Wave-Mechanical α

Power-law α¹ scaling confirmed via sub-wavelength dipole source coupling. This establishes the leading-order behaviour of the fine-structure constant from first principles.

Last updated: August 2026

The Investigation

The fine-structure constant is one of the most precisely measured constants in physics. Its derivation from first principles — without appeal to experiment — is a longstanding goal of any fundamental theory.

The wave-mechanical approach investigates whether the power-law dependence of (i.e., whether the coupling scales as , , etc.) can be determined from the Weber force structure alone, without knowing the numerical value.

The Dipole Coupling Setup

The investigation models the electron as a sub-wavelength dipole source — a dipole whose size (Compton wavelength ) is much smaller than the wavelength of the radiation it emits ().

The absorbed power fraction for such a sub-wavelength dipole scales with a power of the coupling constant . The question is: which power?

Sub-wavelength dipole absorption power scaling

The Result

Finding GAP2-WM-01 · Status [E] · Banked August 2026

The absorbed power from a sub-wavelength dipole source in the Weber electrodynamic framework scales as exactly (linear in the fine-structure constant). This rules out and power laws. Combined with the known numerical value, this constrains the geometric derivation to produce linear-in-α at leading order.

What This Establishes and What Remains Open

[E]Power-law exponent n = 1 confirmed for sub-wavelength dipole coupling

[E]Weber force structure gives this result consistently across two independent calculation methods

[M]The geometric prefactor that gives the numerical value α ≈ 1/137 from S³ geometry is viable but not yet frozen

[O]Full first-principles derivation of the numerical value of α — open investigation

Integrity Status

[E]

Established. The power-law result

is confirmed and banked as of August 2026. The source document is a_geom_gap2_wave_mechanical_alpha_results. This result does not depend on any [M] or [O] upstream result — it is a direct consequence of the Weber force structure and sub-wavelength dipole coupling.

Source Documents

The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.

a_geom_gap2_wave_mechanical_alpha_results.md

Documents open in the CPT Research Library — a formatted viewer for all source research files.