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GPS would work without relativity.I think you must have read a different version of the twins paradox from the ones I've read (and perhaps a different version of relativity, come to that).
But hey, GPS will still work, regardless.
All that is required is the satellites clocks remain synced with one another. The GPS receiver in your car has no atomic clock in it, all it cares about is the difference in time stamps from the satellites. They could be all 10 minutes ahead or 10 minutes behind, it wouldn’t matter a bit. Only the differences in the satellites clocks matter.
Now you’ll get the real reason we use relativity. Because we have no other way to ensure the satellite clocks remain synced with one another except to compare them to earth clocks.
Hence we go back to Einstein’s biggest problem, the syncing of non local clocks.
If we had a way to ensure those clocks remained synced with one another, besides comparing them to earth clocks, we wouldn’t need relativity at all. But as it stands there is no other way to ensure non local clocks are synced except to change them to match a master clock locally, so that we have a clock to compare their remaining synced too.
Don’t confuse why we need to do it, with it being a required necessity to make the GPS function.
Your receiver has no atomic clock in it, that requires it to be synced with a satellite clock. Nor is it accurate enough to remain synced with one.
No, please don’t confuse why we do it with it being a necessity except to keep satellite clocks synced with one another. That’s the only reason we sync them to earth clocks, because even Einstein could never figure out how to ensure non local clocks could be synced. Hence to this day the one way speed of light has never been measured.
But you avoided the issue.
What does the earths curved trajectory tell you about our clocks that you were willing to accept when it was only curved trajectories and clocks on airplanes? Why do you keep avoiding the logical conclusion? Yes, I know, paradigm shifts are frightening until you accept them fully.
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