Momentum and rest mass of the covariant state of light in a medium

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 E₀ in vacuum, the OCD simulations of the light pulse propagating in a crystal having refractive index n give the same momentum p = nE₀/c and the transferred mass δm = (n²-1)E₀/c² 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.