- Accepted Paper
Probabilistic causality from graviton fluctuations
Phys. Rev. D - Accepted 2 November, 2026
DOI: https://doi.org/10.1103/v7p6-qcq3
Phys. Rev. D - Accepted 2 November, 2026
DOI: https://doi.org/10.1103/v7p6-qcq3
We compute the commutator of a scalar field minimally coupled to gravity at leading order in . 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 . In the large-time limit, the uncertainty of the lightcone position is given by where is the displacement from the classical lightcone at . We obtain this result by subtracting a universal vacuum contribution that is logarithmically UV divergent and subleading at late times.
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