Quantum Vibrational Coherence in Microtubules: Mesoscale Superposition Without Consciousness-Specific Geometry — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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
Related
- Quantum Microtubules as Consciousness Substrate: Hexagonal Lattice Coherence Evidence — E8 Intelligence Research
- Quantum Coherence in Microtubules: Testing Orch-OR via Entanglement and Geometric Constraints — E8 Intelligence Research
- Quantum Coherence in Microtubules: Simulation Insights, Experimental Evidence Still Lacking — E8 Intelligence Research
- Orch-OR Review Finds No New Evidence or Equations for Quantum Coherence in Microtubules — E8 Intelligence Research
- Testing Orch-OR: Quantum Coherence in Microtubules and Unmeasured Gravitational Collapse Timescales — E8 Intelligence Research
BibTeX
@misc{caldin2026quantum,
title = {{Quantum Vibrational Coherence in Microtubules: Mesoscale Superposition Without Consciousness-Specific Geometry — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23553652},
url = {https://zenodo.org/records/23553652},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Vibrational Coherence in Microtubules: Mesoscale Superposition Without Consciousness-Specific Geometry — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23553652
UR - https://zenodo.org/records/23553652
AB - 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
ER -