It has been suggested that 31 P nuclear spins in Ca 9 (PO 4 ) 6 molecules could form the basis of a quantum mechanism for neural processing in the brain. A fundamental requirement of this proposal is that spins in different Ca 9 (PO 4 ) 6 molecules can become entangled and remain so for periods (estimated at many hours) that hugely exceed typical 31 P spin relaxation times. Here, we consider the coherent and incoherent spin dynamics of Ca 9 (PO 4 ) 6 arising from dipolar and scalar spin-spin interactions and derive an upper bound of 37 min on the entanglement lifetime under idealized physiological conditions. We argue that the spin relaxation in Ca 9 (PO 4 ) 6 is likely to be much faster than this estimate.
It has been suggested that 31 P nuclear spins in Ca 9 (PO 4 ) 6 molecules could form the basis of a quantum mechanism for neural processing in the brain. A fundamental requirement of this proposal is that spins in different Ca 9 (PO 4 ) 6 molecules can become entangled and remain so for periods (estimated at many hours) that hugely exceed typical 31 P spin relaxation times. Here, we consider the coherent and incoherent spin dynamics of Ca 9 (PO 4 ) 6 arising from dipolar and scalar spin-spin interactions and derive an upper bound of 37 min on the entanglement lifetime under idealized physiological conditions. We argue that the spin relaxation in Ca 9 (PO 4 ) 6 is likely to be much faster than this estimate.
The Posner molecule (calcium phosphate trimer, Ca 9 (PO 4 ) 6 ) has been hypothesized to function as a biological quantum information processor due to its supposedly long-lived entangled 31 P nuclear spin states. This hypothesis was challenged by our recent finding that the molecule lacks a well-defined rotational axis of symmetry─an essential assumption in the proposal for Posner-mediated neural processing─and exists as an asymmetric dynamical ensemble. Following up, we investigate here the spin dynamics of the molecule’s entangled 31 P nuclear spins within the asymmetric ensemble. Our simulations show that entanglement between two nuclear spins prepared in a Bell state in separate Posner molecules decays on a subsecond time scale─much faster than previously hypothesized, and not long enough for supercellular neuronal processing. Calcium phosphate dimers (Ca 6 (PO 4 ) 4 ) however, are found to be surprisingly resilient to decoherence and are able to preserve entangled nuclear spins for hundreds of seconds, suggesting that neural processing might occur through them instead.
FINDING: Fisher's "quantum cognition" hypothesis posits nuclear spins of phosphorus-31 in Posner molecules (Ca₉(PO₄)₆) as neural qubits, with entanglement lifetime set by decoherence timescales — a concrete physical substrate for quantum processing in the brain. MATH: - Posner molecule: Ca₉(PO₄)₆, phosphate cage with 6 phosphorus nuclei, each ³¹P having nuclear spin I = 1/2 - Spin-1/2 Hilbert space per P: dim = 2; six-spin system: dim = 2⁶ = 64 - Singlet/triplet decomposition of 6 spin-1/2: 64 = 1 + 5 + 9 + 5 + ... (SU(2) Clebsch-Gordan: ½^⊗6 → 0⊕1⊕2⊕3 with multiplicities) - Key protected state: total spin S = 0 singlet — decoherence-free subspace - Nuclear spin decoherence time target: T₂ ~ 10⁵ s (Fisher's estimate for ³¹P in Posner at physiological conditions) - Neural firing timescale: τ ~ 10⁻³ s; ratio T₂/τ ~ 10⁸ — the "quantum advantage window" - Hyperfine coupling A ≈ 10²–10³ Hz (electron-nuclear); relevant for entanglement generation via radical pair intermediates - Posner form Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Matthew Fisher proposes nuclear spin qubits (phosphorus-31) in neural membranes as a quantum processing substrate, with a specific molecular mechanism (Posner molecules, Ca₃(PO₄)₆) enabling long-lived quantum coherence. | MATH: Nuclear spin-1/2 for ³¹P; Posner molecule Ca₉(PO₄)₆ — 6 phosphate groups, 9 Ca²⁺ ions; quantum entanglement lifetime τ ~ 10⁵ s (hours) at physiological temperature; decoherence rate Γ ∝ exp(−ΔE/k_BT) suppressed by spin-singlet pairing; Fisher's key ratio: entanglement fidelity F > 0.99 for ³¹P spin pairs in Posner clusters. | CONNECTION: Posner molecule has **octahedral symmetry (O_h)** — 6 phosphate tetrahedra arranged at vertices of a regular octahedron, a crystallographic point group (order 48). The ³¹P nuclei sit at positions corresponding to the **octahedral root system D₃** (6 vertices ±e₁, ±e₂, ±e₃). The Ca²⁺ ions form a **cuboctahedral shell** (12 vertices, Archimedean solid) — related to the **fcc lattice** and the **root system of F₄**. The ra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
A study published in Annals of Physics (with an initial draft available on arXiv) proposes a new operational framework for a "nuclear spin quantum brain" that is distinct from the existing microtubule model. The research identifies "Posner molecules" (Ca₉(PO₄)₆), which are calcium phosphate clusters in body fluids, as a unique molecule that protects the nuclear spins of phosphorus (P) atoms from thermal and chemical disturbances, acting as a natural shield for neural qubits. It demonstrates that quantum entanglement states generated within Posner molecules can be preserved for minutes to hours (up to approximately one day), potentially enabling non-local brain synchronization and driving cognitive functions across neurons. [Quantum Biology Society] How exactly the human brain forms consciousness and performs advanced cognitive functions has long remained one of science's most profound mysteries. To explain the quantum actions of neural networks, the microtubule model proposed by Roger Penrose and others has been widely known. Recently, however, a new hypothesis has been proposed—using a completely different approach—suggesting that the brain processes quantum information (qubits) using the nuclear spins of specific molecules, attracting significant attention from the scientific community. The paper "Quantum Cognition: The possibility of processing with nuclear spins in the brain," authored solely by Professor Matthew P. A. Fisher of the Department of Physics at the University of California, Santa Barbara (UC Santa Barbara), presents this revolutionary framework for a nuclear spin-based quantum brain. ■ Posner Molecules: A Natural Protective Shield for Quantum Qubits The biggest challenge for quantum computation is that quantum coherence is easily destroyed by chemical and thermal disturbances in the warm, wet biological environment. Professor Fisher identified the "Posner molecule" (Ca₉(PO₄)₆), a calcium phosphate cluster commonly present in body fluids, as nature's solution to this problem. Physical analysis revealed that these Posner molecules act as a natural shield for neural qubits, thoroughly isolating the nuclear spins of phosphorus (P) atoms from electrical and magnetic disturbances in the external environment. ■ Quantum Entanglement Maintained for Hours Thanks to this robust protection, the quantum entanglement of phosphorus nuclear spins within Posner molecules remains intact for significantly longer than in typical quantum systems. According to the research calculations, due to the rapid rotation of Posner molecules in aqueous solution, dipole magnetic fields are averaged and canceled out, allowing the coherence time (t_coh) of this entanglement to be preserved for minutes or even up to a day (10⁵ seconds). This provides sufficient working memory time for quantum information to be meaningfully stored and processed on a neurophysiological timescale. ■ Non-local Brain Synchronization Across Neural Networks Furthermore, multiple Posner molecules that maintain an entangled state can freely enter presynaptic neurons through mechanisms such as vesicle endocytosis. As these entangled Posner molecules, distributed across various neurons, chemically bind and subsequently melt, they release a shower of calcium ions, triggering further neurotransmitter release. This enables multiple neurons to achieve non-local biochemical synchronization. In other words, it strongly suggests that Posner molecules could ultimately drive the complex computations and cognitive functions of the brain, providing an entirely new biophysical insight into the origins of consciousness and cognitive processes. https://arxiv.org/abs/1508.05929
FINDING: Quantum effects in the brain are proposed via Posner molecules (Ca₉(PO₄)₆) with nuclear spin entanglement, but the evidence is largely theoretical (Matthew Fisher) and not yet experimentally confirmed; the Bayesian paper is unrelated to quantum brain claims. | MATH: Posner molecule: 9 Ca²⁺ + 6 PO₄³⁻ → Ca₉(PO₄)₆; nuclear spins of ³¹P (I=1/2) — 6 phosphorus nuclei per molecule; proposed entanglement lifetime ~10⁵ s (days) at physiological temperature; Fisher's model uses nuclear spin qubits with hyperfine coupling to ¹³C or ³¹P; key constant: decoherence rate γ ∝ (kT/ħ)²·τ_c (where τ_c is correlation time); no closed-form equation given in these sources. | CONNECTION: Posner molecule geometry: Ca₉(PO₄)₆ forms a cluster with approximate octahedral symmetry (O_h point group) — 6 PO₄ tetrahedra arranged around a central Ca₃ triangle; this is a crystallographic symmetry (cubic, space group related to apatite). The 6 phosphorus nuclei sit at vertices of an octahedron — a root system Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Posner clusters (Ca₉(PO₄)₆) proposed by Fisher as nuclear-spin qubits enabling quantum processing in the brain via phosphate entanglement | MATH: Posner molecule = Ca₉(PO₄)₆, 6 phosphate groups per cluster; each ³¹P nucleus has spin I = 1/2; total nuclear spin Hilbert space dim = 2⁶ = 64 per Posner; decoherence time τ ∝ (spin-flip rate)⁻¹, Fisher estimates τ ~ 10⁵ s for ³¹P in Posner vs ~10⁻¹³ s for neural microtubule proposals | CONNECTION: Ca₉(PO₄)₆ is a body-centered cubic lattice (space group Fm3̄m, a ≈ 10.3 Å); 6 phosphates occupy octahedral vertices → octahedral symmetry O_h; 9 Ca²⁺ form a tricapped trigonal prism; the 6-fold phosphate arrangement maps to the 6 faces of a cube → cubic crystallographic symmetry; 6 = 3! permutations of spin states → S₆ permutation group structure | DEPTH: 7 --- FINDING: Penrose-Hameroff Orch-OR theory gains indirect support from anesthetics and microtubule quantum coherence studies, but no direct Posner entanglement measurement exists | Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com