[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
[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
[5 Application] This paper presents the first systematic application of the geometric framework introduced in A Model of an Electron Including Two Perfect Black Bodies (DOI: 10.5281/zenodo.16759284). It marks a conceptual step toward linking the 0-Sphere electron model with stochastic processes in quantum mechanics. The analysis builds on the closed geometric equationE₀ = E₀ ( cos⁴(θ/2) + sin⁴(θ/2) + 1/2 sin²(θ) ),assigning it a quantum-mechanical interpretation. This allows the two-kernel model to account algebraically for random walk and Brownian motion phenomena. A key insight comes from the temporal phase dynamics between kernels A and B. During inter-kernel transitions, the photon sphere oscillates harmonically. At the π time phase, all electron energy transfers to kernel B, giving sin⁴(θ/2) = 1. At this instant, the photon sphere’s energy drops to zero, creating a unique geometric state in which motion becomes differentiable across all temporal domains. The next kernel is then chosen probabilistically, forming the stochastic basis of the model. The study advances from one-dimensional random walks (drunkard’s walk) to two-dimensional lattice configurations. This dimensional progression shows how instantaneous velocity nullification enables the coexistence of continuous motion with genuine randomness, requiring probabilistic landing points to maintain mathematical continuity. As the first exploration of stochastic applications within the internal-structure model, this work establishes groundwork for explaining how deterministic geometric equations can produce apparently random quantum behaviors, opening a new research direction in the 0-Sphere theoretical program. Relation to Previous Works: 0-Sphere Model — DOI: 10.5281/zenodo.16759284 Coexistence of Dirac Positive/Negative States — DOI: 10.5281/zenodo.16817190 Anomalous Magnetic Moment via Lorentz Contraction — DOI: 10.5281/zenodo.16871305 Community: Satoshi-Hanamura-Papers
[3 Supplement] This 2019 study represents an early and ambitious attempt to extend the two-kernel "oscillatory black-body electron" model (Zenodo:10.5281/zenodo.16759284), first introduced in *A Model of an Electron Including Two Perfect Black Bodies*, into the framework of complex analysis and Riemann surfaces. In the earlier model, the sum of the spinors' thermal potential energy (TPE) and the photon's kinetic energy remained constant and followed the algebraic form:E0 = E0 ( cos⁴(θ/2) + sin⁴(θ/2) + 1/2 sin²(θ) )This paper explores how the two spinor bases could be placed on separate sheets of a Riemann surface, leading to four possible composite spin states within a single electron: |↑↑⟩, |↑↓⟩, |↓↑⟩, |↓↓⟩. A magnetic field gradient or a measurement process is proposed to "disconnect" the analytic continuation between the sheets, collapsing the superposition into a restricted two-state system (|↑↑⟩ or |↓↓⟩). After this work, our research accepted a redefinition of spin via the reinterpretation of Thomas precession. As of 2025, the examination of the four possible composite spin states proposed here is no longer in active use.Within the author's series, this work marks a transitional phase: it preserves the black-body kernel mechanics from the first paper but begins to treat spin as part of a structure embedded in a two-sheeted analytic space. Although later studies refined the interpretation, this paper stands as the first to test the Riemann surface as a mathematical stage for the electron's internal state space. Its domain-disconnection mechanism remains an early foundation for later explorations of measurement and symmetry breaking in the 0-Sphere model. This paper serves as the logical foundation for a subsequently submitted work, Redefining Electron Spin and Anomalous Magnetic Moment Through Harmonic Oscillation and Lorentz Contraction (DOI: 10.5281/zenodo.16861903), which provides predictions that electron Zitterbewegung oscillates at approximately 4% of the speed of light. While some mathematical refinements remain, the work opens a new path for interpreting fundamental equations through internal electron dynamics rather than particle–antiparticle dualism. Relation to Previous Works: 0-Sphere Model — DOI: 10.5281/zenodo.16759284 Coexistence of Dirac Positive/Negative States — DOI: 10.5281/zenodo.16817190 Anomalous Magnetic Moment via Lorentz Contraction — DOI: 10.5281/zenodo.16871305 Community: Satoshi-Hanamura-Papers
This work introduces Time–Space Oscillations (TSO), a deterministic geometric framework that reinterprets fundamental quantum phenomena as natural consequences of oscillatory structures in complex spacetime. Unlike standard quantum mechanics, which is probabilistic and incomplete, TSO provides a complete underlying phase geometry from which uncertainty, quantisation, entanglement, zero-point energy, path integrals, and interference phenomena emerge naturally. This Version presents the framework as a conceptual and structural exploration intended to stimulate discussion and critical engagement. Readers are invited to explore how classical deterministic oscillations can underpin observed quantum behavior, bridging the gap between geometric intuition and the apparent probabilistic rules of the quantum world. This article with its preceding articles on TSO lays the foundation for a future monograph that will consolidate the full theory in a single work.This article, together with the preceding works — Time–Space Oscillations: A Geometric and Deterministic Approach to Relativistic and Quantum Phenomena (DOI: 10.5281/zenodo.17534735), Time Dilation and the Nature of Gravitational and Inertial Forces (DOI: 10.5281/zenodo.17543060), and Time–Space Oscillations and Electromagnetics (DOI: 10.5281/zenodo.17591326) — provides a comprehensive introduction to the TSO model and its deterministic approach to quantum mechanics. This introduction work on TSO is part of the following key works: Time–Space Oscillations: A Geometric and Deterministic Approach to Relativistic and Quantum PhenomenaZenodo DOI: 10.5281/zenodo.17534734The foundational article introducing the TSO framework and its applications to both relativistic and quantum phenomena. Time Dilation and the Nature of Gravitational and Inertial ForcesZenodo DOI: 10.5281/zenodo.17543059Explores the TSO perspective on time dilation and the interplay of inertial and gravitational forces. Time–Space Oscillations and ElectromagneticsZenodo DOI: 10.5281/zenodo.17591325Applies the TSO model to electromagnetic phenomena, revealing novel interpretations of wave propagation and field interactions. Time–Space Oscillations and Quantum Mechanics Zenodo DOI: 10.5281/zenodo.17670668Extends TSO to encompass quantum mechanical principles, including Heisenberg uncertainty, Schrödinger dynamics, path integrals, entanglement, zero-point energy, and the Quantum Zeno effect. For an overview of related work and publications, visit:https://ndl1971.github.io/time-space-oscillations/ Version 0.92 Corrected, mainly section 17. Incomplete normalisation descriptions have been corrected. V and H or E and B of the observer need normalisation through observer E and B. Which is a remark to the reader too. TSO oscillations may become nonoscillative images and patterns after normalisation/projection. Version 0.91 Corrected w_tso_base frequency in: 7.1 & 8 which scales linearly with mass and conform time dilation when accumulated particles arise.
Time–Space Oscillations present a new way to visualize particles as fundamental oscillators with intertwined temporal and spatial components. This approach unifies relativistic effects, matter–antimatter symmetry, and the emergence of forces, offering a deterministic geometric perspective that complements and reinterprets standard quantum and electromagnetic theories. This introduction work on TSO is part of the following key works: Time–Space Oscillations: A Geometric and Deterministic Approach to Relativistic and Quantum PhenomenaZenodo DOI: 10.5281/zenodo.17534734The foundational article introducing the TSO framework and its applications to both relativistic and quantum phenomena. Time Dilation and the Nature of Gravitational and Inertial ForcesZenodo DOI: 10.5281/zenodo.17543059Explores the TSO perspective on time dilation and the interplay of inertial and gravitational forces. Time–Space Oscillations and ElectromagneticsZenodo DOI: 10.5281/zenodo.17591325Applies the TSO model to electromagnetic phenomena, revealing novel interpretations of wave propagation and field interactions. Time–Space Oscillations and Quantum Mechanics Zenodo DOI: 10.5281/zenodo.17670668Extends TSO to encompass quantum mechanical principles, including Heisenberg uncertainty, Schrödinger dynamics, path integrals, entanglement, zero-point energy, and the Quantum Zeno effect. For an overview of related work and publications, visit:https://ndl1971.github.io/time-space-oscillations/
On the basis of quantum-mechanical realism and the philosophical view that “determinism and indeterminism are mutually dual and symbiotically coexisting,” philosophical and physical perspectives are integrated to propose the “constraint–uncertainty” hypothesis in this paper. Combined with a temporal ontology of “a determined history and an open future,” a unified interpretative framework for quantum phenomena is established. First, in conjunction with experimental results on fullerene quantum interference and spin decoherence in diamond NV centers, the core hypothesis is proposed: when a system is subject to a single dominant constraint, its behavior exhibits deterministic characteristics and uncertainty is suppressed; when subject to multiple competing constraints, its behavior becomes indeterministic and determinism is weakened. It is further clarified that the “constraint” in this work refers to a physically real underlying dynamical mechanism. Second, based on this hypothesis and temporal ontology, a self-consistent interpretation is provided for quantum phenomena such as wave-function superposition and quantum entanglement. It is argued that the “constraint–uncertainty” hypothesis offers an ontological basis for the Heisenberg uncertainty principle, thereby correcting the imprecise characterization in mainstream quantum theory that reduces uncertainty to an intrinsic property of particles. This paper further explores the tension between quantum mechanics and general relativity, suggesting that they correspond to different physical regimes governed by distinct constraint structures. A complete constraint-based model should naturally incorporate gravity, potentially offering a new perspective for the unification of the two theories. This paper further elaborates on the issues concerning temporal ontology. The author holds that variability serves as the meta-setting of physics, and the irreversibility of time is essentially a combination of variability and uncertainty, which also gives rise to the openness of the future. The uniqueness of the subject’s existential position determines the definiteness of history.
The RQF is primarily a quantum foundations solution. Its chief motivation is to answer basic story-telling questions about Nature that the last 125 years have been unable to answer, owing to foundational disarray stemming from the conceptual intractability that has pervaded quantum physics. The RQF is all about the what, where, when, and how of quantum physics, as it plays out in the space-time arena of special and general relativity. It is based on a quantum ontology consisting of two fundamental ontic entities, called W-state and P-state, that respectively account for the wave- and particle-like aspects of quantum systems. W-state is wave-like, local, physical state, embodying the physicality of matter-energy, whereas P-state is particle-like, global, informational state, mediating entanglement effects and particle holism. Historically, the single most difficult challenge of putting quantum theory on a realist footing has been to provide mechanistic explanation of how weak non-locality, manifest in entanglement phenomenology, can be squared with the no-signaling stricture of special relativity (SR). The challenge is so centrally important to making sense of quantum physics that the theoretical minimum of the RQF is dedicated exclusively to addressing and resolving it. Work to date consists of four papers: [1] The pilot paper (https://dx.doi.org/10.2139/ssrn.5920722) focuses principally on quantum foundations and the theoretical minimum of W-state and P-state, showing how the two separate realms of reality can interoperate to produce non-local entanglement effects fully compliant with the causal structure and no-signaling stricture of special relativity. [2] https://dx.doi.org/10.2139/ssrn.6194219 is a shorter paper, identifying multi-situationality, not probability, as the central metaphor of quantum physics. Multi-situationality signifies the facet of physical reality that permits two or more situations to coexist, despite their being mutually incompatible by all classical reckoning. The RQF interprets the uncertainty principle as a mandate for a minimal level of multi-situationality in quantum systems. [3] zenodo.org/records/20581089 elaborates on the detailed structure of W-state, which is the structure of elementary particle matter in the Standard Model: leptons, neutrinos, and quarks. Quantum theory and the core subject matter of nuclear physics are rebuilt from the ground up in the new realist framework. [4] zenodo.org/records/20671848 extends the RQF to cosmology, addressing the key topics of quantum gravity, origin of inertia, and phasal polarity (matter and anti-matter). It offers an Analysis of Alternatives that was historically lacking in the acceptance of Lemaitre's primeval atom.