Quantum Coherence in Microtubule Tryptophan Networks: Superradiant Scaling from N to N² — E8 Intelligence Research

FINDING: Dicke superradiance theory applied to microtubule tryptophan networks shows collective emission scaling transitions from N to N², with molecular-dynamics-derived geometries determining coherence length and optical response. | MATH: Dicke cooperativity parameter \( Γ_N = N Γ_1 + ∑i≠ j Ωᵢⱼ cos(k rᵢⱼ) \); superradiant decay rate \( Γₛᵤₚᵣₐ ∝ N^2 Γ_1 \) for fully coherent ensemble; subradiant modes scale as \( Γsub ∝ Γ_1/N \); tryptophan network excitonic coupling \( Jᵢⱼ = {μ_i μ_j}{4πε_0 rᵢⱼ^3} (1 - 3cos^2θᵢⱼ) \) (dipole-dipole, near-field); UV absorption peak ~280 nm (tryptophan), emission ~340 nm; coherence length \( L_c ~ λ/(2π n) \) sets effective N via \( Neff = ρ L_c^3 \). | CONNECTION: Microtubule lattice is a 13-protofilament helical structure with 8 nm tubulin dimer repeat — this is a **cylindrical crystallographic lattice** with scre Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com