Φ³ - The Origin of the Fine-Structure Constant - The Electron Suspended Between Light and Mass

This work presents a geometric interpretation of the fine-structure constant α from the spiral dynamics of the fundamental Φ³ field. In this model, the electron is not treated as a point particle nor merely as a probabilistic wave, but as an intermediate spiral structure suspended between two limiting configurations of the field: the fully uncoiled spiral of light and the maximally compressed spiral of the proton. The constant α emerges as a measure of the spiral tension required for the electron to maintain a stable state between these two limits. In the original spiral-tension formulation, the model reproduced the experimental value of α with a relative deviation of approximately 0.07%. In the revised version, this result is strengthened by introducing a corrected golden-phase interpretation of α⁻¹. The inverse fine-structure constant is expressed through a Φ-based decomposition previously explored in golden-ratio approaches, but here reinterpreted as the phase floor underlying the Φ³ spiral field: α⁻¹ ≈ 360φ⁻² − 2φ⁻³ + (3φ)⁻⁵. This corrected phase formulation gives: α⁻¹ = 137.0359991648, compared with the CODATA/NIST value: α⁻¹ = 137.035999177(21). The absolute deviation is therefore approximately 1.2 × 10⁻⁸, within the current CODATA/NIST uncertainty interval. Relative to the initial ~0.07% spiral-tension estimate, the effective deviation is reduced by several million times. The corrected Φ-decomposition may not yet be the most elegant possible expression of the underlying structure. Rather, it should be read as a precise surface trace of a deeper Φ³ field law still to be fully derived. The aim of this work is not to claim priority over every numerical appearance of Φ in α, but to show that these Φ-based structures may belong to a coherent field dynamics. Within this framework, α⁻¹ behaves as a corrected golden phase, while α itself measures the coupling tension generated by the deformation of that ideal phase. This work proposes a unified geometric interpretation of light, charge, mass, and electromagnetic coupling, offering a potential bridge between quantum mechanics, field structure, and nuclear geometry.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-20
DOI
https://doi.org/10.5281/zenodo.17818532
Primary Topic
Quantum and Classical Electrodynamics
Type
preprint
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preprint

Φ³ - The Origin of the Fine-Structure Constant - The Electron Suspended Between Light and Mass

Zenodo (CERN European Organization for Nuclear Research)
Quantum and Classical Electrodynamics
preprint

Φ³ - The Origin of the Fine-Structure Constant - The Electron Suspended Between Light and Mass

preprint en

Abstract

This work presents a geometric interpretation of the fine-structure constant α from the spiral dynamics of the fundamental Φ³ field. In this model, the electron is not treated as a point particle nor merely as a probabilistic wave, but as an intermediate spiral structure suspended between two limiting configurations of the field: the fully uncoiled spiral of light and the maximally compressed spiral of the proton. The constant α emerges as a measure of the spiral tension required for the electron to maintain a stable state between these two limits. In the original spiral-tension formulation, the model reproduced the experimental value of α with a relative deviation of approximately 0.07%. In the revised version, this result is strengthened by introducing a corrected golden-phase interpretation of α⁻¹. The inverse fine-structure constant is expressed through a Φ-based decomposition previously explored in golden-ratio approaches, but here reinterpreted as the phase floor underlying the Φ³ spiral field: α⁻¹ ≈ 360φ⁻² − 2φ⁻³ + (3φ)⁻⁵. This corrected phase formulation gives: α⁻¹ = 137.0359991648, compared with the CODATA/NIST value: α⁻¹ = 137.035999177(21). The absolute deviation is therefore approximately 1.2 × 10⁻⁸, within the current CODATA/NIST uncertainty interval. Relative to the initial ~0.07% spiral-tension estimate, the effective deviation is reduced by several million times. The corrected Φ-decomposition may not yet be the most elegant possible expression of the underlying structure. Rather, it should be read as a precise surface trace of a deeper Φ³ field law still to be fully derived. The aim of this work is not to claim priority over every numerical appearance of Φ in α, but to show that these Φ-based structures may belong to a coherent field dynamics. Within this framework, α⁻¹ behaves as a corrected golden phase, while α itself measures the coupling tension generated by the deformation of that ideal phase. This work proposes a unified geometric interpretation of light, charge, mass, and electromagnetic coupling, offering a potential bridge between quantum mechanics, field structure, and nuclear geometry.

Zenodo (CERN European Organization for Nuclear Research)
Quantum and Classical Electrodynamics
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Φ³ - The Origin of the Fine-Structure Constant - The Electron Suspended Between Light and Mass · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS