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In response to a question asking if it's a fair statement that I expect
a line drawn from E1 to E2 to "coincide" in different frames, I replied:
No, I don't expect the line to coincide in different reference
frames. In the case I gave, the lines don't coincide in F and
F', but the point I'm trying to make is that they don't coincide
in spacetime, either. When I say they don't coincide in
spacetime, I mean, they don't coincide independently and apart
from either reference frame.