Can ‘Unsharp Objectification’ Solve the Quantum Measurement Problem?

Abstract

The quantum measurement problem is formulated inthe form of an insolubility theorem that states theimpossibility of obtaining, for all available objectpreparations, a mixture of states of the compound object and apparatus system that wouldrepresent definite pointer positions. A proof is giventhat comprises arbitrary object observables, whethersharp or unsharp, and besides sharp pointer observables a certain class of unsharp pointers, namely,those allowing for the property of pointer valuedefiniteness. A recent result of H. Stein is applied toallow for the possibility that a given measurement may not be applicable to all possible objectstates, but only to a subset of them. The question israised whether the statement of the insolubility theoremremains true for genuinely unsharp observables. This gives rise to a precise notion of unsharpobjectification.