Posner Clusters as Nuclear-Spin Qubit Substrates for Brain Quantum Information — E8 Intelligence Research

FINDING: Nuclear-spin qubits in Posner clusters (Ca₉(PO₄)₆) are proposed as a decoherence-resistant substrate for quantum information in the brain — the O_h octahedral symmetry of the phosphate groups is the structural anchor. | MATH: Posner cluster = Ca₉(PO₄)₆, space group P4̄3m (cubic, tetrahedral point group T_d for the cluster; PO₄³⁻ tetrahedra sit at O_h-related sites). Key claim (Fisher 2015, Ann. Phys. 362:593): spin–spin relaxation T₂ scales as T₂ ∝ 1/(n·γ⁴·ℏ²·τ_c) where n = ³¹P nuclear density, γ = gyromagnetic ratio, τ_c = correlation time. Fisher's estimate: T₂ ~ 10⁵ s for ³¹P spins in Posner clusters — 5–6 orders of magnitude longer than typical neural timescales (~ms). ³¹P has I = 1/2 (spin-½, no quadrupole coupling → intrinsically low decoherence). | CONNECTION: The Posner cluster's cubic/tetrahedral symmetry (T_d ⊂ O_h) means the ³¹P nuclear sites are symmetry-equivalent under the point group — this symmetry enforces degeneracy of local magnetic environments, suppressing Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com