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I'm just saying that they lead to a paradox when you compare the[snip]
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.
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).
No.[snip]
That is, assuming that the x-axis for both frames lies along the
LA-San Diego vector, that both will get the same value for x^2 -
c^2*t^2, as measured by instruments in their own reference frames. It
doesn't mean that either x or t will be seen to be the same in both
frames, because they won't.