[yor_on]

When it comes to me differing between what I call locality and a global definition then I think both Einstein and Minkowski went out from a same position, defining a 'global' universe using the postulate of lights speed in a vacuum being a 'global'  as well as 'local' constant. There is a subtle difference in defining it globally versus locally. You can from repeatable experiments define 'global constants' but the experiments done are always local.
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Looked at that way we seem to consist of something in between those two barriers, and that is when scales becomes very interesting to me. Physics use decoherence as one of its definitions. Also, what I use is what I call locality, and defined that way all clocks are equal locally defined, your wristwatch relative your life span if I express it that way. And those repeatable experiment builds on a similar assumption, us being in a same 'frame of reference'.

And so do physics, it refers not to 'grains' as much as it refers to laws, properties, symmetries, conservation laws etc. that we place 'globally' as defining the whole universe. So those that looks for a different type of universe 'further away', f.ex having different constants, also seem to imply that they don't trust those definitions, as I see it.

Maybe I can summarize it as the universe, looked at 'globally', becomes an abstraction.
Locally a practical reality.