Nuclear-Spin Qubits in Biological Phosphate/Calcium Clusters for Long-Lived Quantum Coherence — E8 Intelligence Research

FINDING: Nuclear-spin qubits in biological phosphate/calcium clusters are proposed to sustain quantum coherence far longer than electronic spins, making them candidate substrates for quantum information in living systems. | MATH: Key quantities — nuclear spin quantum number I (e.g., ³¹P: I=1/2; ⁴³Ca: I=7/2); Larmor frequency ω_L = γB (γ = gyromagnetic ratio); decoherence time T₂; relaxation scaling T₁ ∝ ω_L⁻ⁿ (n≈2 for quadrupolar, ~1–2 for dipolar). Fisher's Posner-molecule proposal: ³¹P nuclear spins in Ca₉(PO₄)₆ "Posner clusters" (hydroxyapatite precursor, ~0.9–1 nm diameter) coupled via intra-cluster exchange/J-coupling, with predicted coherence times up to ~10⁵ s under shielding. | CONNECTION: Posner cluster Ca₉(PO₄)₆ is a crystallographic structure with 6-fold (hexagonal) phosphate arrangement — Ca₉ sits on a 3-fold axis; PO₄ tetrahedra occupy sites of the cubic/hexagonal close-packing motif. This is a root-system/lattice symmetry (A₃ × hexagonal packing), not a φ-ratio structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com