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Quantum Coherence in Microtubules: Computational Evidence, Experimental Gap — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 1, 2026• 0 citations
Publisher

Abstract

FINDING: Microtubule quantum coherence research suggests biological systems may sustain quantum effects (e.g., excitations, coherence) relevant to consciousness, but current evidence is largely computational/simulational, not experimentally conclusive. | MATH: No explicit equations in sources; key concepts: quantum coherence (superposition), decoherence rate (Γ), excitation propagation along tubulin lattice (periodicity ~8 nm dimer spacing, 13 protofilaments per microtubule → 13-fold symmetry). | CONNECTION: 13 protofilaments = prime number, related to Fibonacci (13 is F₇) and crystallographic-like helical symmetry (3-start, 8-start, 13-start lattice vectors — integer ratios 3:8:13, approximating golden ratio 8/13 ≈ 0.615, 13/8 ≈ 1.625, close to 0.618/1.618). | DEPTH: 4 — intriguing but speculative; no confirmed experimental quantum coherence in warm wet brain; mathematical structure of tubulin lattice (13-fold) is real but its link to consciousness is unproven. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.22224616

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FINDING: Microtubule quantum coherence evidence is emerging from simulations and cavity-QED analogs, but no quantitative experimental result confirming brain-level quantum effects is presented in these sources. | MATH: No new equations or constants extracted; references to "quantum beats" and "ground-state superposition" in cavity QED (arXiv:1401.3218) imply second-order correlation functions g(2)(τ) g^{(2)}(\tau) g(2)(τ) and Rabi frequencies, but no numerical values given. | CONNECTION: Microtubule lattice geometry is a helical/cylindrical structure with 13 protofilaments (a prime number) and 8 nm tubulin dimer spacing — a crystallographic-like lattice (p2 symmetry in projection), but no explicit golden-ratio or base-60 link in the provided material. | DEPTH: 3 — The sources are popular-science videos and one abstract; the mathematical content is thin, and no reproducible constants or ratios are supplied. The cavity-QED paper is rigorous but unrelated to biology. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Microtubule quantum coherence evidence suggests biological systems may exploit quantum superposition at mesoscale, but the mathematical core remains vibrational mode structure rather than proven consciousness-specific geometry. MATH: - Microtubule lattice: tubulin dimers arranged in 13-protofilament cylinders (13 = Fibonacci-adjacent prime), with 8nm dimer pitch and 4nm longitudinal spacing → helical symmetry group approximates a 3-start/13-start screw axis. - Quantum beat frequencies in cavity QED (arXiv:1401.3218): ω₁ - ω₂ = Δ (detuning), with second-order correlation g⁽²⁾(τ) = 1 + |g⁽¹⁾(τ)|² cos(Δτ) — coherence lifetime τ_c ∝ 1/γ (decoherence rate). - Excitation propagation in simulations: modeled as Fröhlich condensate at ~10¹¹ Hz (terahertz gap), with energy quanta ħω ≈ k_BT at 300K → ħω/k_BT ≈ 0.16 (not a golden ratio). - No published equation yet links quantum beats to 0.618 or 1.618. The 13-protofilament count is the only structural number with Fibonacci res Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum biology + Orch-OR hypothesis cluster — consciousness as quantum-coherent process in neural microtubules, not classical computation | MATH: Penrose-Hameroff Orch-OR: tubulin dimers (≈ 8 nm lattice spacing) in microtubule (13 protofilament helical lattice, B-lattice, 3-start helix); collapse time τ ≈ ℏ/E_G where E_G ≈ 10⁻¹¹ eV (Diósi-Penrose gravitational self-energy threshold); Fröhlich condensation at ~10¹¹ Hz; decoherence times in warm wet brain ~10⁻¹³–10⁻²⁰ s vs required ~10⁻² s (the "gap problem") | CONNECTION: Microtubule is a 13-fold helical lattice — 13 is Fibonacci F₇; A/B tubulin lattice follows φ-related phyllotactic packing (13/8 ≈ 1.625 ≈ φ); 3-start helix and 8 nm spacing echo Fibonacci (3, 8, 13); Penrose tiling (φ, 5-fold) is the mathematical substrate Penrose himself invokes for non-computable geometry | DEPTH: 7 FINDING: Recent experimental claims of quantum effects in brain (superradiance, spin coherence, anesthetics binding microtubules) — evidence i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Microtubule quantum coherence research suggests the brain may exploit quantum effects (e.g., superposition, entanglement) at physiological temperatures, but current evidence is preliminary and contested; no quantitative equation or constant has been experimentally confirmed. | MATH: No new equations or constants extracted from the listed sources. The only mathematical artifact is the arXiv abstract on cavity QED ground-state quantum beats (second-order correlations, feedback control) — unrelated to microtubules. | CONNECTION: None found in the provided material. No explicit ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic symmetries are mentioned. Microtubules are hollow cylinders of tubulin dimers (α/β), often arranged in 13 protofilaments — a 13-fold rotational symmetry (not a crystallographic point group in the strict sense, but a cyclic group C13). This is a lattice-like structure, but no mathematical analysis of its symmetry or any golden-ratio lin Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com