Why the need for more sophisticated atomic clocks? Why is there such a huge effort in building more sophisticated atomic clocks when the current ones achieve $1$ second of error every few hundred million years? Some achieve frequency stability close to $3\cdot 10^{-13}\tau^{−1/2}$, where $\tau$ is the Allan deviation used to measure frequency stability of atomic clocks. So why the need to build even more sensitive atomic clocks?
 A: I don't know the intended, specific purpose of those better clocks, but I can speak to the question on a more general front.

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*"Mo betta accuracy" has generally been a plus in the past, especially when we thought we had things figured out. It's historically been one of our best ways to find new phenomena, right alongside being able to measure new things (e.g. gravitational waves, x-rays, neutrinos).


*Depending on what you're measuring in quantum electrodynamics, our existing accuracy runs somewhere in the one-part-in $10^8$ to $10^{12}$ range, so working on a timer that's accurate to one part in $10^{13}$ seems pretty reasonable (if difficult) when it comes to improving other measurements.


*Uncertainty can also compound when measurements are combined, so you always want better accuracy than it might seem like you need at first.
A: There are various reasons; I will just give two examples and I hope someone may give a more thorough answer.
One can divide the uses of improved clocks roughly into two areas: support for any scientific investigation that needs ultra-high time/frequency precision, and more direct experiments using atoms to investigate fundamental physics.
In the first category you can place things like astrophysics experiments involving synchronous detection on many antennas, where one wants to combine the signals so as to get an interference effect which makes a group of antennas behave like one big antenna. The better the timing, the more precise is the interferometric combination.
In the second category you can place things like measurements on atoms which test whether basic constants are in fact not constant but changing very slowly with time. Ideas in basic physics (quantum field theory and the like) sometimes suggest that there could be slow change in a quantity such as the fine structure constant which indicates the strength of electromagnetic interactions. By 'slow' here we mean the cosmic timescale of billions of years, so ultra-precise frequency standards are needed to test it on the timescale of human technology.
But in the end, when it comes to the pursuit of precision, I think experimental physicists continue to climb this mountain simply because it is there.
A: A lot of technology is facilitated and enabled by the ability to better measure things. And you never know what you might need it for until you need it. You could ask the same thing about a lot of research: "What's it good for right now?"
People try to design around limitations if they can, but if they can't and are forced to deal with it head on, that can kill the project right then and there unless the project budget and schedule can also accommodate for the development of a more accurate atomic clock. But, seriously, how many projects have the additional budget, time, and expertise for that? Very few indeed. Maybe DARPA, maybe NASA, maybe CERN. But that's about it. But if measurement capability already exists people will find uses for it and it will be ready for them when they do.
