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Relativistic Behaviour of Moving Terrestrial Clocks

Abstract

EINSTEIN concluded in his 1905 paper on relativity that “a balance-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”1. At that time, of course, he had not yet developed the general theory and did not realize that the difference in the gravitational potential at the equator and poles would just cancel the time dilatation from the difference in surface speeds, as has been pointed out recently by W. J. Cocke2. Cocke has also shown that, in so far as the Earth assumes the shape of the geoid (and weak tidal fields can be neglected), its entire surface is an “equal time” surface. There remains an interesting question, however: What would be the rate of a standard clock that is moving relative to stationary standard clocks on the geoid ? The standard answer that moving clocks run slow by the well known factor (1 - v2/c2)1/2 is almost certainly incorrect. The purpose of this note is to discuss this question of the rate of moving terrestrial clocks relative to stationary ones.

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References

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HAFELE, J. Relativistic Behaviour of Moving Terrestrial Clocks. Nature 227, 270–271 (1970). https://doi.org/10.1038/227270a0

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