A Planck-Mass Threshold Fifth Force: A Phenomenological Model for Short-Range Gravitational Deviations

This research proposes a new short-range force—a "fifth force"—that becomes significant at distances below a millimeter and depends on how the masses of interacting bodies compare to the Planck mass. The force law includes a sign function that switches behavior depending on whether a mass is above or below a certain Planck-scale threshold, and it scales with the energies of the objects involved. The model aims to explain small anomalies in short-range gravity experiments and suggests that this force could be mediated by a new scalar field. Specific predictions are made about when and how the force would appear, including conditions under which it might cancel out or become repulsive. The work outlines theoretical underpinnings, proposes values for its free parameters, and identifies experimental setups where this force could be detected or constrained.