Bell's theorem

In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen argued that quantum mechanics might not give a complete account of physical reality. One possible alternative would add hidden variables—information about measurement outcomes not represented in the quantum state. The issue is not simply whether distant particles can influence one another, but whether quantum correlations can be explained by a theory meeting clearly specified assumptions about locality and the independence of measurement settings.

In 1964, physicist John Stewart Bell derived mathematical constraints on correlations predicted by a broad class of local hidden-variable theories. These constraints, often called Bell inequalities, differ from the correlations quantum mechanics predicts for suitably prepared entangled systems and selected measurement settings. The inequalities make the debate experimentally testable: researchers compare repeated measurements on paired systems and test whether the observed correlations exceed the relevant bound.

John Clauser and collaborators developed early experimental tests using entangled photons; subsequent experiments, including Alain Aspect's, refined the apparatus and addressed important loopholes. In 2015, separate experiments reported Bell-inequality violations while closing major detection and locality loopholes together. Further tests have used different physical platforms. No single experiment proves every philosophical interpretation, but the observed results are incompatible with the tested class of local hidden-variable explanations under the experiment's assumptions and agree with quantum predictions.

Bell-test results establish a distinctive form of quantum correlation, often called Bell nonlocality. They do not allow controllable faster-than-light messaging: individual outcomes are not under an experimenter's control, and usable communication still requires ordinary classical signals. Nor does the theorem rule out every conceivable hidden-variable theory; alternatives can reject or modify one or more of the assumptions used in deriving an inequality. Care is needed to separate the mathematical result and experimental evidence from broader interpretations of quantum mechanics.

Bell's theorem transformed a foundational dispute into a program of precise experiments. The ability to create, test and use entangled states now informs quantum information research, including secure communication, quantum networks and computation. The 2022 Nobel Prize in Physics recognized Alain Aspect, John Clauser and Anton Zeilinger for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.