The H & K tests prove nothing. The accuracy of the clocks would need to be two orders of magnitude better to give confidence in the results. The actual test results, which were not published, were changed by H & K give the impression that they confirm the theory.

Hafele-Keating Experiment In 1971, Joseph Hafele and Richard Keating deonstrated time dilation using caesium-beam atomic clocks. Twelve clocks were used in total. Four clocks were flown on a plane in an eastward direction, four were flown in a westward direction, and the last four remained on Earth.

Bailey et al. (1977) measured the lifetime of positive and negative muons sent around a loop in the CERN Muon storage ring. This experiment confirmed both time dilation and the twin paradox, i.e. the hypothesis that clocks sent away and coming back to their initial position are slowed with respect to a resting clock.