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Kochen-Specker Theorem

Mathematical Physics

Quantum mechanics is inconsistent with the idea that measurement outcomes are determined by hidden variables assigning definite, context-independent values to all observables simultaneously. Proved by Simon Kochen and Ernst Specker, it is a foundational no-go theorem about the interpretation of quantum mechanics, complementary to Bell's theorem.

Facts
Statement
For a Hilbert space of dimension three or greater, no function can assign a definite 0 or 1 value to every projection operator consistent with the sum rule for every orthogonal set of projections, ruling out any non-contextual hidden variable model of quantum mechanics. Kochen and Specker gave an explicit finite set of state vectors realizing this contradiction in 1967; a related no-go result was proved independently by John Bell in 1966. 1
Proof Year
1967 1
Classification
Statement Form
Impossibility Theorem 1
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Proved By

Source Kochen-Specker Theorem (Wikipedia)
Source Kochen-Specker Theorem (Wikipedia)
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Sources
1. Kochen-Specker Theorem (Wikipedia)
Wikimedia Foundation
  • lead paragraph, first sentence
    In quantum mechanics, the Kochen-Specker (KS) theorem, also known as the Bell-KS theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967.
  • Proved By: Simon B. Kochen, Lead
    In quantum mechanics, the Kochen-Specker (KS) theorem, also known as the Bell-KS theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967.
  • Proved By: Ernst Specker, Lead
    In quantum mechanics, the Kochen-Specker (KS) theorem, also known as the Bell-KS theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967.
  • In Group: Quantum Mechanics and Quantum Field Theory, Lead section
    In quantum mechanics, the Kochen-Specker (KS) theorem, also known
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