Bell's theorem

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Bell's theorem

[′belz ‚thir·əm]
(quantum mechanics)
A theorem which states that any hidden variable that satisifies the condition of locality cannot possibly reproduce all the statistical predictions of quantum mechanics, and which places upper limits, for the predictions of any such theory, on the strength of correlations between measurements of spatially separated objects, whereas quantum mechanics predicts very strong correlations between such measurements.
References in periodicals archive ?
Questions have also been raised on the limited applicability of Bell's inequality [19-21], based on the assumptions used in its derivation.
Landau, "On the violation of Bell's inequality in quantum theory," Physics Letters A, vol.
Title: Testing Bell's Inequality with Cosmic Photons
Zeilinger, "Violation of Bell's inequality under strict Einstein locality conditions," Physical Review Letters, vol.
(9) Creating a formalism now known as "Bell's Theorem," the notion of additional but concealed variables required to retain a local realism was mathematically systematized and "shown to be incompatible with the statistical predictions of quantum mechanics [or for any] theory which reproduces exactly the quantum mechanical predictions." (10) By logical argument, Bell demonstrated that, if EPR-styled supplementary parameters were present, statistically averaged results collected from an appropriate measurement regimen must comply with an algebraic inequality derived from the theorem, now termed "Bell's Inequality," and thus, at least in principle, permit adjudication by experiment.
Organization is in 20 chapters beginning with a brief survey of analytical dynamics and ending with chapters on quantum theory of free electromagnetic field, interaction of radiation with matter, and Bell's inequality.
There are reasonable discussions of some aspects of physics, such as his introduction to Bell's inequality and the EPR paradox, but most are cursory and some even suggest misconceptions.
Topics include the unification of classical and quantum probability theories, EPR-Bohm and the original EPR experiments, Bell's inequality, interpretations of its violation and loopholes, simulation of EPR-Bohm co-relations in the local realistic approach, nonlocality, contextual probabilistic models, subjective probability and quantum information, quantum logic, and results of recent experiments in quantum information, model theory, discrete time, dynamics, and the philosophic foundations of probability.
First he argues that both the Kochen-Specker theorem and the violation of Bell's Inequality are best interpreted as due to ontological contextuality.
Bell's inequality [1-3] sets constraints for the existence of local hidden variable theories in quantum mechanics.
Consider a test of Bell's inequality in which a quantum system produces a pair of particles that fly off in opposite directions.