Symmetry Breaking in Ca₉(PO₄)₆: Dynamical Ensemble Defies Static Point Group — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 21, 2026• 0 citations

Abstract

FINDING: The Posner molecule Ca₉(PO₄)₆, previously assumed to possess high symmetry (likely T or O point group), is shown to have a dynamical ensemble that breaks this symmetry — the static point group is not the operative symmetry for its quantum-relevant states. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺ + 6 PO₄³⁻. Nuclear spin count: ⁴³Ca (I=7/2) — 9 such nuclei give a Hilbert space dimension (2I+1)⁹ = 8⁹ = 134,217,728. The paper (arXiv:2108.08822v2) demonstrates that the *dynamical* symmetry group is a proper subgroup of the static point group; the effective Hamiltonian's invariant subspace is smaller than the full rotational-symmetry sector. Key invariant: the nuclear spin singlet state (total I=0) requires a specific permutation symmetry among the 9 Ca sites — if the point group is broken (e.g., from T_d to C_3v or lower), the singlet subspace dimension changes, altering the decoherence-free subspace dimension. | CONNECTION: The number 9 (Ca sites) and 6 (PO₄ groups) — ratio 9:6 = Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22873635

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