Agenda

In quantum mechanics, quantum nonseparability is at the core of philosophical debates regarding its meaning. Interestingly, the more general context of the process matrix formalism features another kind of nonseparability, called causal nonseparability. It characterises quantum processes (connecting the inputs and outputs of different local quantum operations) that are incompatible with any definite causal structure among interacting parties. The present work discusses the possible interpretations of causal nonseparability under the assumption that it points towards novel objective features of nature.

 

It is first defended that a scientific realist approach towards the process matrix formalism, which is an operational theory generalising quantum mechanics, is as much legitimate as any possible antirealist reading, contrary to certain views found in the literature. The reason is that operational formalisms are ontologically and epistemically neutral. From there, the theoretical concept of interest, namely causal nonseparability and its model-independent counterpart called noncausality, are analysed in more details, in order to highlight in what sense they are distinct from the standard notions of quantum nonseparability and nonlocality in quantum mechanics. The discussion then focuses on noncausality. It is argued that noncausality has an interesting connection with a notion of temporal nonlocality, which is a more constraining principle than that of local causality used in Bell’s theorem. In the same way that Bell nonlocality is given different underlying explanations depending on the details of the chosen quantum mechanics’ account, noncausality can be given a variety of underlying descriptions depending on the exact way to interpret the process matrix formalism. The last chapter focuses precisely on this particular point, namely on the various ways to understand process matrices and causal nonseparability in a realist context. In order to explore the potential impact of causal nonseparability on spacetime, we shift from the notion of (indefinite) causal structure to (indefinite) spatiotemporal ones. This shift is allowed under a set of reasonable assumptions regarding the properties of a physical spacetime manifold and the connection between an operational and relativistic notion of causal relations. While different readings are suggested for indefiniteness of spatiotemporal relations, we insist in particular on an objective understanding appealing to the concept of metaphysical indeterminacy. It is argued that such an approach could prove useful in a more general theoretical context such as quantum gravity, while being already partly supported in standard quantum mechanics.