Hafele-Keating experiment
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The Hafele-Keating experiment was a test of the theory of relativity. In October of 1971, J. C. Hafele and Richard E. Keating took four cesium-beam atomic clocks aboard commercial airliners and flew twice around the world, first eastward, then westward, and compared the clocks against those of the United States Naval Observatory.
Overview
According to special relativity, the speed of a clock is greatest according to an observer who is not in motion with respect to the clock. In a frame of reference in which the clock is not at rest, the clock runs slower, and the effect is proportional to the square of the velocity. In a frame of reference at rest with respect to the center of the earth, the clock aboard the plane moving eastward, in the direction of the earth's rotation, is moving faster than a clock that remains on the ground, while the clock aboard the plane moving westward, against the earth's rotation, is moving slower.
According to general relativity, another effect comes into play: the slight increase in gravitational potential due to altitude that speeds the clocks back up. Since the aircraft are flying at roughly the same altitude in both directions, this effect is more "constant" between the two clocks, but nevertheless it causes a difference in comparison to the clock on the ground.
The results were published in Science in 1972:
| nanoseconds gained | ||||
|---|---|---|---|---|
| predicted | measured | |||
| gravitational (general relativity) | kinematic (special relativity) | total | ||
| eastward | 144±14 | -184±18 | -40±23 | -59±10 |
| westward | 179±18 | 96±10 | 275±21 | 273±7 |
The published outcome of the experiment was consistent with special relativity, and the observed time gains and losses were reportedly different from zero to a high degree of confidence.
That result was contested by Dr. Kelly who examined the raw data: he found that the final published outcome had to be averaged in a biased way in order to claim such a high precision. Also Louis Essen, the inventor of the atomic clock, published an article in which he discussed the in his opinion inadequate accuracy of the experiment.
Nevertheless, the above experiment has been repeated a number of times. One notable repetition took place on the 25th anniversary of the original experiment, using more precise atomic clocks, and the results were verified to an even higher degree of accuracy. [link]. Thus any doubt about the validity of the predictions has been removed. Today, relativistic effects such as time dilation are routinely incorporated into the calculations used for the GPS system.
GPS
A similar, real-world example of the time dilation experiment is occurring continuously in the GPS satellite constellation. Here, the time dilation can be written as:Total time dilation
- [\Tau = \Delta\tau_v + \Delta\tau_g + \Delta\tau_s]
- [\Delta\tau_v = \frac \sum_^v_i^2 \Delta\tau_i]
- [\Delta\tau_g = \frac \sum_^ (h_i - h_0) \Delta\tau_i]
- [\Delta\tau_s = - \frac \sum_^ R_i^2 cos^2 \phi \Delta\lambda_i]
You'll have to imagine a ground station sending a signal to a moving satellite from a rotating earth and then down to another ground station.
References
- J.C. Hafele and R. Keating, Science 14 July 1972 177: 166-168
- J.C. Hafele and R. Keating, Science 14 July 1972 177: 168-170
- L Essen, Electron. Wireless World 94 (1988) 238.
See also
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