The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? What happens when we address these questions from the standpoint of quantum mechanics in a new framework for multipartite correlations that does not assume a pre-defined global causal structure but only the validity of quantum mechanics locally? All known situations that respect causal order, including space-like and time-like separated experiments, are captured by this framework in a unified way. Surprisingly, we find correlations that cannot be understood in terms of a definite causal order. These correlations violate a 'causal inequality' that is satisfied by all space-like and time-like correlations. It also means that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition.
One of the striking features of quantum mechanics is that it challenges the view that physical properties are well defined before and independent of their measurement. This motivates an operational approach to the theory, where primitive laboratory procedures, such as measurements and preparations, are basic ingredients. Although significant progress has recently been made in this direction, most approaches still retain a notion of space-time as a pre-existing 'stage' in which events take place. Even the most abstract constructions, in which no explicit reference to space-time is made, do assume a definite order of events: if a signal is sent from an event A to an event B in the run of an experiment, no signal can be sent in the opposite direction in that same run. But are space, time and causal order truly fundamental ingredients of nature? Is it possible that, in some circumstances, even causal relations would be 'uncertain', similarly to the way other physical properties of quantum systems are?
Does quantum mechanics allows for such a possibility - at least in a framework that describes all correlations that can be observed by two experimenters under the assumption that in their local laboratories physics is described by the standard quantum formalism, but without assuming that the laboratories are embedded in any definite causal structure? These include non-signalling correlations arising from measurements on a bipartite state, as well as signalling ones, which can arise when a system is sent from one laboratory to another through a quantum channel. Surprisingly, in such a system, more general correlations are possible, which are not included in the standard quantum formalism. These correlations are incompatible with any underlying causal structure: they allow performing a task—the violation of a 'causal inequality'—that is impossible if events take place in a causal sequence. This is directly analogous to the famous violation of local realism: quantum systems allow performing a task—the violation of Bell's inequality—that is impossible if the measured quantities have pre-defined local values. The inequality considered here, unlike Bell's, concerns signalling correlations: it is based on a task that involves communication between two parties. Nevertheless, it cannot be violated if this communication takes place in a causal space-time. Previous works about relativistic causality in quantum mechanics focused on non-signalling correlations between space-like separated experiments or on a finite speed of signalling.