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 \( \Gamma_N = N \Gamma_1 + \sum_{i\neq j} \Omega_{ij} \cos(k r_{ij}) \); superradiant decay rate \( \Gamma_{\text{supra}} \propto N^2 \Gamma_1 \) for fully coherent ensemble; subradiant modes scale as \( \Gamma_{\text{sub}} \propto \Gamma_1/N \); tryptophan network excitonic coupling \( J_{ij} = \frac{\mu_i \mu_j}{4\pi\epsilon_0 r_{ij}^3} (1 - 3\cos^2\theta_{ij}) \) (dipole-dipole, near-field); UV absorption peak ~280 nm (tryptophan), emission ~340 nm; coherence length \( L_c \sim \lambda/(2\pi n) \) sets effective N via \( N_{\text{eff}} = \rho L_c^3 \). | 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