Logical approach to the quantum-to-classical transition

Abstract

The standard descriptions of the quantum-to-classical transition of quantum systems focuses on the evolution of quantum states. The main idea is to appeal to the decoherence process in order to explain the disappearance of the interference terms of the quantum states. These approaches give an adequate description of several aspects of the classical limit process. However, they do not explain how the logical structure of quantum properties becomes classical. In this chapter, we present an alternative approach to the quantum-to-classical transition, based on the evolution of the observables instead of the states. We show that if the observables of the system evolve over time in such a way that they become commutative, then the logical structure of quantum properties becomes a classical logic. Moreover, we illustrate the general idea of this approach considering four different models.