The Quantum Measurement Problem and Cluster Separability

Abstract

A modified Beltrametti-Cassinelli-Lahti model of the measurement apparatus that satisfies both the probability reproducibility condition and the objectification requirement is constructed. Only measurements on microsystems are considered. The cluster separability forms a basis for the first working hypothesis: the current version of quantum mechanics leaves open what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. The second working hypothesis is that registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This implies that the separation status of a microsystem changes during both preparation and registration. A new rule that specifies what happens when these changes occur and that guarantees the objectification is formulated and discussed. A part of our result has certain similarities with ‘collapse of the wave function’.