Deriving mu, alpha and the proton charge radius from Webers Force and Base-12 Geometry

Abstract The Standard Model treats the proton-to-electron mass ratio μ ≈ 1836.153, the fine-structure constant α ≈ 1/137.036, and the proton charge radius r_p ≈ 0.841 fm as independent empirical inputs. No first-principles explanation exists for any of them. This paper investigates whether all three quantities can be derived from a single geometric structure built on Weber's 1848 electromagnetic force law. The method is to promote Weber's pairwise force to a cosmological retarded-wave field (the Weber-Resonance field) by summing over all charges in the Hubble volume with a base-12 phase-resonance. The fundamental phase resonance is set by the abundance of hydrogen atoms in the universe. The helium correction exponents are derived from the eigenmode structure of the field equation. All inputs are discrete integers (12, 3), the geometric constant 4π, and the observed BBN helium fraction; no continuously adjustable parameters are used. Three principal results are obtained. (1) The mass ratio μ = 12³ × (17/16) × (1 + πα²/2) = 1836.154. (2) The fine-structure constant 1/α = [1728/(4π)] × (1 − 1/288) × (1 + α²/2) = 137.036. (3) The proton charge radius r_p = 4ħ/(m_p c) = 0.8412 fm. The framework predicts opposite-sign drift Δμ/μ ≈ −18 × Δα/α, distinguishable from GUT predictions. The results suggest that μ, α, and r_p are not independent parameters but reciprocal projections of a single base-12 resonance architecture perturbed by cosmic helium. The central open problem is whether the base-12 quantization can be derived from the field equation itself, rather than postulated. The predicted anti-correlation of constant drift provides a near-term observational test. Acknowledgment of AI Assistance: During the preparation of this manuscript, the author used Claude (Anthropic, 2025–2026) for the purposes of assisting with English-language editing, structuring prose, and reviewing the Python simulation code for clarity and correctness. All mathematical derivations, physical reasoning, numerical results, and scientific conclusions were produced solely by the author. The author has reviewed and edited all AI-assisted output and takes full responsibility for the content of this publication.