Hafele and Keating Experiment

"During October, 1971, four cesium atomic beam clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicted that the flyng 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 nanosecond during the westward trip, where the errors are the corresponding standard deviations. These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks."

J.C. Hafele and R. E. Keating, Science 177, 166 (1972)


Description of experiment

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Around the World

In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, D.C., they had gained about 0.15 microseconds compared to the ground based clock.

Eastward Journey Westward Journey
Predicted -40 +/- 23 ns + 275 +/- 21 ns
Measured -59 +/- 10 ns + 273 +/- 7 ns

Quote from original paperMore detail
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Around-the-World Atomic Clocks

In October 1971, Hafele and Keating flew cesium beam atomic clocks around the world twice on regularly scheduled commercial airline flights, once to the East and once to the West. In this experiment, both gravitational time dilation and kinematic time dilation are significant - and are in fact of comparable magnitude. Their predicted and measured time dilation effects were as follows:
Predicted: Time difference in ns
Eastward Westward
Gravitational 144 +/- 14 179 +/- 18
Kinematic -184 +/- 18 96 +/- 10
Net effect -40 +/- 23 275 +/- 21
Observed: -59 +/- 10 273 +/- 21
Gravitational calculationKinematic calculation
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Gravitational Time Shifts

For small changes in gravitational field associated with changes in altitude above the earth, the approximate time dilation expression is
if a comparison is made between a clock on the Earth's surface and one at height h above the surface. Hafele and Keating predicted a time difference of 144 ns on an eastward flight around the world for which the flight time was 41.2 hours. This corresponds to an average height of 8900 m, a reasonable flight altitude for a commercial airline. The time shift is positive (aging faster) for both eastward and westward flights. The predicted value of 179 ns for the westward flight of 48.6 hours duration corresponds to an average altitude of about 9400 meters. 		Index
 
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Kinematic Time Shift Calculation

If the kinematic time dilation expression
is expanded in a binomial expansion, then for small velocities it becomes
For a point on the equator and an aircraft flying over the equator at speed v, the expression becomes
and for the aircraft
The difference for the airborne clock is then

Application

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Aircraft Time Dilation

For an aircraft flying over the equator, its clocks will show a time shift relative to a fixed surface clock according to the expression

For travel eastward, v has a positive sign and the shift will be negative (aging more slowly). But for a westward flight the time shift is positive (aging faster). Hafele and Keating predicted time shifts of -184 ns for an eastward flight around the world and a shift of +96 for a westward flight. 		Index
 
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