Entangled

Measurement basis (the detectors). The angle at which you orient your detector is the measurement basis. For aligned detectors (0°−0°), a singlet pair is perfectly anti-correlated: A up always means B down. For perpendicular detectors (0°−90°), measurements are completely uncorrelated. The quantum correlation follows E(a,b) = −cos(θₐ−θᵦ). The Bell curve shows this. The quantum prediction (smooth cosine) exceeds what any classical hidden-variable theory could produce at angles like 22.5°, 67.5°. That excess is Bell's theorem made visible.

Pair stream. Fire a continuous stream of entangled pairs and watch the statistics accumulate in real time. Individual outcomes are random — A can be up or down on any given shot. But across many measurements, the correlation between A and B converges on the quantum prediction exactly. Randomness at the individual level, precise correlation at the statistical level. This is the structure of quantum probability.

Quantum eraser. Observe particle A — it collapses, and B instantly resolves to the opposite spin. Now erase the which-way information about A — interact with it in a way that destroys the record of its measurement without disturbing B. Check B. It is back in superposition. The correlation is gone — not because anything travelled from A to B, but because the information that determined B's state no longer exists anywhere in the universe. |which-way⟩ → |erased⟩ → B returns to superposition. Reality is not just about what happened. It is about what information is available about what happened.

What the Bell curve is showing. The dotted classical bound marks ±2 in the CHSH inequality (S ≤ 2 classically). Quantum mechanics predicts S ≤ 2√2 ≈ 2.83, and experiments confirm it. No theory built on local realism — no matter how clever — can reproduce the quantum cosine curve everywhere simultaneously. Bell's theorem doesn't just say quantum mechanics is weird. It proves that any correct theory of reality must be non-local, non-real, or both.