Symmetry Breaking in Posner Molecules' Nuclear Spin Dynamics — E8 Intelligence Research

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 tetrahedral (T_d) symmetry assumed for its nuclear spin Hamiltonian. | MATH: The molecule's nuclear spin Hamiltonian is dominated by ³¹P (I=1/2) dipolar couplings; the symmetry group of the static crystal structure is T_d (order 24), but the dynamical ensemble (thermal fluctuations, phosphate group rotations) reduces this to a lower point group — the paper (arXiv:2108.08822v2) shows the ensemble-averaged spin Hamiltonian is not invariant under T_d, implying the effective symmetry is at most C₃ or C₁. The key quantity is the dipolar coupling tensor sum: H_dip = Σ_{i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com