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I hesitate to get into this fray because I know very little about
relativity but here goes.
David Rutherford wrote:
I'm just saying that they lead to a paradox when you compare the
assigned locations of breakfast, in the two frames, at the time of
lunch, which is when you "draw the lines" between breakfast and lunch,
in the two frames.
[snip]
Therefore, both lines (from breakfast) start at time zero, but at
different spatial locations. That means that they start at different
points in spacetime, thus, they don't coincide in spacetime and
cannot describe a geometically invariant quantity (the spacetime
four-vector between the events).