Published August 6, 2026 | Version version 3.0

Maxwell's Electron, Version 3. Spin, Charge, Inertia and Mass from a Single Twist in Elastic Spacetime

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This paper develops a mechanistic, parameter-free account of the electron from two ingredients: Maxwell's equations and MacCullagh's rotationally elastic vacuum. The electron is modelled as one displacement-current spine of a dual-analytic-path photon, severed at pair production and reflected into time. 

This resulting temporal discontinuity---christened here the \textit{Heisenberg Strut}---acts as a topological hub that traps the reflecting displacement current. It stores energy as temporally stretched spacetime in a $\pi$-twist. This stored elastic energy is the \textit{gravitational mass} of the electron, and the topological twist itself is its \textit{spin}. The circulating displacement current leaves the temporal poles at a raised potential, providing the mechanical origin of \textit{charge} and the particle's \textit{magnetic moment}. 

The transverse scale $R_0 = \tfrac34\bar\lambda_C$ is fixed by requiring the parent photon to carry $\hbar$. A single displacement pass then yields half a Bohr magneton, and the two temporal passes reinforce to $\mu_B$, yielding $g=2$ from geometry alone. The charge circulation is even under the temporal reflection and reinforces, while the mechanical angular momentum is odd and cancels. The trapped wave is therefore spin-neutral (as $\beta$-decay requires), and the observed $\hbar/2$ is strictly the handedness of the spacetime tear. 

Inertia emerges as the energetic cost of dragging this locked strain field (which naturally propagates at $c$)
governed by the retarded wave equation of the medium. 
The relativistic Doppler shift of the two phases of the trapped half photon describe the Lorentz equation.
This paper shows inertial and gravitational mass originate in a single field observed in two states of motion.
The temporal power flux driving the $\pi$-twist (across the temporal discontinuity) fixes the defect cross-section
at exactly $8\,l_p^2$, with the rest mass cancelling identically with the photon energy mass equivalent.
Concurrently, the electrostatic self-energy of the temporal poles yields $\tfrac{\alpha}{2\pi}m_ec^2$, the Schwinger coefficient. 

Finally, the charged-lepton mass ratios appear to follow from the pure-shear buckling modes of this same defect (recovering Koide's $K=2/3$). The electron model principally involves the medium's temporal response.
A model for strain in baryons would involve spatial co-deformation
i.e. you use the handles present in leptons to stretch the temporal strut into a gluon.

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Copyrighted
2026-08-06