"Time" not a dimension.

[Zenith]

You may as well try to imagine invisible pink unicorns . Global time is not compatible with relativity.

Actually, I don't think I could: the invisible pink unicorns are not omnipresent.

If I see two events as simultaneous, then someone in motion with respect to me will not.

And that was the fact with the omnipresence that mattered: if two observers see two event A, and B, differently (e.g. one sees it B before A, the other sees A and B in the same time), then an omnipresent being 'notices' the 'correct' order of the events, because he doesn't 'look' from a distance to the event, and is not moving at all. And if we have a 'correct' order of events - from 'someone' who doesn't 'look' from a distance and is not moving at all - then that is a global time. If the logic is correct so far, then it means that even if the omnipresent being does not exist, this 'global time' should exist.

The thing you have explained with the observers sounds something like a "subjective view". And the reason I inserted that omnipresent being was in an attempt to explain an "objective view". I hope you understand what I'm talking about.

As about two events happening simultaneously: imagine the universe scaled so that you would see it all, in front of you (now you see the things objectively), and you see two specific stars at the same time, and one star dies, and after that the other one dies. How do you imagine those two stars in two different local times, dying in the same time, yet one after another? You know, if you regard it objectively, then it sounds like this: you have a box filled with objects (cubes, balls, etc.). And one comes and tells you: these objects in the box do not exist in the same time - they only exist in local times.

and the GPS system has an algorithm built in which corrects for this effect

Can you please give me some more info about this?