Critical investigation of Jauch's approach to the quantum theory of measurement

David Böhm, Jeffrey Bub

In this paper, we examine an argument of Jauch and Piron, which aims to prove the impossibility of hidden variables underlying the quantum theory, on the basis of certain assumptions that are weaker than those used by von Neumann for the same purpose. We show that, while the assumptions of Jauch and Piron are in fact weaker than those of von Neumann, the net result is that they actually prove nothing new at all. The conclusions of Jauch and Piron concerning the nonexistence of hidden variables are indeed seen to follow from a false assumption; i.e., that the impossibility of propositions that describe simultaneously the results of measurements of two noncommuting observables is an "empirical fact." Actually, it is shown that this assumption follows if and only if one first assumes what the authors set out to prove; i.e., that the current linguistic structure of quantum mechanics is the only one that can be used correctly to describe the empirical facts underlying the theory.

Francis Fer

Wolfgang Weidlich

Josef Tkadlec

A Boolean orthoposet is the orthoposet P fulfilling the following condition: if a ^ b = 0 then a ? b. Boolean orthoposets enjoy some properties of Boolean algebras but, in some sense, they are far away of them (3, 4, 8). An important notion in quantum logic theory is the notion of Jauch-Piron state (2, 5, 6, 7). In this paper, we show connections between Boolean orthoposets and orthoposets with a proper number of Jauch-Piron states: We demonstrate that an orthoposet with enough two-valued Jauch-Piron states is Boolean and, on the other hand, we give several examples of Boolean orthoposets without any two- valued Jauch-Piron state.

C. A. Hooker

Professor J. Jauch, in his recent book, Foundations of Quantum Mechanics, claims to resolve the paradox of Einstein, Podolsky, and Rosen. Jauch's approach is representative of that adopted by the majority of physicists. I argue that, although Jauch does exhibit a consistent quantum formalism for dealing with situations of the type involved in the original paradox, that formalism, so far from doing away with the paradox, serves only to highlight the difficulties of providing an acceptable physical understanding of it. The paradox must remain, therefore, as a central clue in the search for a more adequate understanding of quantum theory.

Paul Busch, PEKKA J. LAHTI, Peter Mittelstaedt