Observer-dependent locality of quantum events

TL;DR

This paper introduces a new formalism called causal reference frames that models observer-dependent causality in quantum events, providing insights into non-causal processes and quantum superpositions of causal order.

Contribution

It proposes causal reference frames as a novel way to describe observer-dependent quantum causality, connecting to the process matrix formalism and exploring implications for quantum gravity.

Findings

Equivalence to the pure process matrix formalism.

Insights into the realizability of non-causal quantum processes.

Analysis of superpositions of causal order in gravitational contexts.

Abstract

In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an observer-independent statement. When events are defined with respect to quantum systems however, nothing guarantees that the causal relationship between A and B is definite. We propose to associate a causal reference frame corresponding to each event, which can be interpreted as an observer-dependent time according to which an observer describes the evolution of quantum systems. In the causal reference frame of one event, this particular event is always localised, but other events can be "smeared out" in the future and in the past. We do not impose a predefined causal order between the events, but only require that descriptions from different reference frames obey a global consistency condition. We show that our new formalism is equivalent to the pure process matrix formalism. The latter is known to predict certain multipartite correlations, which are incompatible with the assumption of a causal ordering of the events -- these correlations violate causal inequalities. We show how the causal reference frame description can be used to gain insight into the question of realisability of such strongly non-causal processes in laboratory experiments. As another application, we use causal reference frames to revisit a thought experiment where the gravitational time dilation due to a massive object in a quantum superposition of positions leads to a superposition of the causal ordering of two events.