Humean supervenience and tripartite entanglement relations
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ORIGINAL PAPER
Humean supervenience and tripartite entanglement relations Lorenzo Lorenzetti1 Received: 25 March 2020 / Accepted: 12 October 2020 The Author(s) 2020
Abstract It has been argued that Humean Supervenience (HS) is threatened by the existence of quantum entanglement relations. The most conservative strategy for defending HS is to add the problematic entanglement relations to the supervenience basis, alongside spatiotemporal relations. In this paper, I’m going to argue against this strategy by showing how certain particular cases of tripartite entanglement states – i.e. GHZ states – posit some crucial problems for this amended version of HS. Moreover, I will show that the principle of free recombination – which is strictly linked to HS – is severely undermined if we add entanglement relations to the supervenience basis. I conclude that the conservative move is very unappealing, and therefore the defender of HS should pursue other, more controversial, strategies (e.g. committing to the nomological interpretation of the wave function). Keywords Humean supervenience Quantum mechanics Entanglement relations GHZ state Recombination Locality
1 Introduction This paper concerns the difficult relationship between Humean Supervenience and quantum entanglement. According to the thesis of Humean Supervenience (HS), the world is ‘‘a vast mosaic of local matters of particular fact’’ (Lewis 1986b: ix). That is, all there is in the world are distinct point-sized objects, which instantiate perfectly natural intrinsic properties and which are related by spatiotemporal relations. Several authors have argued that this thesis is at least contingently false, in the light of modern physics. Indeed, it is often claimed that HS is directly in contrast with quantum mechanics. In particular, several philosophers have argued that the
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Axiomathes
phenomenon of quantum entanglement entails that there are some wholes which have properties that are not reducible to the properties of their atomic parts, and that this proves that HS is wrong (see Teller (1986), Maudlin (2007), Karakostas (2009), Darby (2012), Calosi and Morganti (2016)). There are a few ways in which HS can be defended. The less radical move we can pursue (although more radical strategies are viable) consists in adding the problematic entanglement relations to the supervenience basis–the class of entities upon which everything supervenes on—alongside fundamental intrinsic properties and spatiotemporal. By pursuing this strategy, we can account for the properties of entangled systems while relying only on relations between independent point-sized objects. Moreover, these relations would be somehow analogous to spatiotemporal relations. In this way, the Humean can argue that she has saved HS. Both Darby (2012) and Calosi and Morganti (2016) propose this kind of solution for the Humean. However, they are also critical with respect to this
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