Unsharp Quantum Reality

Gregg S. Jaeger

Brigitte Falkenburg

Abstract In their paper Unsharp Quantum Reality, Paul Busch and Gregg Jaeger explain the conception of unsharp reality in terms of Positive Operator Valued (POV) measures, potentiality, and single-case probabilities. The present paper discusses their conception from a philosophical point of view, focusing on the ontological interpretation of POV measures employed in it and on its relation to Peter Mittelstaedt’s work on the semantics and ontology of quantum mechanics. Busch and Jaeger extend Mittelstaedt’s approach by adding a realistic interpretation of unsharp quantum properties to it. Their account of unsharp quantum reality generalizes Heisenberg’s potentiality interpretation of quantum states. In order to explain the transition from potential to actual quantum properties, they suggest a Ghirardi-Rimini-Weber (GRW) collapse theory. Their approach comes close to recent work on quantum propensities. However, the question remains what unsharp quantum reality means when no measurement takes place, as for example claimed in the quark model of the subatomic constitution of matter.

Paul Busch

The Einstein-Podolsky-Rosen (EPR) reality criterion is generalized to fit with the notion of positive-operator-valued observables occurring in quantum optics, stochastic quantum mechanics, and other fields of quantum physics. The resulting concept of unsharp reality for quantum systems is illustrated within stochastic spin space where it leads to a notion of unsharp spin property. Finally we investigate the possibility of joint spin measurements and give a brief discussion of the EPR-Bell argument for unsharp spin properties.

Gianpiero Cattaneo, María Luisa Dalla Chiara, Roberto Giuntini

A basic aim of the unsharp approaches to quantum mechanics is to provide a mathematization of some ambigous aspects, that seem to be characteristic of the “concrete reality”. This has suggesten different forms of paraconsistent quantum logic. We work in the framework of a general semantics for physical theories, which concerns both the classical and quantum case.