= Twin paradox clock experiments
The 1972 paper <Around-the-World Atomic Clocks: Observed Relativistic Time Gains by J. C. Hafele and others> reports four cesium-beam <atomic clocks> flown around the world in October 1971, eastward and westward. Their readings were compared with the U.S. Naval Observatory reference time scale before and after travel. An electronic time-interval counter resolved differences to the nearest nanosecond; intercomparisons among the flying clocks continued during travel. The final ensemble results were $-59\pm10\,\mathrm{ns}$ eastward and $+273\pm7\,\mathrm{ns}$ westward; the quoted spreads are <standard deviations>. These are corrected clock offsets, not raw readings or aircraft travel times. Four clocks allowed identification of individual rate changes through patterns in their mutual differences. The authors also report magnetic shielding and laboratory orientation checks. Their analysis could not detect a disturbance common to every flying clock, and the small ensemble limits statistical conclusions. This is a concrete reunited-clock experiment with apparatus, readout and drift controls.<Around-the-World Atomic Clocks: Observed Relativistic Time Gains by J. C. Hafele and others>[pp. 168–170: Table 1, electronic counter, correlated rate-change analysis, magnetic shielding and common environmental effects]{ref}
The companion paper <Around-the-World Atomic Clocks: Predicted Relativistic Time Gains by J. C. Hafele and others> computes $-40\pm23\,\mathrm{ns}$ eastward and $+275\pm21\,\mathrm{ns}$ westward from the recorded flight paths. These are predictions, with flight-data uncertainty estimates. Both <time dilation> from motion and <gravitational time dilation> matter: aircraft clocks at altitude experience a different <gravitational potential>, while the rotating <Earth> means a ground clock is not the inertial home clock of our simple model. Eastward and westward motion change the aircraft's <velocity> relative to an approximately nonrotating <inertial frame>, not merely its <speed> relative to the ground. The measured agreement therefore tests combined <special relativity> and <general relativity>; the westward gain does not contradict the maximum-<proper time> result for fixed endpoints in <Minkowski spacetime>.<Around-the-World Atomic Clocks: Predicted Relativistic Time Gains by J. C. Hafele and others>[pp. 166–167: Table 1, equations 1–4, gravitational potential term and integration of actual flight paths]{ref}
A complementary microscopic test is <Measurements of relativistic time dilatation for positive and negative muons in a circular orbit by J. Bailey and others>. The authors measured <muon decay> lifetimes in a storage ring at <Lorentz factor> $\gamma=29.33$: $64.419\pm0.058\,\mathrm{\mu s}$ for <positive muons> and $64.368\pm0.029\,\mathrm{\mu s}$ for negative <muons>. The reported positive-<muon> lifetime agrees with the independently measured lifetime at rest and <special relativity> to a fractional error of $2\times10^{-3}$ at 95% confidence. This is a decay-lifetime readout under continuous <centripetal acceleration>, rather than a reunion of portable clocks. It supports the <clock hypothesis> for this physical process and regime; the inspected abstract does not establish universal immunity of every clock mechanism to <acceleration>. <Measurements of relativistic time dilatation for positive and negative muons in a circular orbit by J. Bailey and others>{ref}
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