Interferometric trilemma for ultraviolet-softened gravity
Abstract
Ultraviolet-softened extensions of general relativity can weaken gravity at short distances, whereas a positive Källén--Lehmann spectral density forbids gravity from falling below Newtonian strength. Which property of the mediator must such a weakening sacrifice? For Lorentz-invariant Gaussian mediators coupled linearly to the conserved stress tensor, we formulate three independent interferometric conditions that jointly imply this bound: visibility is never amplified, decoherence is fixed by the energy radiated by the difference source, and no interferometer responds to a later one. At tree level, the three ghost prescriptions of quadratic gravity each violate exactly one: negative-norm ghosts amplify coherence, negative-energy ghosts decohere without positive energy transfer from the difference source, and a time-symmetric fakeon response produces advanced fringe shifts. Any universal short-distance weakening of gravity therefore certifies that its mediator violates one of these conditions, and the observables proposed to certify quantum gravity become consistency tests of its ultraviolet completion.
Related
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BibTeX
@misc{matsui2026interferometric,
title = {{Interferometric trilemma for ultraviolet-softened gravity}},
author = {Hiroki Matsui},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25994},
eprint = {2610.25994},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25994},
}
RIS
TY - UNPB
TI - Interferometric trilemma for ultraviolet-softened gravity
AU - Hiroki Matsui
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25994
UR - https://arxiv.org/abs/2610.25994
AB - Ultraviolet-softened extensions of general relativity can weaken gravity at short distances, whereas a positive Källén--Lehmann spectral density forbids gravity from falling below Newtonian strength. Which property of the mediator must such a weakening sacrifice? For Lorentz-invariant Gaussian mediators coupled linearly to the conserved stress tensor, we formulate three independent interferometric conditions that jointly imply this bound: visibility is never amplified, decoherence is fixed by the energy radiated by the difference source, and no interferometer responds to a later one. At tree level, the three ghost prescriptions of quadratic gravity each violate exactly one: negative-norm ghosts amplify coherence, negative-energy ghosts decohere without positive energy transfer from the difference source, and a time-symmetric fakeon response produces advanced fringe shifts. Any universal short-distance weakening of gravity therefore certifies that its mediator violates one of these conditions, and the observables proposed to certify quantum gravity become consistency tests of its ultraviolet completion.
ER -