Humean supervenience and tripartite entanglement relations

Lorenzo Lorenzetti

doi:10.1007/s10516-020-09522-7

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).

Highlights

This paper concerns the difficult relationship between Humean Supervenience and quantum entanglement
I will try to show that the strategy of adding entanglement relations to the supervenience basis clash with Lewis’s idea that ‘anything can coexist with everything’ and that there are no necessary connections between the intrinsic nature of distinct entities
Such contrast highlights the fact that entanglement relations cannot be included within the supervenience basis, if we want to retain the principle of free recombination

Summary

Introduction

This paper concerns the difficult relationship between Humean Supervenience and quantum entanglement. I will try to show that the strategy of adding entanglement relations to the supervenience basis clash with Lewis’s idea that ‘anything can coexist with everything’ and that there are no necessary connections between the intrinsic nature of distinct entities Such contrast highlights the fact that entanglement relations cannot be included within the supervenience basis, if we want to retain the principle of free recombination. These strategies all hinges on questionable assumptions, which are still a matter of discussion To put it roughly, the Humean would have to either endorse Bohmian mechanics or the nomological account of the wave function–and one can point out that it would be quite radical to endorse Bohmian mechanics only to save HS. What I claim in the present paper is that, if one wants to defend HS, the conservative strategy of adding the entanglement relations to the supervenience basis is very problematic, and one of the more radical options should be adopted instead

The humean mosaic and its relations

Entanglement relations in the humean mosaic?

Humean supervenience and the GHZ state

Entanglement relations and free recombination

Conclusion