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I would be interested to know if my thinking is confused on either of
these points, but at the moment I'm wondering if plain old vanilla
'mass' would be a better term.
...... the term 'invariant mass' seems to me to conflict
with a genuine geometric model of spacetime. In particular we must
ask 'invariant with respect to what?'. Presumably, the invariance is
with respect to a particular class of coordinate systems, but mass
transcends these coordinate systems.