Gravity · 2026

Gravity's Coupling is an Area: α_G = Planck-area / Compton-area, and the classical double copy made geometric

R. G. Measey

Abstract

The gravitational fine-structure constant of the electron, α_G = Gm_e²/ℏc ≈ 1.75 × 10⁻⁴⁵, is usually treated as an inexplicably tiny number. In the CPT framework, it is an exact ratio of areas: the Planck area over the Compton area. This is the classical double copy made geometric: matter is a confined photon (spin-1), gravity is its electrodynamics squared (spin-2), and squaring a length (the single-copy charge l_Pl/λ_C) produces an area (the spin-2 coupling). This square is fully spent on the area: it carries zero residual factor of α, refuting the hope that a factor of α falls out of the double copy. The mass hierarchy remains an input; gravity's weakness is thus geometrised, not derived.

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