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Modal Interpretations of Quantum Mechanics

Olímpia Lombardi

Published Feb 19, 2026• 0 citations
Publisher

Abstract

Abstract Since the aim of this book is to introduce the Modal-Hamiltonian Interpretation (MHI) in a comprehensive way, this chapter focuses on the family of Modal Interpretations of quantum mechanics, to which the MHI belongs. The purpose is, then, to recall the common features of the Modal Interpretations as well as the differences between them. In particular, the original proposal of van Fraassen is presented, and the Biorthogonal-Decomposition Modal Interpretation, the Spectral-Decomposition Modal Interpretation, the Atomic Modal Interpretation, and the Perspectival Modal Interpretation are described, pointing out their advantages and limitations.

DOI
10.1093/9780198951407.003.0003

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Abstract Since the aim of this book is to introduce the Modal-Hamiltonian Interpretation (MHI) in a comprehensive way, this chapter focuses on the family of Modal Interpretations of quantum mechanics, to which the MHI belongs. The purpose is, then, to recall the common features of the Modal Interpretations as well as the differences between them. In particular, the original proposal of van Fraassen is presented, and the Biorthogonal-Decomposition Modal Interpretation, the Spectral-Decomposition Modal Interpretation, the Atomic Modal Interpretation, and the Perspectival Modal Interpretation are described, pointing out their advantages and limitations.
Abstract 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).
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.
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.
Before considering the particulars of the different versions of the modal interpretation in the next chapter, I first present their common characteristics. Then I list the starting points from which I develop these modal interpretations to fully-fledged descriptions of reality. Finally, I give the criteria I think interpretations should meet and present a number of desiderata I hope they meet. General characteristics The name ‘modal interpretation’ originates with Van Fraassen (1972) who, in order to interpret quantum mechanics, transposed the semantic analysis of modal logics to the analysis of quantum logic. The resulting interpretation was for obvious reasons called the modal interpretation of quantum logic. Since then, the term modal interpretation has acquired a much more general meaning and lost its direct kinship with modal logics. In particular new interpretations of quantum mechanics developed in the 1980s by Kochen (1985), Krips (1987), Dieks (1988), Healey (1989) and Bub (1992) became known as modal interpretations and also older traditions like Bohmian mechanics (Bohm 1952; Bohm and Hiley 1993) were identified as modal ones. But why are all these interpretations still called modal? And what is the present-day meaning of this term? I think part of the answer to the first question has to do with public relations. The name ‘modal’ is short, sounds nice and is rather intriguing. Furthermore, I guess that also Van Fraassen's prestige as a philosopher of science adds a special gloss to the term. But, apart from all this, I believe the name ‘modal interpretation’ is quite suited.
Abstract Standard Quantum Mechanics is a theory that has been applied to many concrete physical situations and by means of which an impressive amount of experimental evidence has been accounted for. Therefore, a “good” interpretation must not only meet the traditional interpretative challenges of the theory, but must also show its agreement with the orthodox practice of physics. This chapter is devoted to argue for the physical relevance of the MHI by applying it to well-known models and experimental results, which will be presented in the usual physical language. In particular, it is applied to the free particle, free particle with spin, harmonic oscillator, free hydrogen atom, Zeeman effect, fine structure, decoherence, the Born-Oppenheimer approximation, the problem of symmetry in quantum chemistry.
Abstract In Chapter 4, the MHI was introduced in terms of interpretative postulates that define the ontological reference of each physical term of quantum mechanics in its standard formulation. On the basis of that presentation, an ontology of properties, framed in the algebraic formalism of quantum mechanics, was proposed. The aim of this chapter is to set out in detail the structure of the ontology proposed by the MHI, now with the technical metaphysical resources developed in the previous chapter. In particular, the nature of the properties that constitute the fundamental ontological items is discussed, and it is argued that quantum systems are not objects at all, but mere collections of properties that do not retain their identity either synchronically or diachronically. More precisely, quantum systems turn out to be non-objectual bundles of properties.