Posner Molecule Quantum Coherence Real but Ensemble Symmetry Broken — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 21, 2026• 0 citations

Abstract

FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence evidence is real but its dynamical ensemble is *not* symmetric, undermining naive claims of long-lived nuclear spin qubits for consciousness. | MATH: Posner molecule stoichiometry: Ca₉(PO₄)₆ — 9 Ca²⁺, 6 PO₄³⁻. Nuclear spin-1/2 on ³¹P (100% abundance). The claimed quantum gate uses ³¹P–³¹P entanglement via dipole-dipole coupling ∝ (μ₀/4π)(γ₁γ₂ℏ²/r³)(3cos²θ−1). The symmetry breaking: point group of the dynamical ensemble is *not* T_d (tetrahedral) nor O_h (octahedral) — the arXiv paper (2108.08822) shows the ensemble averages over multiple conformers, reducing symmetry to C₁ or C_s at best. | CONNECTION: The *idealized* Posner molecule has a near-tetrahedral arrangement of phosphate groups — tetrahedral symmetry is the root system A₃ (crystallographic), with dihedral angles 109.47° (cos⁻¹(−1/3)). The golden ratio appears in the ratio of the tetrahedron's circumradius to inradius: R/r = 3, but the *edge-to-vertex* ratio involves √2, n Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22873909

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