Posner Molecules as Neural Qubits: Phosphorus-31 Nuclear Spins in Quantum Cognition — E8 Intelligence Research

FINDING: Fisher's "quantum cognition" hypothesis posits nuclear spins of phosphorus-31 in Posner molecules (Ca₉(PO₄)₆) as neural qubits, with entanglement lifetime set by decoherence timescales — a concrete physical substrate for quantum processing in the brain. MATH: - Posner molecule: Ca₉(PO₄)₆, phosphate cage with 6 phosphorus nuclei, each ³¹P having nuclear spin I = 1/2 - Spin-1/2 Hilbert space per P: dim = 2; six-spin system: dim = 2⁶ = 64 - Singlet/triplet decomposition of 6 spin-1/2: 64 = 1 + 5 + 9 + 5 + ... (SU(2) Clebsch-Gordan: ½^⊗6 → 0⊕1⊕2⊕3 with multiplicities) - Key protected state: total spin S = 0 singlet — decoherence-free subspace - Nuclear spin decoherence time target: T₂ ~ 10⁵ s (Fisher's estimate for ³¹P in Posner at physiological conditions) - Neural firing timescale: τ ~ 10⁻³ s; ratio T₂/τ ~ 10⁸ — the "quantum advantage window" - Hyperfine coupling A ≈ 10²–10³ Hz (electron-nuclear); relevant for entanglement generation via radical pair intermediates - Posner form Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com