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Let me try to explain what my point here is. I think it will take
some doing. I'll start with an assertion and try to back it up. What
we refer to as the kinetic energy of a particle is not really energy
of that particle but rather energy of a system whose center of mass
is at rest relative to the inertial reference frame in which the
particle is said to have that kinetic energy. As far as the
explanatory and predictive power of the concept, what we call the
kinetic energy of a particle only matters insofar as it is the
kinetic energy of a system consisting of that particle and something
else with which that particle is interacting, will interact, or could
conceivably interact.
For instance, if we have two elementary particles on a collision
course with each other and you want to know what set of elementary
particles there might be after the collision, what matters is the
energy in the center of mass frame
It is in this sense that I say that, for any control mass system, all
energy of the system is internal energy.
I think it would be inconsistent for someone to consider the mass of
a particle to be invariant but to consider what we generally refer to
as the kinetic energy of a particle to actually belong to that
particle. If it were to belong to that particle then it would
contribute to the mass of the particle.
I think the notion that what we call the kinetic energy of a particle
does not really belong to the particle eliminates what I perceive to
be a problem, namely that the energy of a particle depends on the
inertial reference frame from which we view that particle.
What I do with the fact that the gravitational potential energy
associated with the interaction between a baseball and the earth is
energy of the earth+ball system, not energy of the ball, is to say
that for such cases the energy is really energy of the
earth/baseball system but for accounting purposes I am going to
assign it to the baseball.