Generalizations of Kochen and Specker’s theorem and the effectiveness of Gleason’s theorem (2004)
| Venue: | Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35, 177194 |
| Citations: | 3 - 1 self |
BibTeX
@INPROCEEDINGS{Hrushovski04generalizationsof,
author = {Ehud Hrushovski and Itamar Pitowsky},
title = {Generalizations of Kochen and Specker’s theorem and the effectiveness of Gleason’s theorem},
booktitle = {Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35, 177194},
year = {2004},
pages = {10--1016}
}
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Abstract
Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated. 1. Gleason’s Theorem and Logical Compactness Kochen and Specker’s (1967) theorem (KS) puts a severe constraint on possible hidden-variable interpretations of quantum mechanics. Often it is considered an improvement on a similar argument derived from Gleason (1957) theorem (see, for example, Held. 2000). This is true in the sense that KS provide an explicit construction of a finite set of rays on which no two-valued homomorphism exists. However, the fact that there is such a finite set follows from Gleason’s theorem using a simple logical compactness argument (Pitowsky 1998, a similar point is made in Bell 1996). The existence of finite sets of rays with other interesting features
