From Quantum Fisher to Entropic Coherence: First-Principles of 1/E^2 Suppression

We propose a universal, energy‐dependent suppression law scaling as 1/E^2 that governs the transition from quantum to classical behavior across all fundamental interactions. Drawing on five independent derivations—effective field theory (one‐loop RG), phase‐space localization (Wigner/Jaynes entropy), quantum Fisher information, de Broglie/WKB semiclassics, and the empirical running of the fine‑structure constant—we show they all point to the same “coherence‐decay” function G_eff(E) = G0 / f(E), where f(E) = 1 + (E/E0)^2 ⇒ f(E)^(-1) ~ E0^2 / E^2 (for E ≫ E0), which (i) preserves coupling ratios, (ii) resolves classical singularities, and (iii) yields falsifiable predictions. We then compare fits of α(E) to the conventional logarithmic RG form and to the 1/E^2 ansatz, unify our notation across all derivations, and discuss the key open problem of determining the suppression scale E0.