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

Andrew Stewart Caldin

Published Sep 23, 2026• 0 citations

Abstract

FINDING: Matthew Fisher proposes nuclear spin qubits in phosphorus atoms (¹³C-³¹P bonds) as the physical substrate for quantum cognition, with decoherence timescale ~10⁻¹⁰ s for electron spins but ~10⁵ s for nuclear spins in phosphate ions. | MATH: Key constants: ¹³C gyromagnetic ratio γ_C ≈ 6.728 MHz/T; ³¹P γ_P ≈ 17.235 MHz/T; J-coupling between ¹³C and ³¹P in phosphate ≈ 100–200 Hz (hyperfine interaction); decoherence time T₂ ~ 10⁵ s for nuclear spins at physiological temperature (300 K); quantum error threshold ~10⁻⁴ per gate operation. The proposed "Posner molecule" Ca₉(PO₄)₆ has octahedral symmetry (O_h point group, order 48), with 6 phosphate groups arranged at vertices of a regular octahedron — bond angles 90° and 180°, corresponding to the root system of the B₃ Lie algebra (24 roots). | CONNECTION: The octahedral symmetry of Posner molecules is crystallographic — O_h is the full octahedral group, isomorphic to S₄ × C₂, with character table containing irreducible representations Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22910156

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