Bargmann-invariant witness of the graviton commutator
Abstract
We identify the phase of a Bargmann invariant of two matter-wave interferometers as a quantum gravity signature that cannot be reproduced by any branchwise-definite classical gravitational field. For matter coupled linearly to linearized gravity, the interferometric coherence factorizes exactly into a conservative Newtonian phase, the characteristic functional of the graviton state, and a commutator phase. For Wigner-positive graviton states, the first two are classically reproducible; therefore, decoherence alone cannot certify that gravity is quantized. The Bargmann phase isolates the commutator, which is independent of the graviton state and of all Newtonian interactions and is bounded by which-path decoherence. For gravity, this radiation-reaction effect is sixty orders of magnitude below experimental reach, but trapped-ion analogs can test it at order unity.
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BibTeX
@misc{matsui2026bargmanninvariant,
title = {{Bargmann-invariant witness of the graviton commutator}},
author = {Hiroki Matsui},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35253},
eprint = {2610.35253},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35253},
}
RIS
TY - UNPB
TI - Bargmann-invariant witness of the graviton commutator
AU - Hiroki Matsui
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35253
UR - https://arxiv.org/abs/2610.35253
AB - We identify the phase of a Bargmann invariant of two matter-wave interferometers as a quantum gravity signature that cannot be reproduced by any branchwise-definite classical gravitational field. For matter coupled linearly to linearized gravity, the interferometric coherence factorizes exactly into a conservative Newtonian phase, the characteristic functional of the graviton state, and a commutator phase. For Wigner-positive graviton states, the first two are classically reproducible; therefore, decoherence alone cannot certify that gravity is quantized. The Bargmann phase isolates the commutator, which is independent of the graviton state and of all Newtonian interactions and is bounded by which-path decoherence. For gravity, this radiation-reaction effect is sixty orders of magnitude below experimental reach, but trapped-ion analogs can test it at order unity.
ER -