This is how the redefinition of the second will work, by using many different kinds of optical clocks, instead of the single cesium-based microwave clock that is used now.
In fact, today the big laboratories have many atomic clocks, whose clock frequencies are averaged to compute the time, even when the clocks are of the same kind. The international atomic time, TAI, is computed by averaging the clocks of all important laboratories.
When the frequency of one clock is 10 times greater than the frequency of another, it is hard to find a significance for any other kind of mean, except the geometric.
More clearly, if the input frequencies have the same relative uncertainty, the geometric mean will preserve that relative uncertainty. If the input frequencies have different relative uncertainties, the geometric mean will have a relative uncertainty that is intermediate between them.
Other kinds of means do not offer guarantees about the relative uncertainty when the ratio of the inputs is high. If one frequency is much bigger than the others, the arithmetic mean will depend only on that frequency, the others will not matter.
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).
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.
> This strongly suggests that the recommended frequency value for the secondary representation of the second is offset from the unperturbed transition frequency by approximately twice its assigned uncertainty of 1.3×10^-15.
> the recommended frequency value is strongly dominated by a single absolute frequency measurement [53], which in light of recent results is to be considered suspect.
So I guess we don't have a usable theoretical reference value here.
We can only solve these with assumptions, like assuming that protons or neutrons are indivisible particles with experimentally determined sizes and perfectly spherical shapes - even though we know very well that they are in fact collections of quarks and gluons whose size and shape is fully determined by more fundamental intercations. We are nowhere near a point where we could compute anything about a whole hydrogen atom using only the standard model and no other assumptions. Quantum chromodynamics is far to complex to allow for a perfect simulation like this.
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.
wglb•7mo ago
adrian_b•7mo ago
https://iopscience.iop.org/article/10.1088/1681-7575/ad17d2
of which these experiments are a step towards this goal.