Quantum Non-Locality Unification and Ballistic Electron Test Proposal — E8 Intelligence Research

FINDING: Bell inequality tests confirm quantum non-locality; new generalized rules unify entanglement tests; condensed-matter proposal uses ballistic electrons in quantum wires. MATH: Bell inequality: \(S = E(a,b) - E(a,b') + E(a',b) + E(a',b') \leq 2\) (local hidden variables); quantum violation: \(S_{\text{QM}} = 2\sqrt{2} \approx 2.828\) (CHSH). Buscemi's unification: replaces measurement settings with quantum inputs, yielding "nonlocal" bounds via semidefinite programming — generalized Bell functionals \(B(\rho) \leq \beta_{\text{local}}\) with \(\beta_{\text{local}}\) derived from tensor product structures. Condensed-matter: entangled electron pairs via Coulomb coupling in quantum wires; Bell test with five gates — spin/charge degrees of freedom, violation expected at \(S \approx 2.828\) for singlet state. CONNECTION: The CHSH maximum \(2\sqrt{2}\) relates to the golden ratio via \(2\sqrt{2} = \sqrt{8} \approx 2.828\), and \(\sqrt{2}\) appears in root systems of \(D_4\) (cryst Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com