Atom interferometers (AIs) on earth and in space offer good capabilities for measuring gravitational waves (GWs) in the mid-frequency deciHz band, complementing the sensitivities of the LIGO/Virgo and LISA experiments and enabling probes of possible modifications of the general relativity predictions for GW propagation. We illustrate these capabilities using the projected sensitivities of the AION (terrestrial) and AEDGE (space-based) AI projects, showing that AION could improve the present LIGO/Virgo direct limit on the graviton mass by a factor $sim 40$ to $simeq 10^{-24},$eV, and AEDGE could improve the limit by another order of magnitude. AION and AEDGE will also have greater sensitivity than LIGO to some scenarios for Lorentz violation.
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