John, I'm not sure I understand your comment, "This is true even in
classical non-relativistic low-speed mechanics: The KE of a whole
collection is not the sum of the individual KEs. People throw around
terminology such as "total KE" but there are at least two things the term
could mean. Sometimes it takes a lot of head-scratching to figure out
what they're talking about."
Is it that you're alluding to the fact that the "translational kinetic
energy" 0.5M_sys*v_cm^2 is different from the sum of all the kinetic
energies of the particles that make up the system, sum(0.5m_i*v_i^2)? Or is
there more to your comment than I'm understanding?