Probabilistic Causality from Graviton Fluctuations
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) =4GNTt/3 , 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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BibTeX
@misc{cintia2026probabilistic,
title = {{Probabilistic Causality from Graviton Fluctuations}},
author = {Giordano Cintia and Federico Piazza and Samuel Ramos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.02729},
eprint = {2606.02729},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.02729},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Probabilistic Causality from Graviton Fluctuations
AU - Giordano Cintia
AU - Federico Piazza
AU - Samuel Ramos
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2606.02729
UR - https://arxiv.org/abs/2606.02729
AB - We compute the commutator of a scalar field minimally coupled to gravity at leading order in G_N. 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) =4G_NTt/3 , 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.
ER -