Quantum entanglement and a metaphysics of relations

Abstract

This paper argues for a metaphysics of relations based on a characterization of quantum entanglement in terms of non-separability, thereby regarding entanglement as a sort of holism. By contrast to a radical metaphysics of relations, the position set out in this paper recognizes things that stand in the relations, but claims that, as far as the relations are concerned, there is no need for these things to have qualitative intrinsic properties underlying the relations. This position thus opposes a metaphysics of individual things that are characterized by intrinsic properties. A principal problem of the latter position is that it seems that we cannot gain any knowledge of these properties insofar as they are intrinsic. Against this background, the rationale behind a metaphysics of relations is to avoid a gap between epistemology and metaphysics.

Introduction

The aim of this paper is to propose a philosophical characterization of quantum entanglement within a broader metaphysical framework.¹ The framework is the one of a metaphysics of relations in contrast to a metaphysics of individual things that are characterized by intrinsic properties. A metaphysics of relations is a minority view in contemporary philosophy. According to the mainstream of metaphysical thought, the world consists of independent individual things that are embedded in space–time. These things are individuals, because (a) they have a spatio-temporal location, (b) they are a subject of the predication of properties each and (c) there are some qualitative properties by means of which each of these things is distinguished from all the other ones (at least the spatio-temporal location is such a property).

Qualitative properties are all and only those properties whose instantiation does not depend on the existence of any particular individual; properties such as being that individual are hence excluded. These things are independent, because their basic properties are intrinsic ones. Basic properties are fundamental in that they are not reducible to other properties, and they are not disjunctive; that is to say, properties such as “being round or square” are excluded. Intrinsic are all and only those qualitative properties that a thing has irrespective of whether or not there are other contingent things; all other qualitative properties are extrinsic or relational. That is to say: having or lacking an intrinsic property is independent of accompaniment or loneliness.²

A metaphysics of this type can be traced back to Aristotle at least. Aristotle assumes that there is a plurality of individual things (substances) that are characterized by intrinsic properties (forms) each.³ A prominent contemporary conception is David Lewis’ thesis of Humean supervenience:⁴ at the basic level of the world, there are only local qualities in the sense of intrinsic properties instantiated by space–time points or point-sized particles or field sources at space–time points. Space–time points can qualify as individual things in the above-mentioned sense. Everything there is in a world like ours supervenes on the distribution of basic intrinsic properties over all space–time points. Whether really everything supervenes on that distribution is not relevant to the present paper. What is important here is the claim that, except for spatio-temporal relations, all the relations between the things at the basic level supervene on their intrinsic properties.

It is well known that quantum physics—notably quantum entanglement—poses a challenge to Lewis’ Humean supervenience. This paper argues that quantum physics can be taken to suggest replacing a metaphysics of intrinsic properties with a metaphysics of relations. This is, of course, a matter of weighing arguments in the interpretation of a physical theory. There is no direct route of logical implication from physics to a particular metaphysics. A metaphysics of relations is often dismissed out of hand, for it seems to be paradoxical. It seems that (a) relations require relata, that is, things which stand in the relations, and that (b) these things have to be something in themselves, that is, must have intrinsic properties over and above the relations in which they stand.⁵ However, a metaphysics of relations merely has to reject the second part of this claim: one can maintain that (a) relations require relata, that is, things which stand in the relations, but that (not b) these things do not have any intrinsic properties that underlie the relations in which they stand. There is nothing paradoxical in this latter claim. This paper argues for no more than this claim.

By a “thing”, I mean anything that is a subject of the predication of properties, including relational properties (relations), without being itself predicated as a property of something. I do not distinguish relations from relational properties: relations are properties as well (albeit not monadic ones) in that they are predicated of things. Moreover, something can be a thing without being an individual thing; for something to be an individual thing (an individual), further conditions may have to be met such as (a) being distinguishable from all the other things by means of the predication of some qualitative properties or (b) having a primitive thisness (haecceity).⁶

A metaphysics of relations can grant that things may have non-qualitative properties over and above the relational ones such as the property of being this thing, that is, a primitive thisness; but this position does not have to admit primitive thisness. Accepting that relations require things which stand in the relations does not commit one to the view that these things have a primitive thisness. It simply means taking into account that properties, including relations, are predicated of something; this does not imply that there is more to the related things than standing in the relations. If one does not endorse primitive thisness, one may say that a thing is a bundle of properties (or tropes); how a thing can be a bundle of relational properties (or relational tropes) is no more—and no less—a problem than how it can be a bundle of intrinsic properties (or intrinsic tropes). Hence, both the view of things as being characterized by primitive thisness and the view of things as bundles of properties (or tropes) are compatible with a metaphysics of relations.

The plan of the paper is as follows: Starting from a conceptualization of quantum entanglement in terms of non-supervenient relations, the next section argues for conceiving quantum entanglement as a case of non-separability (that is, a case of holism). It is shown how this interpretation of quantum entanglement leads to a metaphysics of relations. The third section then establishes that this is a moderate metaphysics of relations in contrast to a radical one. Finally, this interpretation of quantum entanglement is put into the broader framework set out in this introduction: it is argued that this interpretation avoids a gap between epistemology and metaphysics, whereas a metaphysics of intrinsic properties invites such a gap.