³¹P Nuclear Spins in Posner Molecules as Room-Temperature Qubits for Quantum Cognition — E8 Intelligence Research

FINDING: Matthew Fisher (UCSB) proposes nuclear spins of phosphorus-31 in Posner molecules (Ca₉(PO₄)₆) as room-temperature qubits for neural quantum processing — "quantum cognition" via decoherence-resistant nuclear spin entanglement. MATH: - Posner molecule: Ca₉(PO₄)₆, phosphate cage with 6 P nuclei (I = 1/2, ³¹P) - Nuclear spin qubit: ³¹P, spin-1/2, gyromagnetic ratio γ ≈ 1.08 × 10⁸ rad·s⁻¹·T⁻¹ - Hyperfine coupling A ≈ 10²–10³ Hz (weak, hence long coherence) - Decoherence time target: T₂ ~ 10⁵ s (days) for nuclear spins in Posner geometry - Entanglement via spin-spin coupling through phosphate oxygens; singlet-triplet states - Posner binding energy: ~ 10 kT (thermal stability at 310 K) - Symmetry group of Posner: octahedral O_h (6 P at vertices of octahedron) CONNECTION: - Octahedral symmetry O_h — root system A₃/B₃; 6 vertices = 6 spin-1/2 sites → SU(2)⁶ Hilbert space, dim = 2⁶ = 64 - 6-fold coordination echoes base-60 (6 × 10) and hexagonal/cubic close-packing - Singlet state ( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com