Phosphorus Nuclear Spins as Qubits: Quantum Coherence Constraints in Fisher's Hypothesis — E8 Intelligence Research

FINDING: Fisher's quantum cognition hypothesis centers on phosphorus nuclear spins as qubits, with the key constraint being the need for long coherence times (~10⁴–10⁵ s) and a specific spin‑1/2 system isolated from decoherence. | MATH: The relevant Hamiltonian for a single phosphorus nucleus in a phosphate ion (PO₄³⁻) under a magnetic field B is \( H = -\gamma_n \hbar \mathbf{I}\cdot\mathbf{B} + \mathbf{I}\cdot\mathbf{A}\cdot\mathbf{S} \), where \(\gamma_n\) is the nuclear gyromagnetic ratio (for ³¹P, \(\gamma_n/2\pi \approx 17.235\) MHz/T), \(\mathbf{I}\) is the nuclear spin (I=1/2), \(\mathbf{A}\) is the hyperfine tensor coupling to the electron spin \(\mathbf{S}\). Decoherence time \(T_2\) for ³¹P in a hydrated environment is estimated via \(1/T_2 \propto \sum_i (A_i^2 / \omega_i) \coth(\hbar\omega_i/2k_BT)\) over phonon modes. Fisher's key ratio: the number of phosphorus atoms per neuron (~10⁸) and the required entanglement time window (~10⁻¹ s) vs. thermal fluctuation time (~10⁻¹ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com