<Dd> U = G M i r i (\ displaystyle U = (\ frac (GM_ (i)) (r_ (i)))) is the Newtonian potential, equivalent to half of the escape velocity squared . </Dd> <P> The above equation is exact under the assumptions of the Schwarzschild solution . It reduces to velocity time dilation equation in the presence of motion and absence of gravity, i.e. β e = 0 (\ displaystyle \ beta _ (e) = 0). It reduces to gravitational time dilation equation in the absence of motion and presence of gravity, i.e. β = 0 = β ∥ (\ displaystyle \ beta = 0 = \ beta _ (\ shortparallel)). </P> <Ul> <Li> Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the earth in commercial airliners, to compare the elapsed time against that of a clock that remained at the U.S. Naval Observatory . Two opposite effects came into play . The clocks were expected to age more quickly (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the trip (c.f. Pound--Rebka experiment). But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel . From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40 ± 23 nanoseconds during the eastward trip and should have gained 275 ± 21 nanoseconds during the westward trip . Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59 ± 10 nanoseconds during the eastward trip and gained 273 ± 7 nanoseconds during the westward trip (where the error bars represent standard deviation). In 2005, the National Physical Laboratory in the United Kingdom reported their limited replication of this experiment . The NPL experiment differed from the original in that the caesium clocks were sent on a shorter trip (London--Washington, D.C. return), but the clocks were more accurate . The reported results are within 4% of the predictions of relativity, within the uncertainty of the measurements . </Li> <Li> The Global Positioning System can be considered a continuously operating experiment in both special and general relativity . The in - orbit clocks are corrected for both special and general relativistic time dilation effects as described above, so that (as observed from the earth's surface) they run at the same rate as clocks on the surface of the Earth . </Li> </Ul> <Li> Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the earth in commercial airliners, to compare the elapsed time against that of a clock that remained at the U.S. Naval Observatory . Two opposite effects came into play . The clocks were expected to age more quickly (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the trip (c.f. Pound--Rebka experiment). But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel . From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40 ± 23 nanoseconds during the eastward trip and should have gained 275 ± 21 nanoseconds during the westward trip . Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59 ± 10 nanoseconds during the eastward trip and gained 273 ± 7 nanoseconds during the westward trip (where the error bars represent standard deviation). In 2005, the National Physical Laboratory in the United Kingdom reported their limited replication of this experiment . The NPL experiment differed from the original in that the caesium clocks were sent on a shorter trip (London--Washington, D.C. return), but the clocks were more accurate . The reported results are within 4% of the predictions of relativity, within the uncertainty of the measurements . </Li>

How can time slow down at the speed of light