• Accepted Paper

Probabilistic causality from graviton fluctuations

Giordano Cintia, Federico Piazza, and Samuel Ramos

Phys. Rev. D - Accepted 2 November, 2026

DOI: https://doi.org/10.1103/v7p6-qcq3

Abstract

We compute the commutator of a scalar field minimally coupled to gravity at leading order in GN. The commutator is operator-valued, with terms involving derivatives of Dirac deltas supported on the Minkowski light cone. When evaluated on classical/coherent graviton states, these terms ``bend" the support of the commutator in precisely the way required to recover standard causality on a classical curved spacetime. However, these terms are also associated with a variance and are thus a source of uncertainty in the causal relations between events. We quantify this effect for a thermal state of gravitons at temperature T. In the large-time limit, the uncertainty of the lightcone position is given by Var(δx)=4GNTt3, where δx is the displacement from the classical lightcone at |x⃗|=t. We obtain this result by subtracting a universal vacuum contribution that is logarithmically UV divergent and subleading at late times.

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