1998/02/03 by P. Busch
Physics and Astronomy · #quant-ph
published as Int.J.Theor.Phys. 37 (1998) 241-247 · 8 pages, LaTeX, Contribution to the Quantum Structures Conference, Berlin, 1996
arxiv created 1998/02/03 · arxiv updated 2009/12/01
The quantum measurement problem is formulated in the form of an insolubility theorem that states the impossibility of obtaining, for all available object preparations, a mixture of states of the compound object and apparatus system that would represent definite pointer positions. A proof is given that comprises arbitrary object observables, whether sharp or unsharp, and besides sharp pointer observables a certain class of unsharp pointers, namely, those allowing for the property of pointer value definiteness. A recent result of H. Stein is applied to allow for the possibility that a given measurement may not be applicable to all possible object states but only to a subset of them. The question is raised whether the statement of the insolubility theorem remains true for genuinely unsharp observables. This gives rise to a precise notion of unsharp objectification.