Constructive quantum mechanics, Gleason's theorem and the indeterminacy relations

Rok, strany: 1998, 155 - 164

The paper surveys (without proofs) some recent results in constructive quantum mechanics. The first is a theorem by Conway and Kochen. It states that there is a finitely generated partial Boolean algebra of subspaces whose set of rays is dense (for dimension $≥ 4$). The second is a result by the author that concerns Gleason's theorem. It shows that the continuity of every frame function is a combinatorial fact, it follows from the properties of a finite orthogonality graph structure. Based on this insight one can construct a finite version of the indeterminacy principle. These theorems are interpreted in the framework of quantum logic. If we assume that the relation of mutual exclusion (orthogonality) between propositions is somehow given, then little else is needed to derive the basic principles of quantum mechanics.

ISO 690:

Pitowsky, I. 1998. Constructive quantum mechanics, Gleason's theorem and the indeterminacy relations. In Tatra Mountains Mathematical Publications, vol. 15, no.2, pp. 155-164. 1210-3195.

APA:

Pitowsky, I. (1998). Constructive quantum mechanics, Gleason's theorem and the indeterminacy relations. Tatra Mountains Mathematical Publications, 15(2), 155-164. 1210-3195.