On the Non-Perturbative Nature of the 0-Sphere Model and Magnetic Monopole Absence: A Supplement on Structural Analysis and Physical Interpretation

[42 Supplement]

This supplementary comment discusses why the absence of magnetic monopoles can be naturally understood within the structural framework of the 0-Sphere Model, while explicitly acknowledging that a complete geometric formulation remains under development. The emphasis is placed on clarifying the current scope of the model and connecting the structural features of the energy conservation identity to the physical mechanisms of the two-kernel structure, phase-dependent energy localization, and the distinction between open-path and closed-loop line integrals.

The present note serves as a conceptual clarification complementary to earlier supplements on Zitterbewegung (zenodo.18356895), the anomalous magnetic moment (zenodo.18511664), and observer-dependent torsion (in preparation).

Core Structural Argument

The energy conservation identity of the 0-Sphere Model,

E₀ = E₀ [ cos⁴(ωt/2) + sin⁴(ωt/2) + ½sin²(ωt) ]

exhibits a natural structural asymmetry between its three terms. This asymmetry provides the basis for distinguishing electric charge from magnetization:

• Single-term contribution ½sin²(ωt): kinetic energy of the photon sphere — globally coherent, undivided, and identified with electric charge as a monopole quantity.
• Paired-term contribution cos⁴(ωt/2) + sin⁴(ωt/2): potential energies localized at spatially separated kernels A and B — inseparably coupled, giving rise to magnetization as an intrinsically dipolar quantity.

Because magnetization emerges from the gradient of the paired potential structure, no standalone magnetic monopole degree of freedom appears within the present formulation. The two kernels are dynamically inseparable through the photon sphere, and no mechanism exists to isolate a single kernel and assign it an independent magnetic charge.

Connection to the Line-Integral Framework

The structural prohibition of magnetic monopoles is further understood through the distinction developed in the line-integral trilogy (zenodo.18067760, zenodo.18135855, zenodo.18203433): the primacy of open-path line integrals is incompatible with a closed-surface Gauss's law for magnetism, while the globally coherent photon sphere admits standard enclosure and yields well-defined monopole charge for electricity.

Methodological Stance

This document follows the methodological framework established in the companion supplement on non-perturbative character and methodological scope (zenodo.18603340): conclusions are presented as a working structural hypothesis, not as a completed theoretical derivation. A rigorous geometric framework connecting the energy identity structure to Maxwell-type equations, fiber bundles, Chern classes, and topological invariants (Nakahara 2003) remains under development.

Key Results

• Structural identification of the single-term photon-sphere contribution with electric charge (monopole quantity via Gauss's law)
• Structural identification of the paired-term kernel contribution with magnetization (dipole quantity via Ampère's law)
• Working hypothesis for magnetic dipole inseparability derived from the architecture of the energy identity
• Conceptual alignment with the reinterpretation of the Dirac equation as absorption/emission radiative phases (zenodo.17760132)
• Connection to the predicted Zitterbewegung velocity vₛₛ ≈ 0.04047c via γ = 1 + a (zenodo.17765409, zenodo.18356895)
• Comparison with Dirac (1931) and 't Hooft–Polyakov monopole frameworks (tabular summary)

Open Directions

Future work should address: (i) geometric interpretation of term pairing via fiber bundles and connection structures; (ii) systematic relation to topological charge quantization (Chern classes, winding numbers); (iii) derivation of Maxwell's equations from the energy identity; (iv) experimental verification of the predicted Zitterbewegung velocity as indirect support for the internal circulation picture.

Related Publications

• Foundational framework: zenodo.16759284 (A Model of an Electron Including Two Perfect Black Bodies, 2018)
• Methodological companion: zenodo.18603340 (Non-Perturbative Nature and Fine-Structure Constant, 2026)
• Zitterbewegung supplement: zenodo.18356895 (Geometrical Confinement: Rest Mass and ZB, 2026)
• Gravitational-like phenomena: zenodo.18511664 (Detailed Exposition, 2026)
• Line-integral trilogy: zenodo.18067760, zenodo.18135855, zenodo.18203433
• Vacuum energy / integral ontology: zenodo.18275142
• Dirac equation reinterpretation: zenodo.17760132
• Spin from Berry phase / vₛₛ prediction: zenodo.17765409