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Revision as of 13:25, 16 April 2008
In quantum mechanics, the Kochen-Specker theorem is a certain "no go" theorem proved by Simon 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 theory featuring hidden states. The theorem is a complement to Bell's inequality.
The theorem proves that there is a contradiction between two basic assumptions of hidden variable theories: that all 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 generated by the fact that quantum mechanical observables need not be commutative, making it impossible to embed the algebra of these observables in a (classical) commutative algebra.
The Kochen-Specker proof demonstrates the impossibility of Einstein's assumption, made in the Einstein-Podolsky-Rosen paper, that quantum mechanical observables represent `elements of physical reality'. More generally does the theorem exclude hidden variable theories requiring `elements of physical reality' to be noncontextual (i.e. independent of the measurement arrangement).
Considerably simpler proofs than the Kochen-Specker one were given later by Mermin and by Peres.
References
- S. Kochen and E.P. Specker, "The problem of hidden variables in quantum mechanics", Journal of Mathematics and Mechanics 17, 59-87 (1967).
- N.D. Mermin, "What's wrong with these elements of reality?" Physics Today, 43, Issue 6, 9-11 (1990); N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems", Phys. Rev. Lett. 65, 3373 (1990).
- A. Peres, "Two simple proofs of the Kochen-Specker theorem", J. Phys. A: Math. Gen. 24, L175-L178 (1991).
External links
- Kochen-Specker theorem on arxiv.org
- S. Kochen and E. P. Specker, The problem of hidden variables in quantum mechanics,
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