Asymmetric Posner Molecule Dynamics Break Quantum Coherence Symmetry — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 21, 2026• 0 citations

Abstract

FINDING: The Posner molecule (Ca₉(PO₄)₆) exhibits a dynamical ensemble that is *not* symmetric, breaking the assumed high-symmetry (likely T or O) point group in its functional state, with direct implications for quantum coherence in biology. MATH: - Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. - Nuclear spin count: 9 Ca (some isotopes I=7/2, e.g., ⁴³Ca ~0.145% abundance) + 6 P (I=1/2, 100%) → total nuclear spin Hilbert space dimension = ∏(2I+1) per isotope. For ⁴³Ca: 2(7/2)+1 = 8; for ³¹P: 2(1/2)+1 = 2. - Symmetry order parameter: The dynamical ensemble average ⟨ρ⟩ is not invariant under the full point group G₀ (e.g., T_d or O_h). The broken symmetry is characterized by a non-zero order parameter φ = Tr(Âρ) where is a chiral or polar operator that transforms as a non-trivial irreducible representation (irrep) of G₀. - The paper (arXiv:2108.08822) explicitly shows that the time-averaged density matrix ⟨ρ(t)⟩ ≠ P_G₀ ρ P_G₀ (where P_G₀ is the projector onto symmetric states), Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22873932

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