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Originally Posted by Ut
A body's clock speed depends on both the speed and acceleration (or an equivalent external gravitational field) of said body.
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You should say “atomic clock rate”. The Lorentz-force atomic clock rule, as used by Einstein, applies to atomic clocks only, i.e. to atomic oscillation rates. It does not apply to pendulum clocks, mechanical clocks, balance wheel clocks, thermodynamic clocks, etc., etc.
Geepers, go read the original papers and books on this subject.