How can we test this ?

Proposal A: take two atomic clocks, put one in an airplane and have the airplane fly once around the Earth. Compare the clock with the other one that stayed at rest.  Result: the traveling clock is indeed somewhat behind.

Proposal A: take two atomic clocks, put one in an airplane and have the airplane fly once around the Earth. Compare the clock with the other one that stayed at rest.  Result: the traveling clock is indeed somewhat behind.