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Doing it that way is IMHO vastly easier than doing it terms of Lorentz transformations, time
dilated clocks, Lorentz contracted rulers, velocity-dependent mass, et cetera.
I suspect physicists have fully understood Lorentz transformations. That is why John find
spacetime diagrams, 4-vectors, invariant length, proper time, invariant mass, et cetera to be
*vastly easier*.
Just ask some whether Lorentz transformation is real or apparent;
Then you may ask what do they understand by *real*. Physicists should be honest that they still
do not fully understand relativity. What most understand well is the mathematics behind.