Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Posner Molecule's Broken Symmetry Undermines Quantum Cognition Claims — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 3, 2026• 0 citations
Publisher

Abstract

FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a biological quantum information processor — has a dynamical ensemble that is *not* symmetric, undermining claims of long-lived nuclear spin coherence for quantum cognition. | MATH: Molecular formula Ca₉(PO₄)₆; nuclear spin-1/2 ³¹P nuclei (6 per molecule); the dynamical ensemble symmetry breaking is characterized by the loss of permutation invariance among the six phosphate groups — the relevant group is the symmetric group S₆, whose irreducible representations decompose the nuclear spin Hilbert space (dimension 2⁶ = 64). The paper (arXiv:2108.08822v2) shows the time-evolution operator does not commute with all S₆ permutations, so the coherence lifetime is bounded by the asymmetric coupling terms, not the symmetric dipolar Hamiltonian. | CONNECTION: The number 6 (phosphate groups) relates to hexagonal symmetry (crystallographic point group 6/mmm), but the *broken* symmetry points to a lower-order subgroup — the root system A₅ (SU(6 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.23115490

Related papers

Posmer Molecule's Broken Symmetry Challenges Quantum Coherence Claims — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Posner molecule (Ca₉(PO₄)₆) proposed as biological quantum information processor, but dynamical ensemble symmetry is broken, contradicting earlier assumptions of long-lived nuclear spin coherence. MATH: - Molecular formula: Ca₉(PO₄)₆ → 9 calcium ions, 6 phosphate groups. - Nuclear spin states: \( ^{31}P \) (spin-1/2) and \( ^{43}Ca \) (spin-7/2) are candidate qubits. - Key result from arXiv:2108.08822v2: The dynamical ensemble of the molecule is *not symmetric* under the full permutation group of the phosphate groups. This breaks the assumed \( S_6 \) symmetry, reducing coherence lifetimes. - No specific equations or constants (e.g., decoherence rates, coupling strengths) are provided in the abstract; the finding is structural/symmetry-based. CONNECTION: - The broken symmetry directly relates to crystallographic point groups and root systems. The \( S_6 \) (order 720) symmetry of six phosphate groups is reduced to a lower subgroup, likely \( C_2 \) or \( D_3 \), wh Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Aug 11, 2026•0 citations

Asymmetric Posner Molecule Ensemble Undermines Quantum Cognition Spin Coherence — 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 the assumption of long-lived nuclear spin coherence required for quantum cognition models. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. Nuclear spin-1/2 on ³¹P (6 sites) and spin-7/2 on ⁴³Ca (9 sites). The relevant Hilbert space dimension for ³¹P alone: 2⁶ = 64; with ⁴³Ca: (2×7/2+1)⁹ = 8⁹ = 134,217,728. The paper (arXiv:2108.08822v2) shows the dynamical ensemble (time-averaged density matrix under internal Hamiltonian) lacks the full octahedral (Oₕ) or even tetrahedral (T_d) symmetry previously assumed. | CONNECTION: The *idealized* Posner cluster has approximate octahedral symmetry (6 PO₄ tetrahedra around a central Ca₃ triangle motif) — a crystallographic point group Oₕ (order 48). The broken symmetry in the dynamical ensemble means the nuclear spin states do not decompose into irreducible representations of Oₕ in the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Sep 21, 2026•0 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, 2026•0 citations

Posner Molecule Quantum Coherence Refuted by Broken Spin Symmetry — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence claims are undermined by its dynamical ensemble lacking the symmetric structure required for long-lived nuclear spin entanglement. | MATH: Molecular formula Ca₉(PO₄)₆; the paper (arXiv:2108.08822v2) demonstrates the dynamical ensemble is *not* symmetric — breaking the permutation symmetry that would permit a decoherence-free subspace (DFS). Key mathematical object: the Lie group structure of the nuclear spin Hamiltonian; absence of SU(2) or higher symmetry → no protected subspace dimension > 1. | CONNECTION: The *failure* of symmetry here is the geometric link. Crystallographic point group of Ca₉(PO₄)₆ (likely C₃ or S₆, related to 60° rotations — base-60/hexagonal motif) does not lift to a dynamical symmetry of the spin ensemble. This is a negative result against the 0.618/1.618 harmonic idealization of biological quantum processing — the molecule's actual symmetry breaking destroys the golden-ratio-like coherence longevity. | DEPT Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Oct 22, 2026•0 citations

Posner Molecule Lacks Symmetric Ensemble, Undermining Quantum Spin Coherence Viability — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a biological quantum information processor — is shown to lack the symmetric dynamical ensemble previously assumed, undermining its viability for long-lived nuclear spin coherence. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. Point group symmetry: C₃ (not Tₕ or Oₕ as sometimes implied). Nuclear spin count: ⁴³Ca (I=7/2) and ³¹P (I=1/2) — total spin Hilbert space dimension = (2·7/2+1)⁹ × (2·1/2+1)⁶ = 8⁹ × 2⁶ = 134,217,728 × 64 = 8,589,934,592. The paper (arXiv:2108.08822v2) demonstrates that the dynamical ensemble — the set of accessible spin states under molecular tumbling — is not invariant under the full permutation group S₉ × S₆, breaking the symmetric subspace assumption. | CONNECTION: The C₃ symmetry axis (120° rotation) is a crystallographic point group element, but the lack of higher symmetry (no S₆, no inversion) means the molecule does not support the full root-system symmetry (e.g., A₈ or D₆) needed for error-protect Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Oct 5, 2026•0 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, 2026•0 citations
FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a biological quantum information processor — has a dynamical ensemble that is not symmetric, undermining claims of long-lived nuclear spin coherence for quantum cognition. | MATH: Molecular formula Ca₉(PO₄)₆; nuclear spin-1/2 ³¹P nuclei (6 per molecule); the dynamical ensemble symmetry breaking is characterized by the loss of permutation invariance among the six phosphate groups — the relevant group is the symmetric group S₆, whose irreducible representations decompose the nuclear spin Hilbert space (dimension 2⁶ = 64). The paper (arXiv:2108.08822v2) shows the time-evolution operator does not commute with all S₆ permutations, so the coherence lifetime is bounded by the asymmetric coupling terms, not the symmetric dipolar Hamiltonian. | CONNECTION: The number 6 (phosphate groups) relates to hexagonal symmetry (crystallographic point group 6/mmm), but the broken symmetry points to a lower-order subgroup — the root system A₅ (SU(6 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Posner molecule (Ca₉(PO₄)₆) proposed as biological quantum information processor, but dynamical ensemble symmetry is broken, contradicting earlier assumptions of long-lived nuclear spin coherence. MATH: - Molecular formula: Ca₉(PO₄)₆ → 9 calcium ions, 6 phosphate groups. - Nuclear spin states: 31P ^{31}P 31P (spin-1/2) and 43Ca ^{43}Ca 43Ca (spin-7/2) are candidate qubits. - Key result from arXiv:2108.08822v2: The dynamical ensemble of the molecule is *not symmetric* under the full permutation group of the phosphate groups. This breaks the assumed S6 S_6 S6​ symmetry, reducing coherence lifetimes. - No specific equations or constants (e.g., decoherence rates, coupling strengths) are provided in the abstract; the finding is structural/symmetry-based. CONNECTION: - The broken symmetry directly relates to crystallographic point groups and root systems. The S6 S_6 S6​ (order 720) symmetry of six phosphate groups is reduced to a lower subgroup, likely C2 C_2 C2​ or D3 D_3 D3​, wh Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a biological quantum information processor — has a dynamical ensemble that is *not* symmetric, undermining the assumption of long-lived nuclear spin coherence required for quantum cognition models. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. Nuclear spin-1/2 on ³¹P (6 sites) and spin-7/2 on ⁴³Ca (9 sites). The relevant Hilbert space dimension for ³¹P alone: 2⁶ = 64; with ⁴³Ca: (2×7/2+1)⁹ = 8⁹ = 134,217,728. The paper (arXiv:2108.08822v2) shows the dynamical ensemble (time-averaged density matrix under internal Hamiltonian) lacks the full octahedral (Oₕ) or even tetrahedral (T_d) symmetry previously assumed. | CONNECTION: The *idealized* Posner cluster has approximate octahedral symmetry (6 PO₄ tetrahedra around a central Ca₃ triangle motif) — a crystallographic point group Oₕ (order 48). The broken symmetry in the dynamical ensemble means the nuclear spin states do not decompose into irreducible representations of Oₕ in the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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
FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence claims are undermined by its dynamical ensemble lacking the symmetric structure required for long-lived nuclear spin entanglement. | MATH: Molecular formula Ca₉(PO₄)₆; the paper (arXiv:2108.08822v2) demonstrates the dynamical ensemble is *not* symmetric — breaking the permutation symmetry that would permit a decoherence-free subspace (DFS). Key mathematical object: the Lie group structure of the nuclear spin Hamiltonian; absence of SU(2) or higher symmetry → no protected subspace dimension > 1. | CONNECTION: The *failure* of symmetry here is the geometric link. Crystallographic point group of Ca₉(PO₄)₆ (likely C₃ or S₆, related to 60° rotations — base-60/hexagonal motif) does not lift to a dynamical symmetry of the spin ensemble. This is a negative result against the 0.618/1.618 harmonic idealization of biological quantum processing — the molecule's actual symmetry breaking destroys the golden-ratio-like coherence longevity. | DEPT Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a biological quantum information processor — is shown to lack the symmetric dynamical ensemble previously assumed, undermining its viability for long-lived nuclear spin coherence. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. Point group symmetry: C₃ (not Tₕ or Oₕ as sometimes implied). Nuclear spin count: ⁴³Ca (I=7/2) and ³¹P (I=1/2) — total spin Hilbert space dimension = (2·7/2+1)⁹ × (2·1/2+1)⁶ = 8⁹ × 2⁶ = 134,217,728 × 64 = 8,589,934,592. The paper (arXiv:2108.08822v2) demonstrates that the dynamical ensemble — the set of accessible spin states under molecular tumbling — is not invariant under the full permutation group S₉ × S₆, breaking the symmetric subspace assumption. | CONNECTION: The C₃ symmetry axis (120° rotation) is a crystallographic point group element, but the lack of higher symmetry (no S₆, no inversion) means the molecule does not support the full root-system symmetry (e.g., A₈ or D₆) needed for error-protect Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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