Unifying Entanglement and Bell Tests via Generalized Non-Locality Rules — E8 Intelligence Research

FINDING: Bell inequality violations remain the core experimental test of quantum non-locality, with CHSH form as the standard mathematical tool; new theoretical work (Buscemi) unifies entanglement and Bell tests via generalized rules. MATH: - CHSH inequality: \( S = E(a,b) + E(a,b') + E(a',b) - E(a',b') ≤ 2 \) (local hidden variables) vs. quantum bound \( SQM = 2√2 ≈ 2.828 \). - Bell's original inequality: \( |P(a⃗,b⃗) - P(a⃗,c⃗)| ≤ 1 + P(b⃗,c⃗) \). - Quantum violation ratio: \( 2√2/2 = √2 ≈ 1.414 \) — note this is NOT the golden ratio, but it is the ratio of the diagonal of a unit square to its side (Pythagorean). - Buscemi's unification: extends Bell inequalities to "semi-quantum" scenarios where one party is classical, one quantum — yields new bounds involving \( √2 \) and \( 2 \) in generalized forms. - No explicit appearance of 0.382, 0.618, 0.786, 1.618, 2.618 in the provided abstracts Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com