  In relativistic mechanics the energy-momentum of a free point mass moving
without acceleration forms a four-vector. Einstein's celebrated energy-mass
relation E=mc^2 is commonly derived from that fact. By contrast, in Newtonian
mechanics the mass is introduced for an accelerated motion as a measure of
inertia. In this paper we rigorously derive the relativistic point mechanics
and Einstein's energy-mass relation using our recently introduced neoclassical
field theory where a charge is not a point but a distribution. We show that
both the approaches to the definition of mass are complementary within the
framework of our field theory. This theory also predicts a small difference
between the electron rest mass relevant to the Penning trap experiments and its
mass relevant to spectroscopic measurements.
