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On algebraic object naturalism and metaphysical indeterminacy in quantum mechanics

Tushar Menon

Published Sep 27, 2023• 0 citations
OpenAlex

Abstract

I propose a technique for identifying fundamental properties using structures already present in physical theories. I argue that, in conjunction with a particular naturalistic commitment, that I dub `algebraic naturalism', these structures can be used to generate a standard of metaphysical determinacy. This standard can be used to rule out the possibility of a virulent strain of `deep' metaphysical indeterminacy that has been imputed to quantum mechanics.

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On algebraic naturalism and metaphysical indeterminacy in quantum mechanics

Tushar Menon

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I propose a technique for identifying fundamental properties using structures already present in physical theories. I argue that, in conjunction with a particular naturalistic commitment, that I dub algebraic naturalism', these structures can be used to generate a standard of metaphysical determinacy. This standard can be used to rule out the possibility of a virulent strain of deep' metaphysical indeterminacy that has been imputed to quantum mechanics.
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.
There has been recent interest in formulating theories of non-representational indeterminacy. The aim of this paper is to clarify the relevance of quantum mechanics to this project. Quantum-mechanical examples of vague objects have been offered by various authors, displaying indeterminate identity, in the face of the famous Evans argument that such an idea is incoherent. It has also been suggested that the quantum-mechanical treatment of state-dependent properties exhibits metaphysical indeterminacy. In both cases it is important to consider the details of the metaphysical account and the way in which the quantum phenomenon is captured within it. Indeed if we adopt a familiar way of thinking about indeterminacy and apply it in a natural way to quantum mechanics, we run into illuminating difficulties and see that the case is far less straightforward than might be hoped.
The scientific realist wants to read the metaphysical picture of reality through our best fundamental physical theories. The traditional way of doing so is in terms of objects, properties, and laws of nature. For instance, there are families of fundamental particles individuated by their properties of mass and charge, which determine how they move. One could call this view an object-oriented metaphysics grounded on properties. In this paper, I wish to present an alternative view that one can dub a thin object-oriented metaphysics grounded on structure: there are fundamental entities with no fundamental properties other than the one(s) needed to specify their nature. I argue that my view has several advantages over the received one. In particular, I compare my proposal to the traditional view in the quantum domain and I argue that my view provides a better fit for both approaches to quantum metaphysics, namely the primitive ontology program and wave-function realism.
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.
It has frequently been suggested that quantum mechanics may provide a genuine case of ontic vagueness or metaphysical indeterminacy. However, discussions of quantum theory in the vagueness literature are often cur- sory and, as I shall argue, have in some respects been mis- guided. Hitherto much of the debate over ontic vagueness and quantum theory has centered on the indeterminate construal of ontic vagueness, and whether the quantum phenomenon of entanglement produces particles whose identity is indeterminate. I argue that this way of framing the debate is mistaken. A more thorough ex- amination of quantum theory and the phenomenon of entanglement reveals that quantum mechanics is best in- terpreted as supporting what I call the property construal of ontic vagueness, where vague properties are understood in terms of determinable properties without the corresponding determinates.