Atom Interferometry Constraints on Scalar Temporal Flow

The Scalar Temporal Field Ontology (STFO) models time as a dynamical scalar field whose spacetime gradients modify inertial motion, curvature, and clock synchronization through an effective disformal metric. In this work, a laboratory-scale test of scalar temporal flow is developed using high-precision atom interferometry. Starting from the effective particle action induced by the STFO metric deformation, the scalar-temporal contribution to the nonrelativistic point-particle Lagrangian is derived and shown to generate a measurable phase shift in atom interferometers. The phase offset depends on the projection of the local scalar temporal gradient onto the spacetime area enclosed by the interferometer loop. Using current experimental phase sensitivities in the range of approximately 10^(-9) to 10^(-12) radians, direct bounds are placed on combinations of the scalar coupling function and the local gradient amplitude of the temporal field. The predicted signal exhibits orientation dependence, sidereal and annual modulation, and species-dependent scaling, enabling decisive null-test strategies through apparatus rotation, latitude comparison, and atomic mass variation. This establishes atom interferometry as a clean terrestrial constraint on scalar temporal flow, complementary to existing solar, fast radio burst, and gravitational-wave propagation tests. Together these channels bound the scalar temporal field across laboratory, astrophysical, and cosmological scales.