Right. perhaps time is indeed based on local properties, but it need not have a sync mechanism if those are the same properties in each place. For me it is helpful to imagine in being in a simulator like Conways game of life. If the speed of transition is mathematically precise, then one need not worry about time drift it wont exist.... as if the whole thing is implemented on a large computer.

I do agree this does require mathematically precise speeds... I just notice that the lower one goes in physics, the more mathematically precise things end up looking.