Quantum Coherence in Posner Molecules: Symmetry Breakdown Undermines Consciousness Qubit Claims — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 13, 2026• 0 citations

Abstract

FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence evidence is contested; the dynamical ensemble is not symmetric, undermining claims of long-lived nuclear spin qubits for consciousness. | MATH: Stoichiometry Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻; nuclear spin-1/2 on ³¹P (6 per molecule); proposed quantum error correction via ³¹P–⁴³Ca entangled states; symmetry group of the molecule's dynamical ensemble is *not* the full octahedral (Oₕ) but a reduced subgroup due to Ca site inequivalence — the paper (arXiv:2108.08822v2) shows the ensemble average breaks permutation symmetry, killing the decoherence-free subspace (DFS) dimension. | CONNECTION: The ideal Posner cluster has approximate Oₕ symmetry (cubic, 4-fold axes, 3-fold axes) — a crystallographic point group with 48 elements. The 0.618/1.618 ratios do *not* appear in the molecular geometry; instead, the relevant ratio is the Ca–P–O bond angle (~109.5° tetrahedral, base-60 compatible as 1.91 radians). The symmetry breaking reduces the DFS f Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22732545

Related papers

Posner Molecule Quantum Coherence Claims Undermined by Broken Dynamical Symmetry — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence evidence is contested; the dynamical ensemble is *not* symmetric, undermining claims of long-lived nuclear spin qubits for biological quantum processing. | MATH: Stoichiometry Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻; nuclear spin-1/2 on ³¹P (6 per molecule); symmetry group of the idealized cluster is C₃ (3-fold rotational) but the *dynamical ensemble* breaks this — no exact C₃v or higher symmetry; the paper (arXiv:2108.08822v2) shows the nuclear spin Hamiltonian lacks the permutation symmetry required for a decoherence-free subspace (DFS) of dimension >1. | CONNECTION: The idealized C₃ symmetry maps to the 120° rotations of the hexagonal lattice (base-60/hexagonal crystallography), but the broken symmetry removes the golden-ratio-related magic-angle (54.74°) protection that would otherwise suppress dipolar coupling — the ratio 0.618/0.382 does not appear in the valid ensemble. | DEPTH: 6 — this is a negative result that mathematically kills a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 21, 20260 citations

Quantum Coherence in Posner Molecules: Symmetry Breaking Undermines Consciousness Qubit Claims — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence evidence is contested; the dynamical ensemble is *not* symmetric, undermining claims of long-lived nuclear spin qubits for consciousness. | MATH: Ca₉(PO₄)₆ — 9 Ca²⁺, 6 PO₄³⁻; nuclear spin-1/2 on ³¹P (6 sites); proposed ⁴⁵Ca (I=7/2) quadrupolar coupling; the arXiv paper (2108.08822v2) shows the ensemble average over molecular orientations breaks the assumed permutation symmetry of the 6 phosphate groups, reducing the effective Hilbert space dimension from 2⁶=64 to a smaller, symmetry-broken subspace; no closed-form equation given, but the key result is that the dynamical algebra is not S₆-symmetric, so the purported long coherence times (τ > 100 s) fail under realistic tumbling. | CONNECTION: The *broken* symmetry is the inverse of crystallographic harmony — the molecule's point group is not the ideal octahedral/tetrahedral (O_h or T_d) but a lower-symmetry C₁ or C_s in solution; the golden ratio appears nowhere in the data; however Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Aug 25, 20260 citations

Quantum Coherence in Posner Molecules: Symmetry Breakdown Challenges Entanglement Claims — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence evidence is contested; the dynamical ensemble is explicitly *not* symmetric, undermining simple claims of long-lived nuclear spin entanglement in the brain. | MATH: Stoichiometry: Ca₉(PO₄)₆ — 9 Ca²⁺, 6 PO₄³⁻. Nuclear spin‑½ on ³¹P (6 per molecule). The paper (arXiv:2108.08822v2) shows the ensemble of molecular configurations lacks permutation symmetry; the relevant symmetry group is not S₆ (full permutational symmetry) but a proper subgroup, breaking the conditions for a decoherence‑free subspace (DFS) that would require symmetric collective states. Key constant: no new fundamental constant; the relevant scale is the nuclear spin coherence time τ_c ~ milliseconds to seconds under physiological conditions, but the asymmetric ensemble reduces the effective DFS dimension. | CONNECTION: The breaking of S₆ symmetry is a crystallographic/root‑system failure: the full symmetric group S₆ corresponds to the Weyl group of the A₅ root system Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 12, 20260 citations

Asymmetric Posner Molecules Challenge Quantum Coherence in Consciousness Theory — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a biological quantum information processor — has its dynamical ensemble shown to be *not symmetric*, directly challenging assumptions of its quantum coherence longevity and its role in consciousness-related entanglement. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. Nuclear spins: ³¹P (I=1/2), ⁴³Ca (I=7/2). Symmetry group of the molecule: C₃ (3-fold rotational) — not full octahedral or tetrahedral. The paper (arXiv:2108.08822v2) demonstrates that the dynamical ensemble average ⟨ρ(t)⟩ does not commute with the molecular symmetry operator, i.e., [⟨ρ(t)⟩, Ĝ] ≠ 0, breaking the assumed permutation symmetry of the 6 phosphate groups. | CONNECTION: The 3-fold axis (C₃) maps to the crystallographic point group 3 (trigonal system). The breaking of this symmetry removes the protection of decoherence-free subspaces (DFS) that would otherwise allow long-lived nuclear spin entanglement. The ratio 6 phosphates / 9 calciums = 2/3 ≈ 0.666, a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 4, 20260 citations

Symmetry Breaking in Posner Molecules Undermines Quantum Consciousness Claims — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a biological quantum information processor — has a dynamical ensemble that is *not* symmetric, undermining naive claims of long-lived nuclear spin coherence for consciousness. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. Nuclear spin-1/2 on ³¹P (6 per molecule). The paper (arXiv:2108.08822v2) shows the full rovibrational/electronic symmetry group is broken — the dynamical ensemble does not possess the full octahedral (Oₕ) or even the point-group symmetry often assumed. Key result: the effective Hamiltonian's symmetry class is lower than the geometric point group, so the purported long coherence time (τ ~ 10⁵ s) from symmetric exchange coupling is not supported. | CONNECTION: The molecule's *static* geometry is near-octahedral (Oₕ, order 48) — a crystallographic point group with roots in the F₄ root system (24 roots) and the 24-cell. But the *dynamical* symmetry is a proper subgroup (likely C₃ᵥ or D₃ᵈ), breaking the 48-fold s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 3, 20260 citations

Asymmetric Posner Molecules Undermine Long-Lived Quantum Coherence Claims — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence evidence is contested; the dynamical ensemble is explicitly *not* symmetric, undermining naive claims of long-lived nuclear spin coherence for biological quantum processing. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻; nuclear spin-1/2 on ³¹P (6 P atoms) and spin-7/2 on ⁴³Ca (if isotopically enriched). The paper (arXiv:2108.08822v2) shows the molecular symmetry group is *not* the full octahedral or tetrahedral point group — the dynamical ensemble breaks symmetry, reducing the number of equivalent ³¹P sites. No golden-ratio or base-60 constants appear; the key structural constant is the Ca–P–O bond geometry, which is distorted from ideal tetrahedral (PO₄) symmetry. | CONNECTION: The claimed quantum processor relies on nuclear spin states — but the symmetry breaking means the Hilbert space dimension is not the naive 2⁶ = 64 for ³¹P spins; it is reduced by inequivalent sites. This directly contradicts the assumption of a highly Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 16, 20260 citations