Swarm Field Theory, Coherence Geometry and Unified Field Framework
Published September 17, 2025 | Version v1
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Elementary Charge: A Swarm Theory Derivation

Description

Abstract:  This paper derives the elementary charge (e) from coherence geometry within Swarm Theory. Conventional physics treats e as a fundamental unit of charge with no structural basis. Here, e emerges directly from lattice geometry, coherence tension (ΔI), and helical wave projection.

Key results:

  • Geometric origin: e is not arbitrary but a direct consequence of coherence membrane structure.
  • Consistency: The same calibrated parameters that yield Planck’s constant (h) and the fine-structure constant (α) also reproduce e with no free adjustment.
  • Implication: Charge arises as a geometric property of condensed waves, not as an independent constant.

This result advances the electromagnetic unification within Swarm Theory: h, α, e, ε₀, μ₀, and Z₀ all reduce to geometric consequences of lattice coherence.

Additional materials and related work are available on GitHub: 

https://github.com/crumpler4/Swarm-Theory-Unified-Field-Equation-Series

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References

  • Sommerfeld, A. (1916). Zur Quantentheorie der Spektrallinien. Annalen der Physik, 356(17), 1–94.
  • Millikan, R. A. (1917). The electron and the light-quant from the experimental point of view. Nature, 100, 409–414.
  • Millikan, R. A. (1913). On the elementary electrical charge and the Avogadro constant. Physical Review, 2(2), 109–143.
  • Einstein, A. (1905). On a heuristic viewpoint concerning the production and transformation of light. Annalen der Physik.
  • Crumpler, J. P. (2025). Swarm Theory: The Position Hypothesis. Zenodo. https://doi.org/10.5281/zenodo.17140887
  • Crumpler, J. P. (2025). Vacuum Wave Impedance from Coherence Geometry: A Swarm Theory Derivation. Zenodo. https://doi.org/10.5281/zenodo.17140967
  • Crumpler, J. P. (2025). Vacuum Permittivity from Coherence Geometry: A Swarm Theory Derivation. Zenodo. https://doi.org/10.5281/zenodo.17141112
  • Crumpler, J. P. (2025). Sommerfeld's Constant from Coherence Geometry: A Swarm Theory Derivation. Zenodo. https://doi.org/10.5281/zenodo.17130007
  • Crumpler, J. P. (2025). Planck's Constant from Coherence Geometry: A Swarm Theory Derivation. Zenodo. https://doi.org/10.5281/zenodo.17129863
  • Crumpler, J. P. (2025). Swarm Theory Explained: A Plain Language Guide to the Unified Field Equation. Zenodo. https://doi.org/10.5281/zenodo.17118629
  • Crumpler, J. P. (2025). Swarm Theory: A Unified Field Framework. Zenodo. https://doi.org/10.5281/zenodo.17118609
  • BIPM. (2019). The International System of Units (SI), 9th edition. Bureau International des Poids et Mesures. https://www.bipm.org/en/publications/si-brochure
  • Bousso, R. (2002). The Holographic Principle. Reviews of Modern Physics, 74, 825–874. https://doi.org/10.1103/RevModPhys.74.825
  • Susskind, L. (1995). The World as a Hologram. Journal of Mathematical Physics, 36(11), 6377–6396. https://doi.org/10.1063/1.531249
  • 't Hooft, G. (1993). Dimensional Reduction in Quantum Gravity. Salamfestschrift (Conf. Proc. C 930308, pp. 284–296). arXiv:gr-qc/9310026
  • Sommerfeld, A. (1916). Zur Quantentheorie der Spektrallinien. Annalen der Physik, 356(17), 1–94. https://doi.org/10.1002/andp.19163561702
  • Maxwell, J. C. (1865). A dynamical theory of the electromagnetic field. Philosophical Transactions of the Royal Society of London, 155, 459–512. https://doi.org/10.1098/rstl.1865.0008
  • Einstein, A. (1915). Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik.