  A self-consistent theory is developed based on the principle of relativity
for a plane wave in a moving non-dispersive, lossless, non-conducting,
isotropic, uniform medium. A light-momentum criterion is set up for the first
time, which states that the momentum of light in a medium is parallel to the
wave vector in all inertial frames of reference. By rigorous analysis, novel
basic properties of the plane wave are exposed: (a) Poynting vector does not
necessarily represent the electromagnetic (EM) power flow when a medium moves;
(b) Minkowski light momentum and energy constitute a Lorentz four-vector in a
form of single EM-field cell or single photon, and Planck constant is a Lorentz
invariant; (c) there is no momentum transfer taking place between the plane
wave and the uniform medium, and the EM momentum conservation equation cannot
be uniquely determined without resorting to the principle of relativity; and
(d) when the medium moves opposite to the wave vector at a
faster-than-dielectric light speed, negative frequency and negative EM energy
density occur, with the plane wave becoming left-handed. Finally, a new physics
of so-called "intrinsic Lorentz violation" is presented as well.
