I saw this paper last week and I might have gotten around to doing a blog post, but for reading Chad’s book, so he beat me to it. (OK: no, not really; I have to many other unfinished posts in the queue) Clock Synchronization Done Right: “A 920-Kilometer Optical Fiber Link for Frequency Metrology at the 19th Decimal Place”
OK, I admit, that’s a lot of zeroes. But why does that matter? Isn’t the whole point of ultra-precise atomic clocks that they all work exactly the same way? Why do you need to compare them? All atomic clocks using a given type of atom have the same basic frequency, but not all clocks are equally well made. The only way to determine the performance of a new one is to compare it to one you know works, but they’re also not very portable, so you need to be able to do the comparison remotely.
A nit: I wouldn’t necessarily characterize this as an issue of not being “equally well made”. One problem is that they are not identical — they are not the ideal clock used in thought experiments: there is noise, and it’s different for each clock. Each component in the clock can impact the clock in slightly different ways. But even if they were identical in all respects, you still have natural processes present in your oscillator, and these will give you white noise in the frequency of the clock. The integral of frequency give you the time, and the integral of white frequency noise is a random walk in phase, i.e. in the time. What does that mean? It means two clocks at identical frequencies will still undergo a random walk away from each other — they will lose synchronization. So you will still need to synchronize clocks, even if you could get them to the exact same frequency and remove all other kinds of noise. (Which you can’t).
Currently we are in a regime where clocks are better than time transfer techniques, at least over interesting distances. One can compare co-located clocks pretty well, but it doesn’t do anyone else any good if the precise time cannot be disseminated to them.
Both Special and General Relativity have a lot to say about synchronizing non-local clocks. Though latitude as such does not matter, height vs. local geoid does – including local mass distribution (sprinklers, rain). A superconducting levitated dual ball gravimeter detects the gee difference of a pack of playing cards inserted beneath its dewar, about four feet below the sensor. That is coarse compared to a fountain clock. Time can vary along the entire fiberoptic length, too. What fun!
With regard to random walk, I think it’s important to note that the combination of two clocks still has a random walk, which should be equal to that of a clock with sqrt(.5) of the random white noise.