Physics
Bell's Inequalities
Quick fact
John Bell derived his inequalities in 1964. Since then, numerous experiments, including Alain Aspect's 1982 tests, have consistently violated Bell inequalities, ruling out local hidden variable theories with high confidence.
Why this is interesting
Imagine two players, each in a sealed room, who must give opposite answers when asked the same question—yet they can't communicate. Quantum particles can perform this trick, but classical ones cannot. Why?
Read the full explanation
Understanding Bell's Inequalities
Bell's inequalities stem from the idea of 'local realism' — the notion that objects have definite properties and influences cannot travel faster than light. Bell showed that if local realism holds, the correlation between measurements on two entangled particles (like electrons with paired spins) can never exceed a certain bound. However, quantum mechanics predicts correlations that can exceed this bound. To visualize, think of a game where Alice and Bob each measure a particle's spin along one of two axes. If they choose different axes, the chances of getting the same result are limited classically. But quantum entanglement allows them to beat that limit. When experiments measure these correlations, the results violate Bell's inequality, meaning the world is not locally realistic.
A deeper explanation
Bell's theorem rests on a statistical inequality, such as the Clauser-Horne-Shimony-Holt (CHSH) version. For two particles and two measurement settings each, the sum of correlation coefficients must lie between -2 and 2 for any local hidden variable theory. Quantum mechanics allows values up to 2√2 ≈ 2.828. Experiments, like those using entangled photons, measure correlations above 2, violating the inequality. This proves that the outcomes cannot be explained by pre-existing properties or local influences. The violation shows that the universe is fundamentally nonlocal: measurement choices on one particle instantaneously affect the other, though this cannot transmit information faster than light. Bell's inequalities are central to quantum information science, including quantum cryptography and teleportation, as they certify genuine entanglement.