Several philosophers of science have claimed that the conceptual difficulties of quantum mechanics can be resolved by appealing to a particular interpretation of probability theory. For example, Popper bases his treatment of quantum mechanics on the propensity interpretation of probability, and Margenau bases his treatment of quantum mechanics on the frequency interpretation of probability. The purpose of this paper is (i) to consider and reject such claims, and (ii) to discuss the question of whether the ψ -function refers to an (...) individual system or to an ensemble of systems. (shrink)

Although the introduction of the modern axiomatic method in physics is attributed to Hilbert, it is only recently that physicists and mathematicians have applied it significantly, i.e. on a basis extensive enough to promise fruitful results. Carnap, for one, stresses the importance of the axiomatic method, yet he considers its application in physics as a task for the future.

Scholars concerned with the foundations of quantum mechanics (QM) usually think that contextuality (hence nonobjectivity of physical properties, which implies numerous problems and paradoxes) is an unavoidable feature of QM which directly follows from the mathematical apparatus of QM. Based on some previous papers on this issue, we criticize this view and supply a new informal presentation of the extended semantic realism (ESR) model which embodies the formalism of QM into a broader mathematical formalism and reinterprets quantum probabilities as conditional (...) on detection rather than absolute. Because of this reinterpretation a hidden variables theory can be constructed which justifies the assumptions introduced in the ESR model and proves its objectivity. When applied to special cases the ESR model settles long-standing conflicts (it reconciles Bell’s inequalities with QM), provides a general framework in which previous results obtained by other authors (as local interpretations of the GHZ experiment) are recovered and explained, and supports an interpretation of quantum logic which avoids the introduction of the problematic notion of quantum truth. (shrink)

A dynamical analysis of standard procedures for subensemble selection is used to show that the state restriction violation proposal in Part I of the paper cannot be realized by employing familiar correlation schemes. However, it is shown that measurement of an observable not commuting with the superselection operator is possible, a violation of the observable restrictions. This is interpreted as supporting the position that each of these restrictions is sufficient but not necessary for the superselection rule. The results do constitute (...) a proposal for superselection rule violation in theories requiring both restrictions, e.g., the axiomatic treatment by Bogolubov, Logunov, and Todorov. It is also concluded that superselection rules place restrictions on procedures for selective state preparations using correlations. More generally, it is conjectured that a mathematically conceivable decomposition of a given density operator does not necessarily represent a possibility for partitioning of the corresponding ensemble into subensembles by any physically realizable means. (shrink)

The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related to the frequency of (...) occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state. (shrink)