Non-separability, locality and criteria of reality: a reply to Waegell and McQueen

Using a 'reformulation of Bell's theorem', Waegell and McQueen, (2020) argue that any local theory which does not involve retro-causation or fine-tuning must be a many-worlds theory. Moreover they argue that non-separable many-worlds theories whose ontology is given by the wavefunction involve superluminal causation, as opposed to separable many-worlds theories (e.g. Waegell, 2021; Deutsch and Hayden 2000). I put forward three claims. (A) I challenge their argument for relying on a non-trivial, unquestioned assumption about elements of reality which allows Healey's approach (Healey, 2017b) to evade their claim. In an attempt to respond to (A), Waegell and McQueen may restrict their claim to theories which satisfy such an assumption, however, I also argue that (B) their argument fails to prove even the so weakened claim, as exemplified by theories that are both non-separable and local. Finally, (C) by arguing for the locality of the decoherence-based Everettian approach (Wallace, 2012) I refute Waegell and McQueen's claim that wavefunction-based ontologies, and more generally non-separable ontologies, involve superluminal causation. I close with some doubtful remarks about separable Everettian interpretations as compared to non-separable ones.