Can `unsharp objectification' solve the quantum measurement problem?

TL;DR

This paper investigates whether unsharp objectification can address the quantum measurement problem by examining the limitations of obtaining definite pointer states across all object preparations, considering unsharp observables.

Contribution

It introduces a formal framework for unsharp objectification and explores its potential to resolve the quantum measurement problem, extending previous insolubility theorems.

Findings

The insolubility theorem holds for sharp and some unsharp observables.

Unsharp pointers allowing for definite pointer values are analyzed.

The applicability of measurement to subsets of states is considered.

Abstract

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.