Time dilation effects on Earth surface: Optical lattice clocks measurements

Recently, Takamoto et al. (2020) have discussed high precision measurements of gravity induced time dilation effects on optical lattice clocks located near the Earth surface. A relative tick frequency change, δν/ν0=(49 337.8±4.3)10-18, is found between two optical lattice clocks, one located at the ground floor, h=0 m, and the second one at an altitude hexp=452.596 m, on the Skytree tower in Tokyo. The results are compared with the predictions of Einstein's equivalence principle (EEP) estimated as an average over gravimeter measurements at h=0 m and h=450 m. We present a different derivation of the EEP prediction based on the calculation of the effective gravitational potential on the ground floor and at h=hexp, in excellent agreement with the value δν/ν0, providing an independent method to validate the differences in time dilation measured experimentally. In addition, we obtain the next-order correction to the present results, which may be tested in future more accurate experiments.