Classical Spacetime

Benjamin F. Dribus

Carlos Rodriguez

Abstract The relationship between quantum mechanics and classical spacetime remains one of the central conceptual problems in modern physics. Quantum theory describes physical systems through superpositions of states, while general relativity treats spacetime as a classical geometric structure. The mechanism by which classical spacetime emerges from an underlying quantum description remains unresolved. This work proposes a conceptual framework in which the transition between quantum coherence and classical spacetime is associated with a scalar parameter describing temporal coherence, denoted as the Q field. In this approach, time is not assumed to be a globally fixed background parameter but emerges from the consistency of interacting physical subsystems. The Q field is introduced as an effective scalar field defined over spacetime, providing a structural criterion for temporal compatibility among configurations. The framework suggests that classical spacetime may emerge when interacting subsystems share a consistent temporal ordering, potentially defining a mesoscopic boundary between quantum and classical behavior. Esto suena mucho más académico.

B. G. Sidharth

Nikola Paunković, Marko Vojinović

We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.

Magdalena Zych

Nikola Paunković, Marko Vojinović

We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.