Einstein's Discomfort
In 1935, Einstein, Podolsky, and Rosen argued that quantum mechanics must be incomplete because it predicted correlations between distant particles that seemed to require 'spooky action at a distance.' For decades this remained a philosophical debate — until John Bell showed in 1964 that local hidden variable theories make testable predictions that differ from quantum mechanics. This simulation lets you explore exactly where classical and quantum predictions diverge.
The CHSH Test
Clauser, Horne, Shimony, and Holt reformulated Bell's inequality into an experimentally practical form. Alice and Bob each choose between two measurement settings and record ±1 outcomes. The CHSH parameter S combines four correlation measurements; classical physics demands S ≤ 2, while entangled quantum states can reach S = 2√2. Alain Aspect's landmark experiments in 1982 confirmed the quantum prediction.
Visibility and Noise
Real experiments never achieve perfect entanglement. Noise, loss, and detector imperfections reduce the effective visibility V of the two-photon state. Below V = 1/√2, Bell violations vanish — but the state may still be entangled. Entanglement witnesses provide a more sensitive test, detecting entanglement even when Bell inequalities cannot be violated, at the cost of assuming the quantum mechanical framework.
The 2022 Nobel Prize
The 2022 Nobel Prize in Physics was awarded to Aspect, Clauser, and Zeilinger for experiments with entangled photons and the violation of Bell inequalities. Their work established that nature is fundamentally nonlocal (or non-realist), and enabled practical quantum technologies including quantum key distribution, quantum teleportation, and entanglement-based quantum computing.