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I would like to emphasize that understanding arithmetic is a
prerequisite for understanding relativity.
How many people on this list -- or their students -- are
aware of any axioms of arithmetic that allow for multiplying
infinity by zero? Not many, I would wager.
Just now I tried googling for such an axiom, and found nothing
... for good reason.
Let's do another little calculation. Again we hypothesize that
P = m U
m = 0
We multiply both sides by 2.
2 P = 2 m U
Since another of the axioms says that multiplication is associative,
we can write this as
2 P = (2 m) U
Now we also have
2 m = m + m
= m + 0
= m
where the last step follows from the axiom that says 0 is the additive
identity.
Collecting results we have
2 P = (2 m) U
= m U
= P
This in turn guarantees that P = 0.
So once again we have "proved" that every photon has zero energy and
zero momentum in every frame (subject to the hypothesis that P = m U
and m = 0).
Again we must reject the hypothesis.