Abstract
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.
Highlights
The notion of causality is one of the most prominent in science, and in philosophy of Nature.Its treatment separates Aristotelian from the modern physics, and its formal meaning within the latter is likely to have played a significant role, over the past centuries since Galileo, in forming our current everyday understanding of the notion of causality
It was argued that the quantum switch, a specific controlled operation introduced in [3], exhibits superpositions of causal orders, in the context of quantised gravity, where genuine superpositions of different states of gravity are present, and in the experimental realisations performed in classical spacetimes with fixed causal structure [4, 5, 6]
We argue that genuine superpositions of different causal orders are to be expected within the quantum gravity (QG) scenario, where superpositions of different states of the gravitational field, with their corresponding causal orders, are manifestly allowed (Hardy was one of the first to discuss the notion of superpositions of causal orders in the context of QG [7])
Summary
The notion of causality is one of the most prominent in science, and in philosophy of Nature. While in Newtonian physics the cause-effect relations were encompassed by a rather simple linear and absolute time, Einstein’s analysis of causal relations was pivotal in the formulation of the theory of relativity It was quantum mechanics (QM) that, through the EPR argument [1], further formalised by Bell [2], showed how quantum nonlocality, rooted in the superposition principle of QM, revolutionised our everyday notion of causality. We explicitly construct two distinct observables that can distinguish between the realisations of the quantum switch in classical spacetimes, and implementations of the gravitational switch in superposed spacetimes This way, we show that the two notions of causal orders, namely one discussed in [4, 5, 6] and the other discussed in this paper, can be experimentally distinguished, in contrast to the opposite claim present in the literature [4].
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