Asymmetric Spin Dynamics in Posner Molecules Break S₉ Singlet Symmetry — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 24, 2026• 0 citations

Abstract

FINDING: The Posner molecule (Ca₉(PO₄)₆) — a candidate for biological quantum information processing — exhibits a dynamical ensemble that is *not* symmetric, breaking the naive nuclear-spin singlet subspace symmetry assumed in prior models. | MATH: The molecule's nuclear spin Hilbert space decomposes under the symmetric group S₉ (permuting the 9 Ca²⁺ ions) into irreps; the singlet subspace (total nuclear spin I=0) is not a single irreducible representation but a direct sum of multiple S₉ irreps, each with distinct permutation symmetry. The dynamical Hamiltonian (dipole-dipole couplings between ³¹P nuclei, each I=1/2) does not commute with the full S₉ action — only with a subgroup, leading to symmetry-breaking in the time-evolution operator U(t) = exp(−iHt/ℏ). The relevant group-theoretic structure: the ³¹P spin space is (ℂ²)⁶, and the singlet sector (dimension 5) splits as 5 = 4 ⊕ 1 under S₉, where the 4-dimensional irrep corresponds to the standard representation (Young diagram [8,1]) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22931135

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