From Light to the Fine Structure Constant: A Mechanical Account of How the Electron and Special Relativity Emerge from Photon Geometry.

This work demonstrates that the electron, special relativity, and the fine structure constant are not independent postulates of physics but geometric consequences of the structure of the photon. Starting from Maxwell's equations alone, a finite, localised, helical electromagnetic field configuration — the Analytic Path (AP) photon — is identified whose angular momentum ℏ\hbarℏ is a topological property of its geometry rather than an assigned quantum number. When a high-energy AP photon splits at its geometric midpoint under the torque of a strong Coulomb field, each half enters a temporal loop — a half-photon bouncing between forward and backward temporal poles separated by δt=ℏ/(mec2)\delta t = \hbar/(m_e c^2)δt=ℏ/(mec2). This object is the electron. Its properties follow without postulation from the loop geometry: rest mass from the trapped field energy, charge from the time-averaged displacement current of the cycling half-photon, spin ℏ/2\hbar/2ℏ/2 from the projection of the loop's angular momentum onto a measurement axis, and g=2g = 2g=2 from the two-lobe structure of the half-photon path. Special relativity emerges from four lines of Doppler algebra. A moving electron's temporal loop has Doppler-shifted forward and backward phases, each carrying half the half-photon's energy. The Lorentz energy relation E=γmec2E = \gamma m_e c^2E=γmec2 and momentum relation p=γmevp = \gamma m_e vp=γmev follow exactly, with no postulates about the nature of space or time. Time dilation and length contraction are properties of objects built from electromagnetic fields, not properties of spacetime itself. The fine structure constant α≈1/137\alpha \approx 1/137α≈1/137 appears naturally as the ratio of the Coulomb energy at the Compton scale to the electron rest mass energy: U(λˉC)=αℏcλˉC=αmec2U(\bar\lambda_C) = \frac{\alpha \hbar c}{\bar\lambda_C} = \alpha m_e c^2U(λˉC)=λˉCαℏc=αmec2This is not a coincidence but a structural consequence of the temporal loop geometry: the electromagnetic coupling constant is precisely the perturbative correction that electromagnetism represents at the scale of the electron's own internal structure, consistent with QED perturbation theory. Additional results include: a mechanical grounding of the energy-time uncertainty relation ΔE Δt≥ℏ/2\Delta E \, \Delta t \geq \hbar/2ΔEΔt≥ℏ/2 as the finite period of the temporal loop rather than an irreducible fuzziness of nature; a resolution of the pair production energy paradox showing that charge cannot be created instantaneously but accumulates over the first loop cycle as a rectified displacement current; a mechanical account of quantum entanglement as the two ends of a single four-dimensional field structure whose correlations satisfy E(α,β)=−cos⁡(2(α−β))E(\alpha,\beta) = -\cos(2(\alpha-\beta))E(α,β)=−cos(2(α−β)) by angular momentum conservation; and a falsifiable prediction of transient decorrelation in Bell experiments with sub-10 ns polariser switching.