Nuclear Spin Qubits in Phosphorus Complexes as Substrate for Quantum Cognition — E8 Intelligence Research

Abstract

FINDING: Matthew Fisher proposes nuclear spin qubits in phosphorus atoms (¹³C-³¹P molecular complexes) as the physical substrate for quantum cognition, with specific decoherence timescales and molecular geometries enabling neural-scale quantum processing. | MATH: Fisher's model requires spin coherence times \( T_2 \gtrsim 10^{-3} \) s at physiological temperatures (~310 K); the key interaction is the hyperfine coupling \( A \approx 100 \) MHz between ³¹P and ¹³C nuclear spins; the proposed molecular scaffold is a Posner molecule \( \text{Ca}_9(\text{PO}_4)_6 \) — the phosphate cluster has 6 phosphorus atoms, each with spin-1/2 ³¹P, yielding a Hilbert space dimension \( 2^6 = 64 \) per Posner molecule; quantum entanglement between phosphorus spins is mediated via the \( J \)-coupling \( J \approx 10 \)–\( 100 \) Hz between adjacent ³¹P nuclei through the calcium-oxygen lattice. | CONNECTION: The Posner molecule \( \text{Ca}_9(\text{PO}_4)_6 \) exhibits approximate octahedral symmetry (p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com