Abstract
Given a physical system, one knows that there is a logical duality between its properties and its states. In this paper, we choose its states as the undefined notions of our axiomatic construction. In fact, by means of well-motivated assumptions expressed in terms of a transition probability function defined on the set of all pure states of the system, we construct a system of elementary propositions, i.e., a complete orthomodular atomic lattice satisfying the covering law. We also study in this framework the important notion of compatibility of propositions, and we define the superpositions and the mixtures of the states of the physical system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. M. Jauch and C. Piron,Helv. Phys. Acta 42, 842–848 (1969).
C. Piron,Helv. Phys. Acta 42, 330–338 (1969).
B. Mielnik,Comm. Math. Phys. 9, 55–80 (1968).
B. Mielnik, private communication.
H. P. Matter, De la décomposition des treillis orthomodulaires, Thesis 1512, Geneva (1970).
G. Szàsz,Introduction to Lattice Theory (Academic Press, 1963).
S. P. Gudder,J. Math. Phys. 11, 1037–1040 (1970).
Ph. Ch. Zabey, Probabilités de transition en axiomatique quantique, Thesis 1594, Geneva (1972).
P. M. Cohn,Universal Algebra (Harper and Row, 1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zabey, P.C. Reconstruction theorems in quantum mechanics. Found Phys 5, 323–342 (1975). https://doi.org/10.1007/BF00717447
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00717447