  Conventionally, theories of electromagnetic waves in a medium assume that
only the energy of the field propagates in a transparent medium and the medium
is left undisturbed. Consequently, the transport of mass density and the
related kinetic and elastic energies of atoms is neglected. We have recently
presented foundations of a covariant theory of light propagation in a medium by
considering a light wave simultaneously with the dynamics of the medium atoms
driven by optoelastic forces between the induced dipoles and the
electromagnetic field. In the previously discussed mass-polariton (MP)
quasiparticle approach, we considered the light pulse as an isolated coupled
state between the photon and matter and showed that the momentum and the
transferred mass of MP follow unambiguously from the Lorentz invariance and the
fundamental conservation laws of nature. In the present work, we combine the
electrodynamics of continuous media and elasticity theory to account for the
space- and time dependent dynamics of the light pulse and the associated mass
and momentum distributions of the mass density wave (MDW). In this optoelastic
continuum dynamics (OCD) approach, we obtain a numerically accurate solution of
the Newtonian continuum dynamics of the medium when the light pulse is
propagating in it. For an incoming Gaussian light pulse having total energy
$E_0$ in vacuum, the OCD simulations of the light pulse propagating in a
crystal having refractive index $n$ give the same momentum $p=nE_0/c$ and the
transferred mass $\delta m=(n^2-1)E_0/c^2$ as the MP quasiparticle approach.
Since the elastic forces are included in our theory on equal footing with the
optical forces, our theory also predicts how the mass and thermal equilibria
are re-established by elastic waves.
