Quantum Coherence in Biology: Photosynthesis Proven, Microtubule Theory Unsupported — E8 Intelligence Research

Abstract

FINDING: Quantum effects in microtubules (Penrose-Hameroff Orch-OR) remain unproven but mathematically constrained by decoherence timescales and lattice geometry; quantum biology (photosynthesis, magnetoreception) shows functional quantum coherence at ambient temperatures. | MATH: Decoherence time τ_d ≈ ħ²/(k_B T · E_coupling) — for microtubules, estimates range 10⁻¹³–10⁻⁴ s, far below neural timescales (10⁻³ s). Orch-OR requires τ_d > 10⁻³ s, implying E_coupling < 10⁻¹¹ eV — unphysical for tubulin dipoles (~1 eV). Quantum biology: exciton coherence length L_c ≈ √(ħD/k_B T) in Fenna-Matthews-Olson complex, D ≈ 10⁻⁹ m²/s, T = 300 K → L_c ≈ 1–2 nm, matching pigment spacing. | CONNECTION: Microtubule lattice is a 13₃ helical symmetry (13 protofilaments, 3-start helix) — a crystallographic screw axis, related to Fibonacci phyllotaxis (13 = Fibonacci number). The 13₃ symmetry yields a pitch ratio ≈ 0.618 (golden angle 137.5° between tubulin dimers). This is the only geometric link: the gold Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com