  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.
