It's a physics thing which affects all clocks.

According to special relativity clocks on the Moon will run slower because the moon is orbiting the Earth, so the clock has a higher relative speed. However, general relativity says the clock will run faster, because the Moon has a smaller gravitational field than Earth.

In this case the second effect will dominate, so even a perfect clock will run faster: it's not the clock which is fast, it is time itself. GPS satellites have to deal with the same issue.

Do you think there are any physical phenomena that can be used that might be sensitive to relativistic effects? Something like a quartz crystal that actually vibrates at different speeds depending on how dilated the current reference frame is? Maybe something external, like if our sun would be emitting some sort of signal at a regular interval that everyone could sync up against.

I wonder if, in the future, we will have a group of timekeeping satellites orbiting our sun. Maybe their orbit could be tweaked to have identical time dilation to Earth, and everyone can just sync off that.

Maybe we can derive some time keeping mechanism from the black hole at the center of our galaxy, or maybe we will just realize that our obsession with timekeeping is a silly terrestrial habit, and not really important at scale.

No it is pesky Einstein guy with his general relativity.

The bigger problem is that our timekeeping is earth based. The time definition should have been based on deep space, with corrections for time on earth.

So earth clock are slow with respect to clocks in deep space. Clocks on the moon are less slow are therefore faster than on earth

Not a physicist, but I was led to understand there is no universal frame of reference. You can't base time on deep space as if time was the same across all deep space, because it isn't. Right? A local time "correction" is easy when you compare against exactly one other point in space but if you want something like an universe-wide UTC that everyone can correct against, it can't be done. Although I don't really understand why.

Not a physicist either, but one practical problem is the speed of light. Time synchronization is likely to become very tricky if you have communicate with time sources that are hundreds of light years away.

They should have written "time runs faster on the Moon than on Earth". Clocks just measure it. You can't solve this with a better clock :)

But you could fix it with a sufficiently heavy clock.

It would change the Moon orbit too :)

It's not about the technology, atomic clocks are extremely accurate - it's time dilation due to relativity.

I assume this is due to time dilation, so it's not a limitation of the clocks.