  The long-standing resolution of the Abraham--Minkowski electromagnetic
momentum controversy is predicated on a decomposition of the total momentum of
a closed continuum electrodynamic system into separate field and matter
components. Using a microscopic model of a simple linear dielectric, we derive
Lagrangian equations of motion for the electric dipoles and show that the
dielectric can be treated as a collection of stationary simple harmonic
oscillators that are driven by the electric field and produce a polarization
field in response. The macroscopic energy and momentum are defined in terms of
the electric, magnetic, and polarization fields that travel through the
dielectric together as a pulse of electromagnetic radiation. We conclude that
both the macroscopic energy and the macroscopic momentum are entirely
electromagnetic in nature for a simple linear dielectric in the absence of
significant reflections.
