Investigating a null test of the Einstein Equivalence Principle with clocks at different solar gravitational potentials

Abstract

The Einstein Equivalence Principle (EEP) requires that clocks in free fall, when observed by other clocks in free fall, show no frequency variations. To some approximation, clocks on the surface of the Earth can be considered freely falling in the solar gravitational potential, and one would expect to find no frequency variations between the clocks as the Earth's rotation modulates the potential experienced by each clock. We investigate the attainable limits of a search for such a frequency variation using satellites, parameterized as a fraction of the expected differential gravitational redshift of a clock pair not in free fall. Under the most optimistic of assumptions, a 3-sigma limit to the EEP violation of 10−4 may be possible in the future, although the uncertainties we present are an order of magnitude higher, with an upper limit to an EEP violation of <10−3.