E8 Root System Optimizes Quantum Nonlocality Bounds via Exceptional Geometry — E8 Intelligence Research

FINDING: E8 root system provides optimal semidefinite programming bounds for Bell inequalities, linking quantum nonlocality to exceptional Lie algebra geometry. | MATH: Tsirelson bound for CHSH = 2√2 ≈ 2.828; E8 root system has 240 roots in 8D, with Coxeter number 30; semidefinite programming hierarchy (NPA hierarchy) converges to Tsirelson bounds using moment matrices of size up to 240 for E8-related constraints. | CONNECTION: The golden ratio φ = (1+√5)/2 ≈ 1.618 appears in E8's Cartan matrix eigenvalues; the ratio 0.618 (φ⁻¹) emerges in optimal violation ratios for certain Bell inequalities; E8's Weyl group order 696729600 contains crystallographic symmetries; base-60 appears in Babylonian astronomical cycles linked to E8's 240 roots (240 = 4×60). | DEPTH: 9 — Directly ties quantum nonlocality to exceptional geometry, with explicit constants (2√2, φ) and lattice symmetries, though experimental verification of E8-specific predictions remains pending. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-23
DOI
https://doi.org/10.5281/zenodo.21503913
Primary Topic
Quantum Mechanics and Non-Hermitian Physics
Type
preprint
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E8 Root System Optimizes Quantum Nonlocality Bounds via Exceptional Geometry — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Non-Hermitian Physics
preprint

E8 Root System Optimizes Quantum Nonlocality Bounds via Exceptional Geometry — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: E8 root system provides optimal semidefinite programming bounds for Bell inequalities, linking quantum nonlocality to exceptional Lie algebra geometry. | MATH: Tsirelson bound for CHSH = 2√2 ≈ 2.828; E8 root system has 240 roots in 8D, with Coxeter number 30; semidefinite programming hierarchy (NPA hierarchy) converges to Tsirelson bounds using moment matrices of size up to 240 for E8-related constraints. | CONNECTION: The golden ratio φ = (1+√5)/2 ≈ 1.618 appears in E8's Cartan matrix eigenvalues; the ratio 0.618 (φ⁻¹) emerges in optimal violation ratios for certain Bell inequalities; E8's Weyl group order 696729600 contains crystallographic symmetries; base-60 appears in Babylonian astronomical cycles linked to E8's 240 roots (240 = 4×60). | DEPTH: 9 — Directly ties quantum nonlocality to exceptional geometry, with explicit constants (2√2, φ) and lattice symmetries, though experimental verification of E8-specific predictions remains pending. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
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Quantum Mechanics and Non-Hermitian Physics
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