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Studies in History and Philosophy of Science Part A

Quantum modal indeterminacy

Claudio Calosi

Published Sep 6, 2022• 25 citations
Publisher

Abstract

The paper investigates the existence and the nature of quantum indeterminacy in a particular realist interpretation of quantum mechanics, that is, the Modal Hamiltonian Interpretation (MHI)-together with an ontology of properties for quantum systems. In doing so, it serves a twofold purpose. First, it advances the debate on quantum ontology by showing precisely how and why indeterminacy arises in a quantum world-as described by the MHI. Second, it offers a naturalistic example of genuine metaphysical indeterminacy, an example coming from our best physics.

DOI
10.1016/j.shpsa.2022.08.012

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The paper investigates the existence and the nature of quantum indeterminacy in a particular realist interpretation of quantum mechanics, that is, the Modal Hamiltonian Interpretation (MHI)-together with an ontology of properties for quantum systems. In doing so, it serves a twofold purpose. First, it advances the debate on quantum ontology by showing precisely how and why indeterminacy arises in a quantum world-as described by the MHI. Second, it offers a naturalistic example of genuine metaphysical indeterminacy, an example coming from our best physics.
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 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.
Abstract Many features of quantum mechanics (QM) suggest that, at the microscopic level, objects sometimes fail to determinately instantiate their properties. In recent years, many have argued that this phenomenon indicates the existence of an ontological kind of indeterminacy, often called metaphysical indeterminacy , which is supposed to affect the ontology of QM. As insisted by Glick ('Against Quantum Indeterminacy, 2017, Thought), however, once we look at the major realist approaches to QM we learn that the indeterminacy disappears from the description of the world at its most fundamental level. This absence might be taken as a good reason for adopting some form of eliminativism towards quantum mechanical indeterminacy. The aim of this paper is to distinguish three ways of defending eliminativism, and to argue that none of them eventually succeeds. The upshot is that QM does in fact suggest the existence of metaphysical indeterminacy, although only as an emergent phenomenon.
The question of whether Everettian quantum mechanics (EQM) justifies the existence of metaphysical indeterminacy has recently come to the fore. Metaphysical indeterminacy has been argued to emerge from three sources: coherent superpositions, the indefinite number of branches in the quantum multiverse and the nature of these branches. This paper reviews the evidence and concludes that those arguments don't rely on EQM alone and rest on metaphysical auxiliary assumptions that transcend the physics of EQM. We show how EQM can be ontologically interpreted without positing metaphysical indeterminacy by adopting a deflationary attitude towards branches. Two ways of developing the deflationary view are then proposed: one where branches are eliminated, and another where they are reduced to the universal quantum state.
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.