Can causal inequalities be violated when spacetime itself is superposed?
This text mentions work from 2024 on. Those parts were partly written without a live literature search and have not been checked by an editor yet.
In plain words
Some theoretical processes give correlations that no fixed, or randomly chosen, order of events could explain; these violate causal inequalities. They cannot appear for events localized in an ordinary fixed spacetime; whether a spacetime in superposition, as quantum gravity may allow, can produce them is unknown.
Precise statement
Causal inequalities bound correlations $p(a,b\mid x,y)$ achievable when parties act in a definite or classically random order. With spacetime-localized operations in a fixed acyclic spacetime they cannot be violated (Vilasini and Renner, PRA 2024), and on time-delocalized subsystems they can (Wechs, Branciard, Oreshkov, Nat. Commun. 2023). Determine whether a violation by spacetime-localized operations is possible when the spacetime geometry itself is in superposition (a gravitating source mass in spatial superposition), and give the minimal source mass and coherence time for it.
What would settle it
A proof that localized realizations are impossible even with superposed geometry, or an explicit physical protocol with a gravitating source in superposition achieving a violation.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Fixed-spacetime localized realizations are excluded (Vilasini and Renner, PRA 2024); time-delocalized realizations exist (Wechs et al., 2023); the dynamical-spacetime case is open.
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