Science › Quantum world
Bell's theorem
1964· Mathematics
ProvenTested many times; part of working physics.
John Bell's 1964 proof that no theory based on hidden, locally pre-set values can reproduce all of quantum mechanics' predictions.
See it on the Science map →How it works
Einstein hoped particles carry hidden 'instruction sheets' that fix measurement results in advance, with no influence faster than light. Bell showed that any such theory puts a ceiling on how often results at two distant detectors can agree across different settings. Quantum mechanics predicts entangled particles break that ceiling. A philosophical dispute became a measurable question: run the experiment and count.
Why it matters
It turned a decades-old philosophical argument into an experiment, and it underpins security proofs for some forms of quantum encryption.
Think of it like
Like auditing two branch offices: if each follows only its own pre-written policy manual, their records can match only so often. Matching beyond that limit means something else is going on.
How we know
It is a mathematical proof, valid given its stated assumptions. Experiments from 1972 onward found the quantum predictions, breaking Bell's limit by wide margins.
Still a mystery
Which assumption to drop: locality, definite pre-existing values, or experimenters' free choice of settings. Bell himself leaned toward accepting non-locality.
Connections (2)
▸The EPR paradox: "spooky action at a distance" was made testable by Bell's theoremProven
The relationship
For thirty years EPR's question, whether hidden pre-set values exist, seemed untestable. Bell showed that any local hidden-value theory limits how strongly results at two distant detectors can agree as their settings vary. Quantum mechanics predicts more agreement than that limit. The philosophical debate became a measurable prediction.
How the link was found
John Stewart Bell, a Northern Irish physicist at CERN, in a 1964 paper written on leave in the United States, inspired partly by David Bohm's hidden-variable theory.
Why it's proven
Bell's theorem is a mathematical proof. Clauser, Horne, Shimony and Holt turned it into a practical experimental test in 1969.
Open questions and mysteries
Which assumption fails, locality or definite pre-existing values, is not settled by Bell's theorem alone.
▸Bell's theorem was checked by Bell tests: nature really is non-local (Nobel 2022)Proven
The relationship
Bell's theorem gives a number: local hidden-value theories cannot exceed a certain correlation score. Experiments measure many entangled pairs at several detector-setting combinations and compute the score. Every serious test has exceeded the limit, matching quantum predictions.
How the link was found
Freedman and Clauser at Berkeley (1972), Aspect at Orsay with rapidly switched settings (1982), Zeilinger's group in Innsbruck (1998), and loophole-free tests in 2015.
Why it's proven
Results break Bell's limit by many standard deviations, repeated in many labs with different technologies. The 2015 tests closed the main loopholes together.
Open questions and mysteries
The 'superdeterminism' loophole, where detector settings are secretly correlated with the particles since the Big Bang, cannot be fully excluded, though most physicists find it implausible.