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.
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Overview
According to special relativity, the speed of the aircraft would slow the clocks as compared to one sitting on the surface. Since the magnitude of the effect varies with the square of speed, the aircraft moving with the Earth would have a somewhat more pronounced slowing than the one moving against it -- compared to the universe as a whole, the eastward moving aircraft has a slightly higher overall velocity than the westward moving one, with the clock on the ground an almost equal amount between the two.
According to general relativity, there is another effect that comes into play, the slight decrease in gravity 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, but nevertheless 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 |
While the published outcome of the experiment points towards a very clear demonstration of relativity, the accuracy of the devices, the setup of the experiment and the methodology for determining the final outcome merits re-examination and perhaps another iteration of the experiment.
The raw data of the experiment has been examined by a number of individuals such as Dr. A G Kelly and found to vary in such extremes that the final published outcome had to be averaged in an extremely convoluted and biased way. Also, Louis Essen, the inventor of the atomic clock, published an article in which he discussed the inadequate accuracy of the experiment.
Nonetheless, the effect is compensated for daily in 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
- <math>\Tau = \Delta\tau_v + \Delta\tau_g + \Delta\tau_s</math>
- <math>\Delta\tau_v = \frac{1}{2c^2} \sum_{i=1}^{k}v_i^2 \Delta\tau_i</math>
- <math>\Delta\tau_g = \frac{g}{c^2} \sum_{i=1}^{k} (h_i - h_0) \Delta\tau_i</math>
- <math>\Delta\tau_s = - \frac{\omega}{c^2} \sum_{i=1}^{k} R_i^2 cos^2 \phi \Delta\lambda_i</math>
Where h = height, v = velocity, <math>\omega</math> = Earth's rotation and i represents each time synchronization signal sent through the system.
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
- L Essen, Electron. Wireless World 94 (1988) 238.