Asymmetric Dynamics Break Symmetry in Posner Molecule's Nuclear Spin Hilbert Space — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 26, 2026• 0 citations

Abstract

FINDING: The Posner molecule (Ca₉(PO₄)₆) — long proposed as a biological quantum information processor — has a dynamical ensemble that is *not* symmetric, breaking the assumed high-symmetry Hilbert space structure. | MATH: The molecule's nuclear spin Hilbert space dimension is not the naive product of ⁴³Ca (I=7/2) and ³¹P (I=1/2) spins under a symmetric group action. The paper (arXiv:2108.08822v2) shows the dynamical ensemble — the set of accessible states under the molecule's internal Hamiltonian and environmental decoherence — does not respect the full permutation symmetry of the 9 Ca²⁺ and 6 PO₄³⁻ units. Key structural constants: 9 calcium sites (each I=7/2 → 8-dimensional spin space per nucleus), 6 phosphate groups (each ³¹P, I=1/2 → 2-dimensional). Naive total Hilbert space dimension: (8)⁹ × (2)⁶ = 2²⁷ × 2⁶ = 2³³ ≈ 8.59 × 10⁹. However, symmetry-adapted subspace under the crystallographic point group (likely D₃ or S₆-related, given the triclinic/rhombohedral Ca₉(PO₄)₆ unit cell) re Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23658352

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