Heisenberg's Electron. From Point Location to Bivortical Region

This article continues the bivortical ontology of The Electron as a Double Vortex, concentrating on the uncertainty relations. Its central claim is direct: the position--momentum and energy--time relations are entirely true --- and entirely logical --- for an extended structure. Their apparent mystery comes from applying them to a point-like entity. In this reading, indeterminacy is a question posed to the wrong object. For a finite, deformable, gradient-structured electron region, the two relations describe complementary projections of one configurational event: position--momentum, the trade-off between regional definition and dynamical reorganisation; energy--time, the energetic cost and characteristic interval of the same event. Under double saturation, the two products become comparable, and their ratios approach \(c\) in the Compton regime. The electron is realised as a finite bivortical region of distributed mass-energy organised around a Bivortical Union Node (NUB), whose electrical signature preserves \(Q_e=-e\). Granting this structure a minuscule but non-zero volume removes the geometrical source of the divergences produced by dividing finite mass-energy by zero volume: for \(0<V_e<\infty\), the energydensity remains finite. These results join the phenomena already unified by the bivortical ontology: spin as torsional saturation, charge as a localised source, wave behaviour as propagated organisation, and now indeterminacy as the structured deformability of an extended region. The article also initiates three connected mathematical developments: configurational dynamics, the quirotor as a representation of internal vortical structure, and chironomy as the dynamics of local redistribution under preserved global invariants.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-24
DOI
https://doi.org/10.5281/zenodo.22946549
Primary Topic
Quantum Mechanics and Applications
Type
preprint
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preprint

Heisenberg's Electron. From Point Location to Bivortical Region

Daniel Avilés Hurtado
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
preprint

Heisenberg's Electron. From Point Location to Bivortical Region

Daniel Avilés Hurtado
preprint en

Abstract

This article continues the bivortical ontology of The Electron as a Double Vortex, concentrating on the uncertainty relations. Its central claim is direct: the position--momentum and energy--time relations are entirely true --- and entirely logical --- for an extended structure. Their apparent mystery comes from applying them to a point-like entity. In this reading, indeterminacy is a question posed to the wrong object. For a finite, deformable, gradient-structured electron region, the two relations describe complementary projections of one configurational event: position--momentum, the trade-off between regional definition and dynamical reorganisation; energy--time, the energetic cost and characteristic interval of the same event. Under double saturation, the two products become comparable, and their ratios approach \(c\) in the Compton regime. The electron is realised as a finite bivortical region of distributed mass-energy organised around a Bivortical Union Node (NUB), whose electrical signature preserves \(Q_e=-e\). Granting this structure a minuscule but non-zero volume removes the geometrical source of the divergences produced by dividing finite mass-energy by zero volume: for \(0<V_e<\infty\), the energydensity remains finite. These results join the phenomena already unified by the bivortical ontology: spin as torsional saturation, charge as a localised source, wave behaviour as propagated organisation, and now indeterminacy as the structured deformability of an extended region. The article also initiates three connected mathematical developments: configurational dynamics, the quirotor as a representation of internal vortical structure, and chironomy as the dynamics of local redistribution under preserved global invariants.

Zenodo (CERN European Organization for Nuclear Research)
Comunidad Autónoma de la Región de Murcia (ES)
Quantum Mechanics and Applications
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Heisenberg's Electron. From Point Location to Bivortical Region — Daniel Avilés Hurtado · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS