Causal nonseparability and its implications for spatiotemporal relations

Abstract: Quantum nonseparability is a central feature of quantum mechanics, and raises important philosophical questions. Interestingly, a particular theoretical development of quantum mechanics, called the process matrix formalism (PMF), features another kind of nonseparability, called causal nonseparability. The PMF appeals to the notion of quantum process, which is a generalisation of the concept of quantum state allowing to represent quantum-like correlations between quantum events over multiple parties without specifying a priori their spatiotemporal locations. Crucially, since the PMF makes no assumption about the global causal structure between quantum events, it allows for the existence of causally nonseparable quantum processes having an indefinite causal structure. This work aims at investigating the philosophical implications of causal nonseparability, especially for the notion of spatiotemporal relations. A preliminary discussion will study the formal connection between quantum and causal nonseparability. It will be emphasised that, although quantum processes can be seen as a generalisation of density matrices, the conceptual distinction between the two notions yields significant differences between quantum and causal nonseparability. From there, it will be shown that, depending on the interpretative framework, causal nonseparability suggests some kind of indeterminacy of spatiotemporal relations. Namely, within a realist context, spatiotemporal relations can be epistemically or metaphysically indeterminate. Finally, it will be argued that, in spite of the disanalogies between standard and causal nonseparability, similar implications for spatial relations can already be defended in the context of standard quantum mechanics. This work highlights the potentially very fruitful explorations of the implications of quantum features on the conception of spacetime.