Bell's Inequality 2D — CHSH Correlation Graph

S (quantum): 0.000 S (local): 0.000 Classical bound: 2 Quantum bound: 2√2 ≈ 2.828 Violation: NO

Measurement angles

Alice a: 0° Alice a': 45° Bob b: 22.5° Bob b': 67.5°

Model

Quantum (entangled) Local hidden variable Both side-by-side

Trials

Trials per run: 2000

Statistics

Trials0

E(a,b)0.000

E(a,b')0.000

E(a',b)0.000

E(a',b')0.000

Regime—

Local hidden-variable theories must obey CHSH: |S| ≤ 2. Quantum mechanics with the singlet state predicts E(a,b) = −cos(a−b), which at the Bell angles (0°, 45°, 22.5°, 67.5°) gives S = 2√2 ≈ 2.828 — the graph plots this curve against the classical bound as the measurement-angle difference varies, and the live trials show S converging to it.