Comment by fsh

The accuracy of atomic clocks is much better than our understanding of fundamental physics.

The best calculable atomic system is atomic hydrogen, and state-of-the-art quantum electrodynamics calculations reach a relative accuracy of around 1E-13 for its energy levels. However, already at the 1E-10 level, the structure of the proton becomes significant which can currently not be calculated from first principles. Instead, the proton size is taken as a free parameter which is determined from the measurements.

In contrast, the best realizations of the SI second are caesium fountain clocks which achieve relative uncertainties in the 1E-16 range. Clocks based on optical transitions (rather than microwave transitions) have now broken the 1E-18 barrier. Calculating atomic structure to this level is currently completely unthinkable, even for a system as simple as hydrogen.