Modal interpretations are non-collapse interpretations, where the quantum state of a system describes its
possible properties rather than the properties that it actually possesses. Among them, the atomic modal
interpretation (AMI) assumes the existence of a special set of disjoint systems that fixes the preferred factorization
of the Hilbert space. The aim of this paper is to analyze the relationship between the AMI and our recently
presented modal-hamiltonian interpretation (MHI), by showing that the MHI can be viewed as a kind of
“atomic” interpretation in two different senses. On the one hand, the MHI provides a precise criterion for the
preferred factorization of the Hilbert space into factors representing elemental systems. On the other hand, the
MHI identifies the atomic systems that represent elemental particles on the basis of the Galilei group. Finally,
we will show that the MHI also introduces a decomposition of the Hilbert space of any elemental system, which
determines with precision what observables acquire definite actual values.
Constructive Empiricism, Partial Structures and the Modal Interpretation of Quantum Mechanics
