Partial Observables in Extended Systems

We consider "unphysical", kinematic observables that do not commute with the constraints of a gauge system in the context of an extension of the system. We show that these observables, while not predictable, can nevertheless be said to have a physical interpretation. They implement Rovelli's concept of partial and relational observables. We investigate the propositional structure of these observables and point out interpretational issues. We find that to make relational statements in the quantum theory one must deal directly with these observables. In particular we argue that in this scenario the spectra of kinematic observables are what is experimentally accessible.