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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 81))

Abstract

A state-independent, additive proof of the Bell-Kochen-Specker theorem with 18 four-dimensional vectors is presented. These vectors can be physically interpreted as a set of 18 propositions concerning a system of two spin-1/2 particles. Geometrically they can be interpreted as some relevant directions of a tesseract (a four-dimensional hypercube).

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References

  1. A. Cabello, J. M. Estebaranz, and G. García Alcaine, “Bell-Kochen-Specker theorem: A proof with 18 vectors,” Phys. Lett. A 212, 183–187 (1996).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. E. P. Specker, “Die Logik nicht gleichzeitig entscheidbarer Aussagen,” Dialcctica 14, 239–246 (1960).

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  3. J. S. Bell, “On the problem of hidden variables in quantum mechanics,” Rev. Mod. Phys. 38, 447–452 (1966).

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  4. S. Kochen and E. P. Specker, “The problem of hidden variables in quantum mechanics,” J. Math. Mech. 17, 59–87 (1967).

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  5. A. Peres, “Two simple proofs of the Kochen-Specker theorem,” J. Phys. A 24, L175–L178 (1991).

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  6. H. S. M. Coxeter, Regular polytopes (Methuen, London, 1948).

    MATH  Google Scholar 

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© 1997 Springer Science+Business Media Dordrecht

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Cabello, A. (1997). A Proof with 18 Vectors of the Bell-Kochen-Specker Theorem. In: Ferrero, M., van der Merwe, A. (eds) New Developments on Fundamental Problems in Quantum Physics. Fundamental Theories of Physics, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5886-2_8

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  • DOI: https://doi.org/10.1007/978-94-011-5886-2_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6487-3

  • Online ISBN: 978-94-011-5886-2

  • eBook Packages: Springer Book Archive

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