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Matches in DBpedia 2015-10 for { ?s ?p "In quantum mechanics, the Kochen–Specker (KS) theorem is a "no go" theorem proved by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden variable theories which try to explain the apparent randomness of quantum mechanics as a deterministic model featuring hidden states. The theorem is a complement to Bell's theorem.The theorem proves that there is a contradiction between two basic assumptions of the hidden variable theories intended to reproduce the results of quantum mechanics: that all hidden variables corresponding to quantum mechanical observables have definite values at any given time, and that the values of those variables are intrinsic and independent of the device used to measure them. The contradiction is caused by the fact that quantum mechanical observables need not be commutative. It turns out to be impossible to simultaneously embed all the commuting subalgebras of the algebra of these observables in one commutative algebra, assumed to represent the classical structure of the hidden variables theory, if the Hilbert space dimension is at least three.The Kochen–Specker proof demonstrates the impossibility of a version of Einstein's assumption, made in the famous Einstein–Podolsky–Rosen paper, that quantum mechanical observables represent 'elements of physical reality'. More specifically, the theorem excludes hidden variable theories that require elements of physical reality to be non-contextual (i.e. independent of the measurement arrangement). As succinctly worded by Isham and Butterfield, the Kochen–Specker theorem "asserts the impossibility of assigning values to all physical quantities whilst, at the same time, preserving the functional relations between them."↑ ↑ ↑ ↑"@en }

• Kochen–Specker_theorem abstract "In quantum mechanics, the Kochen–Specker (KS) theorem is a "no go" theorem proved by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden variable theories which try to explain the apparent randomness of quantum mechanics as a deterministic model featuring hidden states. The theorem is a complement to Bell's theorem.The theorem proves that there is a contradiction between two basic assumptions of the hidden variable theories intended to reproduce the results of quantum mechanics: that all hidden variables corresponding to quantum mechanical observables have definite values at any given time, and that the values of those variables are intrinsic and independent of the device used to measure them. The contradiction is caused by the fact that quantum mechanical observables need not be commutative. It turns out to be impossible to simultaneously embed all the commuting subalgebras of the algebra of these observables in one commutative algebra, assumed to represent the classical structure of the hidden variables theory, if the Hilbert space dimension is at least three.The Kochen–Specker proof demonstrates the impossibility of a version of Einstein's assumption, made in the famous Einstein–Podolsky–Rosen paper, that quantum mechanical observables represent 'elements of physical reality'. More specifically, the theorem excludes hidden variable theories that require elements of physical reality to be non-contextual (i.e. independent of the measurement arrangement). As succinctly worded by Isham and Butterfield, the Kochen–Specker theorem "asserts the impossibility of assigning values to all physical quantities whilst, at the same time, preserving the functional relations between them."↑ ↑ ↑ ↑".