Fifth-Coordinate Consequences for Atom Interferometers: Phase Shifts in Gravimeters, Gradiometers, and a Space-Borne Concept

A companion evaluation bounded a fifth-coordinate coupling to optical clock rates: with nu(chi) = nu0[1 + kappa5(chi - chi0)] and a spatial gradient gamma, null clock comparisons at the 1e-18 level bound |kappa5 gamma| < 1e-18 per metre. That coupling and bound are taken as given input. This paper prices the same coupling in the atom-interferometry channel at saturation of the clock bound, under two explicit readings. Under the universal (metric) reading the gradient is a uniform extra acceleration a5 = c^2 kappa5 gamma = 8.99e-2 m/s^2. A state-of-the-art atom gravimeter (5.5e-8 g at 1 s) excludes saturation by 5.2 orders of magnitude (predicted phase 3.62e3 rad against 2.17e-2 rad phase noise), bounding |kappa5 gamma| < 6.0e-24 per metre; the per-interferometer readout of a 10 m fountain gradiometer excludes it by 6.4 orders, while its ideal differential gravity-gradient readout predicts exactly zero for a uniform acceleration; a space-borne STE-QUEST-type design excludes it by 10.5 orders per cycle. Under the clock-transit reading, the differential phase of the 100 m MAGIS-100 strontium clock gradiometer is 9.0e-8 rad, 2.0 orders of magnitude below its 1e-5 rad design phase-stability scale (4.0 orders below a conservative 1e-3 rad level): a negative result, printed at full size, with the coupling unadjusted. AI-use disclosure: an AI assistant, Dave, assisted in the preparation of this work, including computation and drafting, under the direction of the author.