Symmetry breaking in the Posner molecule qubit register — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 29, 2026• 0 citations

Abstract

FINDING: Posner molecule Ca₉(PO₄)₆ is a candidate biological qubit register; its dynamical ensemble breaks the idealized high symmetry assumed in Fisher's nuclear-spin quantum-coherence proposal. MATH: - Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺ + 6 PO₄³⁻; total nuclear spin carriers dominated by ³¹P (I = 1/2, 100% natural abundance) → 6 phosphorus spins = 2⁶ = 64-dimensional Hilbert space. - Fisher's decoherence time estimate: τ ~ ħ/(k_B T · coupling); phosphate spin-spin coupling J ~ 10⁻²–10⁻¹ Hz scale, giving claimed T₂ ~ 10⁵ s in idealized symmetric cage. - Key result (arXiv:2108.08822): the true dynamical ensemble is NOT symmetric — the C₃ᵥ / octahedral-like idealized symmetry is broken by Ca²⁺ positional disorder and phosphate orientational dynamics. - ³¹P gyromagnetic ratio γ = 1.083 × 10⁸ rad·s⁻¹·T⁻¹; relevant for any spin-bath coupling. CONNECTION: - Idealized Posner geometry: 6 PO₄ tetrahedra at octahedral vertices → O_h point group, isomorphic to the octahedral root system / A₃ la Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23755661

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