Comment by zokier

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.

It's always a question of what precision you want.

For really any physical system, when describing it at ever greater precision, more and more effects become relevant until you can't calculate it anymore (or even your theory itself breaks down). In this case, the precision they need is extremely high so this is a problem.

For the vast majority of systems, there's no point in going there because the precision of experiments is too low (which means that the experiments feature even more poorly controlled effects which would be unreasonable to model).

Our models use single atoms (or single molecules), and for those we have pretty good models that we can solve numerically, at least.

In a gas, the atoms or molecules only interact weakly, so you just get some known effects like a line broadening due to thermal motion of the particles

But you really still want experimental validation before you declare any of these as a new standard, for a whole variety of reasons:

* it's often complicated to calculate multiple excitations

* you might forget something in the models, like isotope ratios

* the models don't really give you a good sense of how impurities in your materials will affect the clocks

* there might be some practical issues, like glass (used in the optical fibers) not being a very good medium for some frequencies of light that would otherwise look promising as a time standard

... and so on.