Bell’s theorem

Definition:
Bell’s theorem is a foundational result in quantum physics that demonstrates that no local theory of hidden variables can reproduce all of the predictions of quantum mechanics. It shows that quantum entanglement gives rise to correlations that defy classical, local explanations.

Scientific context:
Formulated by John Stewart Bell in 1964, the theorem formalizes the idea that if quantum theory is correct, then the world must be non-local—meaning that events separated by space can exhibit correlations that are not mediated by any signal traveling at or below the speed of light. This deeply challenges the principle of locality central to Einstein’s theory of relativity.

Example in practice:
In entangled spin systems (like pairs of electrons in a singlet state), quantum mechanics predicts statistical correlations that vary with the angle between measurement axes. For example, if the angle between the two axes is θ, the probability of opposite outcomes is (1 + cosθ)/2. These predictions violate Bell inequalities, which any local hidden variable theory must satisfy. The famous experiments by Alain Aspect et al. in 1982 provided the first convincing experimental verification, later confirmed by numerous loophole-free tests.

Did you know?
Bell’s theorem has sparked decades of debate not only among physicists but also philosophers, as it touches on fundamental questions about reality, causality, and determinism. It is often cited as one of the most profound results in the history of physics.

References:

1. Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Физика.