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Two events ("light enters train" and "light leaves train") happen
that are identifiable in either frame (otherwise any such analysis
should be abandoned) and we are to compare the distances between
them, x and x', and the time intervals between them, t and t'. I
think the only reasonable criticism of my solution should consist in
offering a solution proving that x/t = x'/t'. Einstein's theory is
expected to be able to resolve problems as simple as
this one.
I disagree. It is not Einstein's THEORY that addresses this
"problem" so much as the primary postulate OF that theory. If "the
speed of light is the same in all reference frames," then x/t =
x'/t'. That is REALLY all there is to it.
It is the spectacular agreement of the many seemingly bizarre
predictions of this theory with every experiment that has been
performed that give us such enormous confidence in the primary
postulate.