The Hafele–Keating experiment was a test of the theory of relativity. In 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks in motion to stationary clocks at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with the predictions of special and general relativity.
Overview
Kinematic time dilation According to special relativity, the rate of a clock is greatest according to an observer who is at rest with respect to the clock. In a frame of reference in which the clock is not at rest, the clock runs more slowly, as expressed by the Lorentz factor. This effect, called time dilation, has been confirmed in many tests of special relativity, such as the Ives–Stilwell experiment and others. Considering the Hafele–Keating experiment in a frame of reference at rest with respect to the center of the Earth (because this is an inertial frame), a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground.
Gravitational time dilation
General relativity predicts an additional effect, in which an increase in gravitational potential due to altitude speeds the clocks up. That is, clocks at higher altitude tick faster than clocks on Earth's surface. This effect has been confirmed in many tests of general relativity, such as the Pound–Rebka experiment and Gravity Probe A. In the Hafele–Keating experiment, there was a slight increase in gravitational potential due to altitude that tended to speed the clocks back up. Since the aircraft flew at roughly the same altitude in both directions, this effect was approximately the same for the two planes, but nevertheless it caused a difference in comparison to the clocks on the ground.
Results The results were published in Science in 1972:
The published outcome of the experiment was consistent with both special and general relativity. The observed time gains and losses were in agreement with relativistic predictions to within the ~10% precision expected of the experiment.
Historical and scientific background In his original 1905 paper on special relativity, Albert Einstein suggested a possible test of the theory: "Thence we conclude that a spring-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions." Actually, it is now known that all clocks located at sea level on the Earth's surface tick at the same rate, regardless of latitude, because kinematic and gravitational time dilation effects cancel out (assuming that Earth's surface is an equipotential one). The kinematic effect was verified in the 1938 Ives–Stilwell experiment and in the 1940 Rossi–Hall experiment. General relativity's prediction of the gravitational effect was confirmed in 1959 by Pound and Rebka. These experiments, however, used subatomic particles, and were therefore less direct than the type of measurement with actual clocks as originally envisioned by Einstein. Hafele, an assistant professor of physics at Washington University in St. Louis, was preparing notes for a physics lecture when he did a back-of-the-envelope calculation showing that an atomic clock aboard a commercial airliner should have sufficient precision to detect the predicted relativistic effects. He spent a year in fruitless attempts to get funding for such an experiment, until he was approached after a talk on the topic by Keating, an astronomer at the United States Naval Observatory who worked with atomic clocks. Hafele and Keating obtained $8000 in funding from the Office of Naval Research for one of the most inexpensive tests ever conducted of general relativity. Of this amount, $7600 was spent on the eight round-the-world plane tickets, including two seats on each flight for "Mr. Clock." They flew eastward around the world, ran the clocks side by side for a week, and then flew westward. The crew of each flight helped by supplying the navigational data needed for the comparison with theory. In addition to the scientific papers published in Science, there were several accounts published in the popular press and other publications.
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