Since their precision is essential to measuring relativistic effects, I'm not sure we're near that limit.

For your precise question, it may already be there.

I know that Google's Spanner[0] uses atomic clocks to help with consistency.

[0] https://en.wikipedia.org/wiki/Spanner_(database)

It hit diminishing returns for most things long, long ago, but this physics is directly related to stuff in quantum computing and studying gravity.

I guess very few systems have better absolute time than a few microseconds. Those systems are probably exclusively found in HFT and experimental physics.

This past week I tried synchronizing the time of an embedded Linux board with a GPS PPS signal via GPIO. Turns out the kernel interrupt handler already delays the edge by 20 us compared to busy polling the state of the pin. Stuff then gets hard to measure at sub microsecond scales.

straight from the abstract:

> we can demonstrate quantum-amplified time-reversal spectroscopy on an optical clock transition that achieves directly measured 2.4(7) dB metrological gain and 4.0(8) dB improvement in laser noise sensitivity beyond the standard quantum limit.

This topic of time being a western construct, it's impact on society and life is one of the subjects in the excellent book "Borderliners" [1] by Peter Høeg. A favorite of mine, though I never read the English translation. It's a fascinating topic, and impacts our live more than we might be aware of or care to admit. I started thinking about it in a different way after reading this book.

[1] https://en.wikipedia.org/wiki/Borderliners