Role of quantum versus classical logic in deriving the classical limit

Determine whether and in what precise manner the non-distributive Hilbert-space quantum logic, contrasted with the Boolean set-theoretic logic of classical physics, can be leveraged to derive deterministic classical physical laws from quantum theory and to clarify the quantum–classical transition.

Background

The paper highlights a fundamental conceptual gap between quantum and classical descriptions: quantum logic formulated on Hilbert spaces is non-distributive, whereas classical physics relies on Boolean set-theoretic logic. The authors suggest that this qualitative difference may be central to understanding how classical deterministic laws emerge from quantum theory but note that a direct logical route remains elusive.

In lieu of a purely logical resolution, the work proposes an interpolation via open-system dynamics and renormalization-group coarse-graining. Nonetheless, the question of whether the logical distinction itself can provide a formal solution remains explicitly unresolved.