Olimpia Lombardi

The purpose of this talk is to briefly recall the main principles of quantum mechanics in order to understand the ontological challenges introduced by the theory. In particular, I will argue that quantum mechanics defies the category of individual for three different reasons: contextuality, non-separability, and indistinguishability. Each one of these three features of the theory violates a traditional ontological principle: the Principle of Omnimode Determination, the Principle of Separability, and the Principle of Identity of Indiscernibles, respectively. Therefore, any interpretation of quantum mechanics should formulate a “global” solution, according to which the three ontological challenges could be adequately tackled in terms of a single ontology.

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.

Up to this point, each one of the chapters has dealt with some topic in an argumentatively ordered way. In this last chapter, on the contrary, I want to present some issues that I consider should not be left out, but which are not closely related to each other. Therefore, the first three sections of this miscellanea chapter can be read in any order. The last one, by contrast, makes sense as a closing section since it introduces my general philosophical position, which explains my interpretative strategy with regard to quantum mechanics.

In the previous chapter, the structure of the ontology proposed by the MHI was introduced. In this ontology, properties are the fundamental items and quantum systems are non-objectual bundles of properties. However, as is well known, metaphysics is underdetermined by physics; in particular, quantum mechanics is compatible with different ontological pictures. Thus, arguing in favor of a certain quantum ontology over others requires showing how fruitful it is in the task of offering reasonable solutions to interpretative problems. This chapter is devoted to show the advantages of the proposed picture for dealing with the ontological challenges of quantum mechanics: contextuality, non-separability, and indistinguishability. Finally, the top-down approach presented in Chapter 8 is revisited, showing how it acquires an ontological significance from the perspective of the ontology of properties proposed by the MHI.

In the present chapter, the Modal-Hamiltonian Interpretation (MHI) is introduced in terms of interpretative postulates. These postulates distinguish between type-properties and case-properties, and define quantum systems as bundles of properties. The Hamiltonian of the system plays a central role in the definition of systems and subsystems. Moreover, according to the MHI-Actualization Rule, the selection of the preferred context is based on the Hamiltonian. In this chapter, the MHI is introduced in a neutral way, without discussing its advantages over other proposals. The arguments supporting it will become clear in the following chapters, where its physical relevance will be explained (Chapter 5) and it will be applied to solve traditional interpretative challenges (Chapter 6).

The purpose of this book is to present an interpretation of quantum mechanics. But what are we talking about when we speak of “quantum mechanics?” Are we talking about a single theory or about many related theories? And what do we mean by “interpretation” here? In this chapter, I will address these questions in an introductory way. Of course, I do not intend to take part in the extensive discussions about what a scientific theory is, what is meant by interpreting a theory, in what situation we encounter equivalent theories, and many other questions related to or derived from these. My aim here is to present some preliminary ideas in a way that I hope will be sufficient to avoid misunderstandings in the following chapters. But, above all, I will state my position as to why, after so many years and so much literature on the subject, the interpretation of quantum mechanics deserves further discussion.

When I first met Mario Castagnino at the end of 2000, he was already an internationally recognized senior physicist, but he had never worked in the field o

The problem of the interpretation of non-relativistic quantum mechanics is certainly one of the most discussed topics in the philosophy of physics, which h

The content of the present book is the result of a work developed over a period of more than fifteen years, to which many students and collaborators, as we