Beyond Qubits: Bell Violations as Structural Limits on Local Realism — E8 Intelligence Research

Abstract

FINDING: Bell inequality tests are being extended beyond standard qubit-pair setups — via Buscemi's unified framework and condensed-matter proposals — revealing that the violation is not merely a quantum artifact but a structural constraint on any local hidden-variable theory, with new bounds emerging from information-theoretic and geometric constraints. MATH: - Standard CHSH inequality: \( S = E(a,b) + E(a,b') + E(a',b) - E(a',b') \leq 2 \) (local hidden variables), quantum max \( S = 2\sqrt{2} \approx 2.828 \). - Ratio \( 2\sqrt{2}/2 = \sqrt{2} \approx 1.414 \) — not directly in golden set, but note \( \sqrt{2} \approx 1.414 \) and \( 1.618 \) are related via \( \phi = (1+\sqrt{5})/2 \), and \( \sqrt{2} \) appears in octahedral/cubic symmetry (root system \( B_3 \)). - Buscemi's unification: Bell inequalities as linear constraints on probability polytopes; violation corresponds to points outside the local polytope — the facet structure of these polytopes encodes all possible Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com