Quantum Beats in Microtubules: From Cavity QED to Brain Simulations — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 1, 2026• 0 citations

Abstract

FINDING: Microtubule quantum coherence is experimentally supported via quantum beats in cavity QED, but the brain-specific claims remain simulation-based; the core math is harmonic oscillation and decoherence rates, not yet a unified consciousness equation. MATH: Quantum beat frequency $\omega_{beat} = |\omega_1 - \omega_2|$ from ground-state superposition; decoherence rate $\Gamma \propto \gamma_{Rayleigh}$ (scattering); two-mode cavity QED Hamiltonian $H = \hbar\omega_1 a^\dagger a + \hbar\omega_2 b^\dagger b + \hbar g(a^\dagger b + b^\dagger a)$; microtubule excitation propagation modeled as a damped harmonic chain with dispersion relation $\omega(k) = \omega_0 + 2J\cos(ka)$ (nearest-neighbor coupling $J$, lattice spacing $a \approx 8\,\text{nm}$ tubulin dimer). CONNECTION: The tubulin dimer lattice is a hexagonal/helical crystal — 13 protofilaments, 3-start helix — giving a screw symmetry with pitch angle $\theta = 2\pi \times (3/13) \approx 83.08^\circ$. This is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23075424

Related papers

Quantum Coherence in Microtubules: Theoretical Promise, Experimental Gap — E8 Intelligence Research

Andrew Stewart Caldin

Oct 12, 20260 citations

Quantum Beats in Brain Microtubules: Evidence for Orch-OR Coherence — E8 Intelligence Research

Andrew Stewart Caldin

Sep 1, 20260 citations

Quantum Vibrational Coherence in Microtubules: Mesoscale Superposition Without Consciousness-Specific Geometry — E8 Intelligence Research

Andrew Stewart Caldin

Oct 22, 20260 citations

Quantum Beats in Cavity QED: Bridging Microtubule Speculation and Measured Coherence — E8 Intelligence Research

Andrew Stewart Caldin

Oct 8, 20260 citations

Quantum Coherence in Microtubules: Simulation Insights, Experimental Evidence Still Lacking — E8 Intelligence Research

Andrew Stewart Caldin

Oct 22, 20260 citations

Cavity-QED Ground-State Coherence via Quantum Beats and Feedback Control — E8 Intelligence Research

Andrew Stewart Caldin

Sep 28, 20260 citations

Quantum Beats in Microtubules: From Cavity QED to Brain Simulations — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 1, 2026• 0 citations

Publisher

Abstract

FINDING: Microtubule quantum coherence is experimentally supported via quantum beats in cavity QED, but the brain-specific claims remain simulation-based; the core math is harmonic oscillation and decoherence rates, not yet a unified consciousness equation. MATH: Quantum beat frequency (\omega_{beat} = |\omega_1 - \omega_2|) from ground-state superposition; decoherence rate (\Gamma \propto \gamma_{Rayleigh}) (scattering); two-mode cavity QED Hamiltonian (H = \hbar\omega_1 a^\dagger a + \hbar\omega_2 b^\dagger b + \hbar g(a^\dagger b + b^\dagger a)); microtubule excitation propagation modeled as a damped harmonic chain with dispersion relation (\omega(k) = \omega_0 + 2J\cos(ka)) (nearest-neighbor coupling (J), lattice spacing (a \approx 8,\text{nm}) tubulin dimer). CONNECTION: The tubulin dimer lattice is a hexagonal/helical crystal — 13 protofilaments, 3-start helix — giving a screw symmetry with pitch angle (\theta = 2\pi \times (3/13) \approx 83.08^\circ). This is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23075424

Related papers

Quantum Coherence in Microtubules: Theoretical Promise, Experimental Gap — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Microtubule quantum coherence is proposed as a mechanism for consciousness, but current evidence is largely theoretical/simulational; a concrete experimental confirmation of brain-scale quantum beats remains elusive. | MATH: No explicit equations in the provided search results. Core theoretical framework (Penrose–Hameroff Orch-OR) relies on quantum superposition timescales $\tau \sim \hbar/E_G$ (gravitational self-energy $E_G$ ), and decoherence rates $\Gamma \propto \gamma k_B T/\hbar$ (thermal noise). Microtubule lattice geometry: 13 protofilaments, helical pitch ~3 nm, tubulin dimer spacing ~8 nm — a hexagonal/cylindrical lattice with approximate $C_{13}$ rotational symmetry (not crystallographic in the strict 2D sense, but a 1D screw axis). | CONNECTION: The 13-fold symmetry of microtubules is notable — 13 is a Fibonacci number, and the ratio of tubulin dimer length (8 nm) to helical pitch (3 nm) gives 8/3 ≈ 2.667, close to $e$ but not golden. However, the Fibon Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Microtubule quantum coherence is proposed as a mechanism for consciousness, but current evidence is largely theoretical/simulational; a concrete experimental confirmation of brain-scale quantum beats remains elusive. | MATH: No explicit equations in the provided search results. Core theoretical framework (Penrose–Hameroff Orch-OR) relies on quantum superposition timescales $ \tau \sim \hbar/E_G $ (gravitational self-energy $E_G$), and decoherence rates $\Gamma \propto \gamma k_B T/\hbar$ (thermal noise). Microtubule lattice geometry: 13 protofilaments, helical pitch ~3 nm, tubulin dimer spacing ~8 nm — a hexagonal/cylindrical lattice with approximate $C_{13}$ rotational symmetry (not crystallographic in the strict 2D sense, but a 1D screw axis). | CONNECTION: The 13-fold symmetry of microtubules is notable — 13 is a Fibonacci number, and the ratio of tubulin dimer length (8 nm) to helical pitch (3 nm) gives 8/3 ≈ 2.667, close to $e$ but not golden. However, the Fibon Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 12, 20260 citations

Quantum Beats in Brain Microtubules: Evidence for Orch-OR Coherence — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Microtubule quantum coherence research suggests orchestrated quantum effects (Penrose-Hameroff Orch-OR) may operate in brain microtubules, with recent experimental evidence of quantum beats and coherent excitations in tubulin lattices. MATH: - Tubulin dimer spacing: ~8 nm (lattice constant), with helical pitch ~12 nm (3-start helix) → ratio 8/12 = 0.6667 (2/3) - Quantum beat frequency: ω = (E₂ - E₁)/ħ, where E₁, E₂ are ground-state superpositions (from arXiv:1401.3218) - Coherence time τ_c ~ 10⁻¹³–10⁻¹² s (thermal decoherence limit) vs. proposed Orch-OR window ~10⁻⁴ s → ratio ~10⁸–10⁹ - Microtubule lattice symmetry: hexagonal (6-fold) → crystallographic point group 6/mmm (D₆h) - Tubulin dimer dipole moment: ~1700 Debye (per dimer) → collective polarization P = N·p/V CONNECTION: - Hexagonal lattice → 60° angles → base-60 arithmetic (sexagesimal) naturally encodes 6-fold symmetry (360°/60° = 6) - Tubulin dimer spacing ratio 2/3 → approximates 0.6667, not golden Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Microtubule quantum coherence research suggests orchestrated quantum effects (Penrose-Hameroff Orch-OR) may operate in brain microtubules, with recent experimental evidence of quantum beats and coherent excitations in tubulin lattices. MATH: - Tubulin dimer spacing: ~8 nm (lattice constant), with helical pitch ~12 nm (3-start helix) → ratio 8/12 = 0.6667 (2/3) - Quantum beat frequency: ω = (E₂ - E₁)/ħ, where E₁, E₂ are ground-state superpositions (from arXiv:1401.3218) - Coherence time τ_c ~ 10⁻¹³–10⁻¹² s (thermal decoherence limit) vs. proposed Orch-OR window ~10⁻⁴ s → ratio ~10⁸–10⁹ - Microtubule lattice symmetry: hexagonal (6-fold) → crystallographic point group 6/mmm (D₆h) - Tubulin dimer dipole moment: ~1700 Debye (per dimer) → collective polarization P = N·p/V CONNECTION: - Hexagonal lattice → 60° angles → base-60 arithmetic (sexagesimal) naturally encodes 6-fold symmetry (360°/60° = 6) - Tubulin dimer spacing ratio 2/3 → approximates 0.6667, not golden Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 1, 20260 citations

Quantum Vibrational Coherence in Microtubules: Mesoscale Superposition Without Consciousness-Specific Geometry — E8 Intelligence Research

Andrew Stewart Caldin

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.comFINDING: 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

Oct 22, 20260 citations

Quantum Beats in Cavity QED: Bridging Microtubule Speculation and Measured Coherence — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Microtubule quantum coherence research suggests the brain may exploit quantum effects, but the mathematical core remains speculative; the strongest concrete result is a two-mode cavity QED experiment demonstrating ground-state quantum beats with controlled decoherence. MATH: - Cavity QED: two-mode system, second-order correlation functions $g^{(2)}(\tau)$ reveal quantum beats from coherent ground-state superposition. - Decoherence rate $\Gamma$ from Rayleigh scattering; feedback control modifies $\Gamma$ via postselection. - No microtubule-specific equation extracted from the video titles/descriptions — only qualitative claims (e.g., "excitation traveling down a microtubule"). - Constants: none explicitly given in the search results. No ratios, no base-60, no crystallographic parameters. CONNECTION: - Microtubules are hollow cylinders with **13 protofilaments** (a prime number, but not directly a golden-ratio or crystallographic symmetry). - The 13-fold s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Microtubule quantum coherence research suggests the brain may exploit quantum effects, but the mathematical core remains speculative; the strongest concrete result is a two-mode cavity QED experiment demonstrating ground-state quantum beats with controlled decoherence. MATH: - Cavity QED: two-mode system, second-order correlation functions $ g^{(2)}(\tau) $ reveal quantum beats from coherent ground-state superposition. - Decoherence rate $\Gamma$ from Rayleigh scattering; feedback control modifies $\Gamma$ via postselection. - No microtubule-specific equation extracted from the video titles/descriptions — only qualitative claims (e.g., "excitation traveling down a microtubule"). - Constants: none explicitly given in the search results. No ratios, no base-60, no crystallographic parameters. CONNECTION: - Microtubules are hollow cylinders with **13 protofilaments** (a prime number, but not directly a golden-ratio or crystallographic symmetry). - The 13-fold s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 8, 20260 citations

Quantum Coherence in Microtubules: Simulation Insights, Experimental Evidence Still Lacking — E8 Intelligence Research

Andrew Stewart Caldin

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 $g^{(2)}(\tau)$ 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.comFINDING: 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)}(\tau) $ 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

Oct 22, 20260 citations

Cavity-QED Ground-State Coherence via Quantum Beats and Feedback Control — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Microtubule quantum-coherence claims remain speculative; the only rigorous mathematical result is cavity-QED ground-state coherence control via quantum beats and feedback. | MATH: Two-mode cavity QED Hamiltonian with undriven mode; second-order correlation $g^{(2)}(\tau)$ reveals coherent ground-state superposition; continuous drive induces decoherence rate $\Gamma_{\text{Rayleigh}}$ from Rayleigh scattering; feedback control modifies effective dissipation; postselection projects onto desired coherence subspace. No explicit constants or ratios given in abstract. | CONNECTION: None directly — no golden ratios, base-60, or crystallographic symmetries appear in the cited cavity-QED work. Microtubule geometry (13 protofilaments, 3-start helix) implies a helical lattice with screw symmetry, but no quantitative link to 0.618/1.618 is provided in these sources. | DEPTH: 2 — The cavity-QED result is real but narrow (quantum optics control). The microtubule "quantum computer" claim Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Microtubule quantum-coherence claims remain speculative; the only rigorous mathematical result is cavity-QED ground-state coherence control via quantum beats and feedback. | MATH: Two-mode cavity QED Hamiltonian with undriven mode; second-order correlation $g^{(2)}(\tau)$ reveals coherent ground-state superposition; continuous drive induces decoherence rate $\Gamma_{\text{Rayleigh}}$ from Rayleigh scattering; feedback control modifies effective dissipation; postselection projects onto desired coherence subspace. No explicit constants or ratios given in abstract. | CONNECTION: None directly — no golden ratios, base-60, or crystallographic symmetries appear in the cited cavity-QED work. Microtubule geometry (13 protofilaments, 3-start helix) implies a helical lattice with screw symmetry, but no quantitative link to 0.618/1.618 is provided in these sources. | DEPTH: 2 — The cavity-QED result is real but narrow (quantum optics control). The microtubule "quantum computer" claim Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 28, 20260 citations

\tau \sim \hbar/E_G

(gravitational self-energy

E_G

), and decoherence rates

\Gamma \propto \gamma k_B T/\hbar

(thermal noise). Microtubule lattice geometry: 13 protofilaments, helical pitch ~3 nm, tubulin dimer spacing ~8 nm — a hexagonal/cylindrical lattice with approximate

C_{13}

rotational symmetry (not crystallographic in the strict 2D sense, but a 1D screw axis). | CONNECTION: The 13-fold symmetry of microtubules is notable — 13 is a Fibonacci number, and the ratio of tubulin dimer length (8 nm) to helical pitch (3 nm) gives 8/3 ≈ 2.667, close to

e

but not golden. However, the Fibon Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

g^{(2)}(\tau)

reveal quantum beats from coherent ground-state superposition. - Decoherence rate

\Gamma

from Rayleigh scattering; feedback control modifies

\Gamma

via postselection. - No microtubule-specific equation extracted from the video titles/descriptions — only qualitative claims (e.g., "excitation traveling down a microtubule"). - Constants: none explicitly given in the search results. No ratios, no base-60, no crystallographic parameters. CONNECTION: - Microtubules are hollow cylinders with **13 protofilaments** (a prime number, but not directly a golden-ratio or crystallographic symmetry). - The 13-fold s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

g^{(2)}(\tau)

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

g^{(2)}(\tau)

reveals coherent ground-state superposition; continuous drive induces decoherence rate

\Gamma_{\text{Rayleigh}}

from Rayleigh scattering; feedback control modifies effective dissipation; postselection projects onto desired coherence subspace. No explicit constants or ratios given in abstract. | CONNECTION: None directly — no golden ratios, base-60, or crystallographic symmetries appear in the cited cavity-QED work. Microtubule geometry (13 protofilaments, 3-start helix) implies a helical lattice with screw symmetry, but no quantitative link to 0.618/1.618 is provided in these sources. | DEPTH: 2 — The cavity-QED result is real but narrow (quantum optics control). The microtubule "quantum computer" claim Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com