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.
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