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But E=mc^2 does permit mass to be converted to energy, and that, of
course, is the whole point of nuclear physics. The energy that binds
the nucleons together comes from the masses of the nucleons
themselves.
And those nuclei that prove to be radioactive are those
for which there is another possible "daughter" nucleus whose mass is
less than the parent nucleus less the radioactive particles emitted.
Systems always tend to the lowest available energy state.
One can get
a lot of mileage out of that idea in discussing nuclei. And nowhere
do we ever use "relativistic mass."
So if we don't need it, why use it? I have to come down on the side
of the professional relativists who have not used the term for years,
if not longer.