Lorentz covariance of the mass-polariton theory of light

Abstract

In the mass-polariton (MP) theory of light formulated by us recently [Phys. Rev. A 95, 063850 (2017)], light in a medium is described as a coupled state of the field and matter. The key result of the MP theory is that the optical force of light propagating in a transparent material drives forward an atomic mass density wave (MDW). In previous theories, it has been well understood that the medium carries part of the momentum of light. The MP theory is fundamentally different since it shows that this momentum is associated with the MDW that carries a substantial atomic mass density and the related rest energy with light. In this work, we prove the Lorentz covariance of the MP theory and show how the stress-energy-momentum (SEM) tensor of the MP transforms between arbitrary inertial frames. We also compare the MP SEM tensor with the conventional Minkowski SEM tensor and show how the well-known fundamental problems of the Minkowski SEM tensor become solved by the SEM tensor based on the MP theory. We have particularly written our work for non-expert readers by pointing out how the Lorentz transformation and various conservation laws and symmetries of the special theory of relativity are fulfilled in the MP theory.

Lagrangian dynamics of the coupled field-medium state of light

“…We show that the well-known physically intuitive Lagrangian densities of the field and the medium lead to intrinsic coupling of the Maxwell's equations of the field and Newton's equation of motion of the medium under the influence of the optical force. From these dynamical equations, we also derive the field and the medium parts of the total SEM tensor of the coupled system, which are in full agreement with the first-order approximations of these tensors presented in our previous work [12]. While our previous work was based on taking the electromagnetic energy and momentum densities as given and neglected the extremely small kinetic energy of atoms resulting from the optical force, in the present work, we exactly describe how small part of the total energy of light is carried as the kinetic energy of atoms.…”

“…In this work, we present the derivation of the MP theory directly from the principle of least action in the case of nondispersive transparent media. Complementary to the proof of the Lorentz covariance of the MP theory of light presented in [12], the present work provides a solid classical field-theoretical basis for the MP theory. We show that the well-known physically intuitive Lagrangian densities of the field and the medium lead to intrinsic coupling of the Maxwell's equations of the field and Newton's equation of motion of the medium under the influence of the optical force.…”

“…Our approximations are mainly the same as those in our previous work [12] with one exception. In our previous work, we assumed that the dynamical variables of the medium do not appear in the field part of the SEM tensor.…”

“…Following our previous work [12], we assume a homogeneous medium where material interfaces are not present. For simplicity, we also assume that the material is nondispersive, optically linear, and that there are no free charges and currents.…”

“…Very recently, the mass-polariton (MP) theory of light has provided a unique resolution to the Abraham-Minkowski controversy [10][11][12]. The MP theory shows that light propagating in a medium must be described as a coupled state of the field and the medium.…”