On the relativistic invariance of the complex phase of plane waves


  • H. C. Ko


Using the covariance of Maxwell's equations, the complex phase of plane waves in lossy media is shown to be invariant under Lorentz transformations. The complex wave vector k = kr + iki and the complex frequency ω = ωr + iωi form two four-vectors, (kr, iωr/c) and (ki, iωi/c). In a lossy medium a homogeneous plane wave in one inertial frame will appear in general as an inhomogeneous plane wave in another moving inertial frame. The general relativistic disperison relation for a moving lossy medium is derived.