Parity Proofs of the Bell-Kochen-Specker Theorem Based on the 600-cell

Foundations of Physics 41 (5):883-904 (2011)
  Copy   BIBTEX

Abstract

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,297

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Generalizations of Kochen and Specker's theorem and the effectiveness of Gleason's theorem.Itamar Pitowsky - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (2):177-194.
Schütte's tautology and the Kochen-Specker theorem.Jeffrey Bub - 1996 - Foundations of Physics 26 (6):787-806.
Generalized Kochen-Specker theorem.Asher Peres - 1996 - Foundations of Physics 26 (6):807-812.
Nonlocality Without Nonlocality.Steven Weinstein - 2009 - Foundations of Physics 39 (8):921-936.
The Bell–Kochen–Specker theorem.D. M. Appleby - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1):1-28.

Analytics

Added to PP
2013-11-22

Downloads
48 (#246,132)

6 months
1 (#450,425)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Mordecai Waegell
Chapman University

References found in this work

Interpreting the Quantum World.Jeffrey Bub - 1998 - British Journal for the Philosophy of Science 49 (4):637-641.
On bell non-locality without probabilities: More curious geometry.Jason Zimba & Roger Penrose - 1993 - Studies in History and Philosophy of Science Part A 24 (5):697-720.
Schütte's tautology and the Kochen-Specker theorem.Jeffrey Bub - 1996 - Foundations of Physics 26 (6):787-806.

Add more references