The central role of the Hamiltonian in quantum mechanics: decoherence and interpretation

Mario Castagnino, Olímpia Lombardi

In this paper we propose a new realist, non-collapse interpretation of quantum mechanics, which moves away from the prevailing trend in the subject by paying special attention to the physical relevance of the interpretation. In particular, our proposal endows the Hamiltonian of the system, systematically ignored in the traditional interpretations, with a central role: it distinguishes between systems and subsystems and is the main ingredient in the selection of the definite-valued observables. We show how this interpretation solves the measurement problem, both in the ideal and in the non-ideal version, and we argue for the physical relevance of the new definite-value assignment.

Olímpia Lombardi

Abstract Since the Modal-Hamiltonian Interpretation (MHI) is based on the formalism and the minimal interpretation of Standard Quantum Mechanics (SQM), this chapter may seem superfluous: it could be argued that everyone knows what SQM is. However, as remarked in the previous chapter, the identification of SQM is not as immediate as is usually assumed. Therefore, if an interpretation of quantum mechanics is to be precisely developed, the underlying theoretical commitments must be clear from the very beginning. The second reason why this chapter is not superfluous is that the MHI differs from the traditional Hilbert space formulation of SQM by adopting the algebraic formalism as its departing point. Although this might seem a minor formal detail, it will play a central role in the ontological picture arising from the MHI interpretation, as will be seen in Chapter 10.

Domenico Giulini

Leonardi Hernández-Sánchez, Efraín Villatoro, Noribeth Fuentes González

The Hamiltonian is one of the fundamental concepts in quantum mechanics. It is traditionally introduced as the operator associated with the total energy of a system; however, its role extends far beyond this formal interpretation, as it organizes the dynamics, defines the relevant observables, and structures the physical description of quantum systems. This work presents a theoretical analysis of the Hamiltonian as a conceptual tool, addressing its role in closed systems and its extension to open systems described by the Lindblad equation. Its implications for the interpretation of quantum dynamics are discussed, as well as its relevance in contemporary applications such as quantum optics and dissipative systems. The study is developed through an analytical review of the literature, highlighting the importance of the Hamiltonian not only as a mathematical operator, but as a central element in the construction of physical knowledge.

Olímpia Lombardi, Mario Castagnino