Signatures of causality and determinism in a quantum theory of events

By representing an event as the joint state of a detector-timer couple that interacts with a system, we recover the familiar tensor product structure, used to describe spatially separated systems, in the context of timelike events. Furthermore, with this approach, we extend the superposition principle to the moment of occurrence of events. We then outline quantum signatures of causality that manifest through coherence in the detector state and correlation functions of time operators. Finally, we expand the scope of quantum information theoretic measures of state discrimination and information content, commonly used to characterize spatially separated systems, to events in spacetime. For causally connected events, we illustrate a deterministic relationship between events (akin to spatially entangled physical systems) where observing a previous event (one subsystem) enables us to delineate a later event (the other subsystem).

Automated summary

By representing events as joint states of detector-timer couples interacting with systems, this study recovers the tensor product structure commonly used to describe spatially separated systems in the context of time events. The superposition principle is extended to the moment of occurrence of events. Quantum signatures of causality are outlined through coherence in the detector state and correlation functions of time operators. Additionally, quantum information theoretic measures commonly used to characterize spatially separated systems are expanded to events in spacetime.