I think they are missing one concept in their analysis. A clock by definition is something that produces a regular series of pulses. In other words its signal

I think they are missing one concept in their analysis. A clock by definition is something that produces a regular series of pulses. In other words its signal is sparse in the frequency domain. To keep it sparse, you constrain it by its geometry (if it’s electrically driven then you contain the fields in a narrow region of space). If it’s mechanical you constrain its physical dimensions etc. And finally you filter out thermal noise by lowering the entropy of the system. This is where standard thermodynamics enters into the picture…to cool the clock (say) you have to increase the entropy of the universe. The “lab conditions” under which you operate the clock though, are a low entropy zone. But the nature of pure oscillations has no dependence on entropy—quite the reverse, the clock itself operates in a low entropy environment. In other words you can predict exactly what frequency state it’s in. Proof of this is the fact that you can print the frequency on the outside of the box in permanent paint. Astronomical bodies float in space and they are already in a sparse environment as far as gravity is concerned. There are 7 major planets besides earth and the sun has most of the mass of the solar system. The spaces between the planets are relatively debris free. The asteroid belt is quasi-uniform. So they move kind of regularly. Where they couple energy between planets that can be predicted using Newtons laws. What makes it a clock is the empty space between the planets. If the solar system was full of dust with storms etc then the motion of the planets would be subject to “weather” like conditions and nobody would treat it like a clock (just as we don’t keep time by the arrival of the rain). We’re spoiled on earth by the presence of this regular motion on the skies above that is independent of all that is happening in earth. So that’s where our notion of a “fixed” absolute clock comes from. What does this mean for atomic clocks? In the lab we try to reproduce these space like conditions (by keeping air currents, external stimuli out) and think that vibrating atoms are telling us something absolute about nature. It’s perhaps better to say that they are relatively more stable than our living environments and independent of whatever we are trying to measure. But is there some master clock in the universe that these atoms are tapping into and recording for us? No. There’s no such thing. They are just drums that beat to their own tune which happens to be defined by their dimensions and the local properties of space around them. The fact that all atoms of the same type under the same conditions are all the same size makes atomic clocks possible.