Relational unsharp properties: A POVM-based ontology for relational quantum mechanics

Since its inception in 1996, Rovelli’s Relational Quantum Mechanics (RQM) has left the status of non-interacting systems notably underexplored. When discussed at all, one prevailing view has maintained that attributing properties to isolated systems within RQM is simply meaningless. However, it has become increasingly evident that without a satisfying account of non-interacting systems, RQM risks sliding toward antirealist interpretations–at least insofar as such systems are concerned. In response to this crucial challenge, two main approaches have been advanced. One is a form of dispositionalism, which suggests that isolated physical systems possess only dispositional properties. The other appeals to a determinable-based account of metaphysical indeterminacy, suggesting that a non-interacting quantum system may bear a determinable property without possessing any unique determinate of that determinable at a given time. In this paper, we offer a new response to the question of what can be meaningfully said about quantum systems prior to measurement in the context of RQM. In particular, drawing on the formalism of Positive Operator- Valued Measures (POVMs), we emphasize that (1) preparation–like measurement– constitutes a physical interaction capable of assigning relational properties to a system, and that (2) POVMs are indispensable for the proper description of observables with continuous spectra. On this basis, we propose that RQM can accommodate an entity-realist interpretation of non-interacting systems by attributing to them what we term relational unsharp properties. As we will show, this theoretical move preserves the relational nucleus of RQM while enabling a physically and philosophically coherent account of non-interacting quantum systems.