The following problem could be given to students. For the derivation
of Lorentz transformations, Einstein introduced
(A) x' = 0 <-> x = vt
He should have introduced, or WE now introduce, in accordance with
the special relativity principle, a premise symmetrical to (A):
(B) x = 0 <-> x' = -vt'
Einstein also introduced, for a beam moving along the x-axis,
(C) x = ct <-> x' = ct'
Now the problem is that (A), (B) and (C) are incompatible. (A) and
(C) are compatible and lead to Lorentz transformations but it is easy
to see that one cannot deduce (B) from Lorentz transformations. (A)
and (B) are also compatible and lead to transformations different
from Lorentz transformations. (B) and (C) are also compatible and
lead to transformations insignificantly different from Lorentz
transformations. So, in order to be able to proceed, we must declare
either (A) or (B) or (C) as false. Which one is false?