Posner Molecule Lacks Symmetric Ensemble, Undermining Quantum Spin Coherence Viability — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 5, 2026• 0 citations

Abstract

FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a biological quantum information processor — is shown to lack the symmetric dynamical ensemble previously assumed, undermining its viability for long-lived nuclear spin coherence. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. Point group symmetry: C₃ (not Tₕ or Oₕ as sometimes implied). Nuclear spin count: ⁴³Ca (I=7/2) and ³¹P (I=1/2) — total spin Hilbert space dimension = (2·7/2+1)⁹ × (2·1/2+1)⁶ = 8⁹ × 2⁶ = 134,217,728 × 64 = 8,589,934,592. The paper (arXiv:2108.08822v2) demonstrates that the dynamical ensemble — the set of accessible spin states under molecular tumbling — is not invariant under the full permutation group S₉ × S₆, breaking the symmetric subspace assumption. | CONNECTION: The C₃ symmetry axis (120° rotation) is a crystallographic point group element, but the lack of higher symmetry (no S₆, no inversion) means the molecule does not support the full root-system symmetry (e.g., A₈ or D₆) needed for error-protect Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23152684

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