Bell's Theorem & Hidden Variables Quantum Optics Bench

Quantum Optical Bench (Interactive)

Laser Emitter:

Alice Polarizer Angle a₁: 0°

Alice Polarizer Angle a₂: 45°

Bob Polarizer Angle b₁: 22.5°

Bob Polarizer Angle b₂: 67.5°

CHSH S-Parameter
2.828
Quantum Boundary: 2√2 ≈ 2.828

Local Realism Bound
|S| ≤ 2.000
EPR Classical Limit

Total Pairs Sampled

10,000

Statistical Coincidence Batch

Bell Violation Status

VIOLATED (+41.4%)

Singlet Quantum State

CHSH Inequality Test Outcome: Observed |S| = 2.828. Quantum correlation exceeds the Classical Local Realism bound |S| ≤ 2.0 by 0.828 (Tsirelson Bound violation), falsifying local hidden variable theories.

Physics Engine Model

Quantum Singlet (|Ψ⁻⟩) True quantum entanglement. Exact correlation E(a,b) = -cos(2(a-b)). Violates CHSH up to S = 2.828.

Local Hidden Variables (EPR) Pre-determined spin instruction sets. Strictly bounded by |S| ≤ 2.0.

Bohmian Non-Local Pilot Wave Deterministic non-local hidden variable theory. Reproduces quantum correlation E(a,b) exactly.

Efficiency Loophole (Fair Sampling) Classical hidden variables exploiting 70% detector efficiency to mimic S > 2.

CHSH Sub-Correlations E(a,b)

Angles (a, b)	Theory	Empirical E(a,b)
E(a₁, b₁) [0°, 22.5°]	-0.707	-0.707
E(a₁, b₂) [0°, 67.5°]	+0.707	+0.707
E(a₂, b₁) [45°, 22.5°]	-0.707	-0.707
E(a₂, b₂) [45°, 67.5°]	-0.707	-0.707