A particular theoretical development of quantum mechanics, called the process matrix formalism (PMF), features what is 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 order (ICO).

As a first step, this work aims at investigating the philosophical implications of causal nonseparability, especially for the notion of spatiotemporal relations. We show that, depending on the interpretative framework, causal nonseparability suggests some kind of indeterminacy of spatiotemporal relations. Importantly, this result hinges on the particular physical implementation of ICOs.

As a second step, we discuss possible implications on the laws of nature, and ask whether these results could help illuminate the status of spacetime in approaches to quantum gravity in which spacetime is emergent, rather than fundamental