charge operators, and size operators. Some of the aspects of such a conception are understand- able in graphic terms which are in consonance with de Broglie's idea about particle structure. A number of conceptual improvements are attained as elimination of non-physical negative energies of free mo- tion and oppositely oriented velocities and momenta, substantiation of the constancy of free-particle size in time, a physical justiflcation of a non-divergent procedure of mass renormalization for a qualita- tive explanation of the anomalous magnetic moment value of elec- trons and muons, a physical explanation of the limits of validity of one-particle theory an the Foldy-Wouthhuysen procedure, etc. In the second part of the paper the ideology is applied to a discussion of the essence of Klein's paradox. A number of applications to elementary particle physics is left for a sequel to the 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.
[16 Supplement] This document presents a comprehensive review of the 0-Sphere electron model, a theoretical framework developed since 2018 that challenges fundamental assumptions in quantum mechanics. The model reconceptualizes elementary particles as inherently spatiotemporal structures rather than point entities, proposing that electrons possess internal oscillatory dynamics that give rise to quantum phenomena through deterministic mechanisms. Central to this framework is the elegant relationship γ = 1 + a, which bridges the Lorentz factor from special relativity with the anomalous magnetic moment from quantum electrodynamics. The model proposes that electrons contain two energy kernels exchanging thermal potential energy through a photon sphere, functioning as a microscopic clock with a predicted Zitterbewegung velocity of approximately 0.040374c—a specific value offering experimental verification pathways. Note: The general relativistic correction yielding this velocity value of 0.040374c has been corrected due to a computational error. The corrected analysis is available in "A Supplementary Correction to the 0-Sphere Model: Dimensional Consistency of G and c²" (https://doi.org/10.5281/zenodo.17765448). Key contributions include: (1) a deterministic reinterpretation of the uncertainty principle as reflecting measurement limitations rather than fundamental indeterminacy; (2) geometric explanations for spin-½ quantization and the 720° rotation property; (3) critical radii predictions for muon (3.43 × 10⁻²⁵ m) and tau lepton (5.71 × 10⁻²⁴ m) decay; (4) novel perspectives on quantum entanglement without nonlocality; (5) reexamination of CP symmetry through mirror-invariant spin interpretation; and (6) potential unification of quantum mechanics with general relativity through proper time integration. This retrospective traces the evolution of the 0-Sphere model from 2018 onwards, documenting its development as an alternative to probabilistic quantum interpretations and its implications for fundamental physics. The summary was prepared with assistance from large language models (LLMs) to synthesize the author's research trajectory and key theoretical advances. Keywords: 0-Sphere model, deterministic quantum mechanics, Zitterbewegung, anomalous magnetic moment, spin geometry, lepton mass hierarchy, quantum-gravity unification, electron internal structure, Thomas precession, proper time
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.