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Philosophy of Science

A New Look at Relational Holism in Quantum Mechanics

Matteo Morganti

Published Dec 1, 2009• 23 citations
Publisher

Abstract

Teller argued that violations of Bell's inequalities are to be explained by interpreting quantum entangled systems according to ‘relational holism’, that is, by postulating that they exhibit irreducible (‘inherent’) relations. Teller also suggested a possible application of this idea to quantum statistics. However, the basic proposal was not explained in detail nor has the additional idea about statistics been articulated in further work. In this article, I reconsider relational holism, amending it and spelling it out as appears necessary for a proper assessment, and application, of the position.

DOI
10.1086/605809

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Teller argued that violations of Bell's inequalities are to be explained by interpreting quantum entangled systems according to ‘relational holism’, that is, by postulating that they exhibit irreducible (‘inherent’) relations. Teller also suggested a possible application of this idea to quantum statistics. However, the basic proposal was not explained in detail nor has the additional idea about statistics been articulated in further work. In this article, I reconsider relational holism, amending it and spelling it out as appears necessary for a proper assessment, and application, of the position.
We put forward a new, ‘coherentist’ account of quantum entanglement, according to which entangled systems are characterized by symmetric relations of ontological dependence among the component particles. We compare this coherentist viewpoint with the two most popular alternatives currently on offer—structuralism and holism—and argue that it is essentially different from, and preferable to, both. In the course of this article, we point out how coherentism might be extended beyond the case of entanglement and further articulated.
Richard Healey has recently defended an interactive and holistic interpretation of quantum mechanics. The present work focuses on the holistic aspects of this interpretation. Healey claims that symmetric causes are responsible for the experimental violations of the Bell inequalities and that relational holism is a metaphysical implication of these violations. Presented in this way, the holistic features of Healey's interpretation appear to provide metaphysical backing to the physical mechanism of symmetric causes. It is argued that relational holism is not a metaphysical implication at all but is actually a physical component of Healey's interpretation. Seen in this light, Healey's interpretation no longer appears to provide further insight into the violations of the Bell inequalities.
Abstract Quantum mechanics is often said to entail holism—that wholes are more than just the sum of their parts—and hence violate Humean supervenience. Certainly an entangled state cannot readily be interpreted in terms of the properties of the individual particles involved. But there is no clear general argument from quantum mechanics to holism. Still, each of the three major interpretations of quantum mechanics—Bohm, GRW, and many worlds—embodies some form of holism. One might try to rescue Humean supervenience by moving to high-dimensional representation of physical systems, or by constructing a theory with backward-in-time causation, but it is unclear if such strategies will succeed. If holism is accepted, some argue further that there are no individuals at the fundamental physical level: Either relations are fundamental, or the whole universe is fundamental. The arguments for these positions are assessed and found to be wanting.
In this article, the weakest possible theorem giving a foundation behind the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelled out in detail. It is argued that, from this approach, a general epistemic interpretation of quantum mechanics is natural. Some applications to the Bell experiment and to decision theory are briefly discussed. The article represents the conclusion of a series of articles and books on quantum foundations.
An argument to the effect that quantum mechanics commits us to the existence of non-supervenient relations, and therefore that we should admit such relations into our quantum ontology as fundamental entities, has been given by Teller and reformulated by French. This paper aims, first, to explicate and evaluate that argument; second, to extend its premises in order to assess its relevance for other interpretations of quantum mechanics; and, third, to clarify its implications for holism and individuation in quantum ontology.