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The accuracy of the hydrogen 1S-2S measurement was mainly limited by the second-order Doppler shift of the moving atoms (and to a lesser degree the AC Stark shift of the excitation laser and the 2S-4P quench light). The comparison between the laser frequency and the Cesium fountain clock was done with an optical frequency comb which introduces a negligible uncertainty (< 1E-19).

Isn't it fun to get your own field of expertise (wrongly) explained to you on the internet?

Edit: I never said that it is easy to derive the corrections listed in the CODATA paper. However, it is relatively easy to calculate them.




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