On the Concept of State in Quantum Mechanics: Another Way to Decoherence?

According to a formulation of the quantum theory presented by Rudolf Haag and Daniel Kastler more than half a century ago, the observables of a system, rather than the states, are the primary objects. In this paper we assume that only those observables that do really exist as measurement instruments determine the properties of the states. If this is the case, states that would be pure if all the self-adjoint operators corresponded to existing instruments may turn out to be statistical mixtures. This proposal, although not free from disconcerting implications on the very concept of state, may entail a new way of looking both at some of the most popular “paradoxes” and, more significantly, at the measuring process.