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The Spiral Structure Model: A Geometric Phenomenology of Wave-Particle Duality, Spin, and Electromagnetic Coupling

Cheng J, Cheng D

2026

Abstract

We present the Spiral Structure Model (SSM), a phenomenological model in the tradition of Bohr's atomic theory: deliberately restricted to kinematics and geometry, it trades computational depth for ontological clarity and exposes its predictions to direct experimental disproof. Three postulates suffice: (I) the photon is a pointlike energy quantum moving on a helical worldline whose axial (signal) speed and azimuthal (tangential) speed both equal c; (II) physical space is an elastic, relativistically covariant medium sustaining vortex excitations; (III) the electron is a stable topological vortex defect of that medium. From these we obtain, with the logical status of every step labeled: the photon's intrinsic angular momentum mc rγ = ℏ as a conditional geometric theorem, anchored in the classical wave identity L = E/ω; a logarithmic vortex self-energy that confines the helical quantum in a genuine stable minimum with zero free parameters; a geometric reason for the two polarization states and the absence of a longitudinal mode; the 720-degree periodicity of the electron, anchored in the homotopy π1(SO(3)) = Z2, yielding spin ℏ/2; the fine-structure constant as a ratio of structural scales, α = re/a0; a phase-coupling account of two-slit interference; a double-helix ontology of entangled pairs reproducing the CHSH value S = 2√2; and two falsifiable discriminants, namely an intrinsic photonic dark core locked to the wavelength and independent of numerical aperture, and a…

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