What is meant by "coming apart from" in this context?

An alternative rule would be to require that all clocks, everywhere on Earth, keep time with Greenwich Mean Time. We don’t usually use that alternative rule, because it’s inconvenient for noon to occur in the middle of the night in some parts of the world, but that doesn’t make it wrong, just less useful. (Indeed, in some circumstances—military operations, for instance—it turns out to be more useful, with the benefits of a shared time outweighing the costs of that time coming apart from Sun and Moon.)

Source: Philosophy of Physics by David Wallace

1 hour ago, Ibrahim Sanad said:

What is meant by "coming apart from" in this context?

An alternative rule would be to require that all clocks, everywhere on Earth, keep time with Greenwich Mean Time. We don’t usually use that alternative rule, because it’s inconvenient for noon to occur in the middle of the night in some parts of the world, but that doesn’t make it wrong, just less useful. (Indeed, in some circumstances—military operations, for instance—it turns out to be more useful, with the benefits of a shared time outweighing the costs of that time coming apart from Sun and Moon.)

Source: Philosophy of Physics by David Wallace

Firstly let me say that I don't think this belongs in the Relativity section.
The extract is very short and I am not familiar withe the source but I think the subject concerns only the ordinary time we measure and live with on the surface of the Earth.

The clue is in the statement "it’s inconvenient for noon to occur in the middle of the night in some parts of the world,".

I would agree that the phraseology is rather poor but I think that 'coming apart from' describes the fact that 'noon' is related to the Sun being overhead and that this will only happen at 12:00 on the Grenwich Meridian.
Everywhere else it will happen at some other time, unless the residents there use a locally adjusted time other than GMT.

 

It is a pity also that his example of the use of standard GMT elsewhere in the world is military.

Surveyors, navigators and astronomers have for centuries used it as the basis for star tables for peaceful purposes as well (and still do).

 

Does this help ?

It means something like "out of sync with". Meaning the time isn't synchronized with the Sun in the usual way, with AM in the morning and PM in the evening.