Kinetic Energy and the Equivalence Principle

Constraints on violation of the Einstein equivalence principle (EEP) can be inferred from tests of the universality of free fall or atom interferometry. In generalized models describing EEP as a perturbation to known physics, such as the standard model extension, the combination of a particle-specific modification of the space-time metric, along with interactions with to a field that is non-metrically coupled to spacetime, makes it possible for the total observable EEP-violation to cancel in the motion of free protons, neutrons, and electrons, while manifesting in the motion of free antiparticles. We show that such hidden forms of EEP-violation can be ruled out using ordinary matter, as modified metric violation of EEP also couples to the internal kinetic energy of bound systems of particles. Using a Woods-Saxon potential to calculate the kinetic energies of nucleons bound within a wide range of atomic nuclei, we estimate the sensitivity of existing and planned tests of EEP to such hidden forms of EEP violation. We show that existing limits on EEP-violation, hidden or otherwise, are significantly better than previously thought, with important implications for future tests of EEP.