Physical content of preparation-question structures and Brouwer-Zadeh lattices
The authors first introduce the concept of a preparation-question structure. Then they provide a model of a preparation-question structure based on a Hilbert space. Analyzing further the preparation-question structures, they derive the poset \(L\) of testable properties and the preparation-question Brouwer-Zadeh lattice. They show that the physical content carried by \(L\) is generally larger than the content carried by the property (Jauch-Piron) lattice \(\mathcal L\) [\textit{J. M. Jauch} and \textit{C. Piron}, Helv. Phys. Acta 42, 842-848 (1969; Zbl 0181.276)]. If, however, a completeness axiom is introduced, which does not seem to be always possible [\textit{D. Aerts}, ``Description of many and separated physical entities without the paradoxes encountered in quantum mechanics'', Foundation of Physics, 12, 1131 (1982)], they show that the contents of \(L\) and \(\mathcal L\) have to coincide.
scientific article; zbMATH DE number 417107