It's not watchmaking per se, but very adjacent. Might be of interest to this crowd. This article crossed my path this morning.
This was in the news a few years back (and actually, I see the article is about that old). My best friend works at JILA, and he built at least part of the resonator used in this clock (his focus is ultra high frequency electronics). The resonator is the equivalent of an escapement. When he told me about it (either over beers or on a hike), he glossed over the coolest part.
Warning, the following is beyond nerdy, and will break some people's brains. If you can follow, it's pretty seriously cool. I'll keep the math out of it.
Back when this came out, it set a record, was in the news, and all the stories were about how it wouldn't lose a second over the entire age of the universe. That's cool, but it's not exactly tangible or relatable. As watchmakers, you all have a firmer grasp on what that means, but here's the really cool part: It is capable of measuring the difference within earth's gravity well over a distance of a mere 2 cm...
According to physics, there is a floor to how small things can get. This smallest possible distance is called the Planck length. Imagine that the universe exists on a three dimensional lattice grid of Planck length cubes as a visual. This lattice of Planck length cubes is the fabric of spacetime.
General Relativity (Einstein's theory of gravity) tells us that this Planck length is... wait for it... relative; it can be larger or smaller depending on various factors. The cubes can be expanded and stretched. One thing that alters the Planck length is gravity. More gravity stretches it out, while less allows it to contract and be smaller. If you're at sea level, the Planck length of the above mentioned lattice grid is larger, and the cubes are bigger. Up here at 7K' above sea level, my Planck length cubes are smaller. When your cubes are bigger, it takes longer for information to be transmitted across them and vice versa. "Information" here means energy, matter, change, what have you; it's kind of a broad technical term. The speed at which this information is able to travel is called Causality, and is the C in E=MC^2 (not the speed of light, as is commonly stated as a more easily explainable concept, thought they are also one and the same). What it means practically for this conversation, is that as the Planck length is stretched, time is slower relative to a space with a shorter Planck length. This slowing of time due to the stretching of spacetime (longer Planck length) is called time dilation. When that time dilation is due to gravity stretching spacetime, it's called gravitational time dilation.
Practically speaking, those of you at sea level experience time more slowly than we do up here in the mountains. It's a very very small difference that we can't actually discern, but it's there and more gravity, or being closer to the source of the gravity means more slowing. On a larger planet, or a black hole as the classic example, as it represents the most extreme of extremes, this difference is far more pronounced. A practical example of time dilation is the time corrections used in satellites. There's some correction made for their speed, but they're also corrected for their position in (or out) of earth's gravity well. The accuracy of these corrections is what allows your favorite navigation app to know where you are in order to tell you when to turn, and increases in that accuracy over time is why those apps have gotten better at figuring out which lane you're in, as an example.
It's difficult to express how tiny the effects of time dilation are on such a tiny scale as earth without getting into the math... Lot's-of-zeros-between-the-decimal-and-any-number-other-than-zeros of a second. For there to be time dilation on a scale that would be noticeable to a person without lots of expensive measuring tools (say, drop the rate of the passage of time by half), you would need a black hole with a mass at least a few times greater than the sun. Then you'd need to get real close to it.... Then you'd notice the universe around you starts to speed up relative to your own experience (and to the rest of the universe, it would look like you were moving in slow motion). Get too close though, and your Planck length gets stretched out so long that time just stops (at least according to an outside observer that's not in the black hole's gravity well with you)/the universe just suddenly ends in an instantaneous fast forward (blinks out, heat death, contraction, dragons, pick your theory)... But that's a different conversation.
Back to the clock now... This puppy is so accurate, it can tell where you are to within 2 cm altitude... What that means, is that it is capable (indirectly) measuring the change in the stretching of spacetime due to a (relatively) tiny mass like the earth! We are talking tiny distances here, and even tinier stretching of those tiny distances. That is absolutely incredible! The technological possibilities with a clock this accurate are huge. It's 150X more accurate than that lame old "THE Atomic Clock". The mind boggles. An incredible feat of engineering, and a huge milestone in the science of horology.
Hopefully that was an interesting read, and anyone finds it as interesting as I do. \nerding