Bell's theorem

Bell's theorem is a result proved by the physicist John Stewart Bell in 1964 showing that no theory built on local hidden variables can reproduce all the predictions of quantum mechanics. It converts the philosophical dispute over whether quantum mechanics is complete into a quantitative test: local hidden-variable theories must obey certain inequalities that quantum mechanics violates. Experiments have repeatedly found the quantum violations, ruling out the local hidden-variable picture.

#The question it answered

In 1935 the Einstein, Podolsky, and Rosen paper argued that the correlations of an entangled pair suggested quantum mechanics was incomplete, and that each particle might carry predetermined values, so-called hidden variables, fixed at the source (quantum entanglement). Such a model would be local if a measurement on one particle could not influence the distant other faster than light. Bell asked whether any local hidden-variable theory of this kind could match every quantum prediction (Bell 1964).

#The inequality

Bell derived a mathematical bound on how strongly the outcomes of measurements on two separated particles can be correlated if the results are set by shared local hidden variables. This bound is a Bell inequality; a commonly tested form is the CHSH inequality introduced by Clauser, Horne, Shimony, and Holt in 1969. Quantum mechanics predicts stronger correlations for certain measurement settings on entangled particles than any local hidden-variable theory allows, so the quantum prediction exceeds the Bell bound (Stanford Encyclopedia of Philosophy). The theorem thus identifies an experimentally measurable gap between the two classes of theory.

#Experimental tests

Testing Bell inequalities requires preparing many entangled pairs, measuring each along chosen settings, and comparing the statistics to the bound.

• In 1972 Stuart Freedman and John Clauser reported an early violation using entangled photons.
• In 1982 Alain Aspect and collaborators strengthened the case by changing the analyzer settings while the photons were in flight, addressing the concern that the two stations could have influenced each other in advance (Aspect et al. 1982).
• In 2015 several groups reported loophole-free experiments that closed the main remaining loopholes, including the locality and detection loopholes, in a single test.

The accumulated results agree with quantum mechanics and violate the Bell inequalities, so any theory that reproduces them must give up locality, give up the assumption that measured properties exist independently of measurement, or both. In 2022 Alain Aspect, John Clauser, and Anton Zeilinger shared the Nobel Prize in Physics for these experiments and for founding quantum information science (Nobel Foundation 2022).

#What it does and does not show

Bell's theorem shows that nature is not described by any local hidden-variable theory. It does not show that information can be sent faster than light: the correlations, though nonlocal, cannot transmit a signal, because each party's local results look random until the two data sets are compared. Nor does it single out one interpretation of quantum mechanics; the Copenhagen, many-worlds, and pilot-wave views each accommodate the result in their own way.

#Significance

Bell's theorem is one of the most important results in the foundations of physics. It moved questions about entanglement and locality from metaphysics into the laboratory and provided the conceptual groundwork for quantum technologies, including device-independent quantum key distribution and quantum teleportation, whose security and function rest on genuine, testable quantum correlations.