Projective colorings

Hales, Alfred; Straus, E. G.

doi:10.2140/pjm.1982.99.31

Cited by 12 publications

(18 citation statements)

References 3 publications

(6 reference statements)

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“…In this phenomenon a particle's trajectory is recorded by an array of detectors. If the detectors are only read after a non-zero time interval, then it can happen that the particle is recorded as having been in one place 9 There are some similarities between this and MKC's approach. Bell and MKC both attempt to circumvent the theorem by only assigning values to a restricted class of observables-a dense subset of S 2 in the case of MKC, positions in the case of Bell. when it was in fact somewhere entirely different.…”

Section: The Physical Significance Of the Bell-ks Theoremmentioning

confidence: 99%

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The Bell–Kochen–Specker theorem

Appleby

2005

Studies in History and Philosophy of Science Part B: Studies in

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Meyer, Kent and Clifton (MKC) claim to have nullified the Bell-KochenSpecker (Bell-KS) theorem. It is true that they invalidate KS's account of the theorem's physical implications. However, they do not invalidate Bell's point, that quantum mechanics is inconsistent with the classical assumption, that a measurement tells us about a property previously possessed by the system. This failure of classical ideas about measurement is, perhaps, the single most important implication of quantum mechanics. In a conventional colouring there are some remaining patches of white. MKC fill in these patches, but only at the price of introducing patches where the colouring becomes "pathologically" discontinuous. The discontinuities mean that the colours in these patches are empirically unknowable. We prove a general theorem which shows that their extent is at least as great as the patches of white in a conventional approach. The theorem applies, not only to the MKC colourings, but also to any other such attempt to circumvent the Bell-KS theorem (Pitowsky's colourings, for example). We go on to discuss the implications. MKC do not nullify the Bell-KS theorem. They do, however, show that we did not, hitherto, properly understand the theorem. For that reason their results (and Pitowsky's earlier results) are of major importance.

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Section: The Physical Significance Of the Bell-ks Theoremmentioning

confidence: 99%

“…His conclusion has, however, been challenged: first by Pitowsky [4,5], and then, using a different set-theoretic argument, by Meyer [6], Kent [7] and Clifton and Kent [8] (MKC). MKC's argument was inspired by the previous work of Hales and Strauss [9] and Godsil and Zaks [10]. It has attracted much comment [11,12,13,14,15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

The Bell–Kochen–Specker theorem

Appleby

2005

Studies in History and Philosophy of Science Part B: Studies in

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“…+ 1 colors can be constructed in a straightforward manner. We refer to [3,4,5] for the theoretical background of the following construction.…”

Section: Coloringsmentioning

confidence: 99%

“…However, they obtained their result in a slightly different way. Following [4] all rational rays are associated with three colors by making the following identification: #1, #2 = #4, #3 = #5 = #6 = #7. This 3-coloring has the property that coplanar rays are always colored by using only two colors; cf.…”

Section: Coloringsmentioning

confidence: 99%

“…The fact that three colors are not sufficient is not so obvious. Here we shall not review Godsil and Zaks' proof based on a paper by A. W. Hales and E. G. Straus [4], but refer to a result of S. Kochen and E. Specker [2], which is of great importance in the present debate on hidden parameters in quantum mechanics. They have proven that there does not exist a reduced two-coloring, also termed valuation, on the one dimensional subspaces of real Hilbert space in three dimensions.…”

Section: The Chromatic Number Of the Real Unit Sphere In Three Dimensmentioning

confidence: 99%

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Colouring the rational quantum sphere and the Kochen-Specker theorem

Havlicek

Krenn²,

Summhammer³

et al. 2001

J. Phys. A: Math. Gen.

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We review and extend recent findings of Godsil and Zaks, who published a constructive colouring of the rational unit sphere with the property that for any orthogonal tripod formed by rays extending from the origin of the points of the sphere, exactly one ray is red, one white and one black. They also showed that any consistent colouring of the real sphere requires an additional colour. We discuss some of the consequences for the Kochen-Specker theorem.

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On lineations

Bognár

Kertész

1986

Acta Math Hung

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Projective colorings

Cited by 12 publications

References 3 publications

The Bell–Kochen–Specker theorem

The Bell–Kochen–Specker theorem

Colouring the rational quantum sphere and the Kochen-Specker theorem

On lineations

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