There are other formulations of relativity which aren't nonlocal!! Like the Tangherlini transformations.
I like this quote:
"Alice wants to synchronize her clock with Bob's, so this is how it might go:
At 12:00:00 pm Alice time, Alice sends out a beam of light to Bob, as a signal for Bob to tell Alice what time he has.
Once Bob receives the beam of light, Bob immediately sends Alice a beam of light telling her the time he has.
At 12:00:02 pm Alice time, Alice receives Bob's time, say 11:41:23 am.
At this point, how should Alice synchronize clocks? Clearly, 12:00:01 pm Alice time is 11:41:23 Bob time. We're done.
But we've unknowingly introduced an assumption here, namely that the speed of light travelling from Alice to Bob is identical to the speed of light travelling from Bob to Alice."
