Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Postulates of the Modal-Hamiltonian Interpretation

Olímpia Lombardi

Published Feb 19, 2026• 0 citations
Publisher

Abstract

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).

DOI
10.1093/9780198951407.003.0004

Related papers

A modal-Hamiltonian interpretation of quantum mechanics

Olímpia Lombardi, Mario Castagnino

The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties.

arXiv:quant-ph/0610121•Oct 15, 2006•1 citation

The Structure of the Modal-Hamiltonian Ontology

Olímpia Lombardi

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.

•Feb 19, 2026•0 citations

Modal Interpretations of Quantum Mechanics

Olímpia Lombardi

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.

•Feb 19, 2026•0 citations

Compatibility between Environment-Induced Decoherence and the Modal-Hamiltonian Interpretation of Quantum Mechanics

Olímpia Lombardi, Juan Sebastián Ardenghi, Sebastián Fortín +1 more

Given the impressive success of environment-induced decoherence (EID), nowadays no interpretation of quantum mechanics can ignore its results. The modal-Hamiltonian interpretation (MHI) has proved to be effective for solving several interpretative problems, but since its actualization rule applies to closed systems, it seems to stand at odds with EID. The purpose of this article is to show that this is not the case: the states einselected by the interaction with the environment according to EID (the elements of the “pointer basis”) are the eigenvectors of an actual-valued observable belonging to the preferred context selected by the MHI.

Philosophy of Science•Dec 1, 2011•22 citations

The Modal-Hamiltonian Interpretation of Quantum Mechanics as a Kind of “Atomic” Interpretation

Juan Sebastián Ardenghi, Olímpia Lombardi

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.

Physics Research International•Oct 30, 2011•11 citations

Standard Quantum Mechanics: Formalism and physical content

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.

•Feb 19, 2026•0 citations
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).
The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties.
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.
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.
Given the impressive success of environment-induced decoherence (EID), nowadays no interpretation of quantum mechanics can ignore its results. The modal-Hamiltonian interpretation (MHI) has proved to be effective for solving several interpretative problems, but since its actualization rule applies to closed systems, it seems to stand at odds with EID. The purpose of this article is to show that this is not the case: the states einselected by the interaction with the environment according to EID (the elements of the “pointer basis”) are the eigenvectors of an actual-valued observable belonging to the preferred context selected by the MHI.
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.
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.