Theory of Electrodynamics in Media in Noninertial Frames and Applications

Abstract

The theory of local electrodynamics of media in given noninertial frames, within the Maxwell-Einstein theory, is constructed in terms of local observable EM fields and physical media parameters of its comoving frame. Localization of tensors to observables for and their relations among observers in different frames are introduced; local and global constitutive tensors and local Maxwell equations are obtained and interpreted. Also, a Lagrangian formulation for both lossless and lossy media is constructed, and boundary conditions, local conservation laws, and energy tensors are obtained. The applications concern linear accelerational and rotational media in flat space-time for which local Maxwell equations in comoving frames are obtained. Then an EM wave propagating in the direction of acceleration is studied in the accelerating frame. The first-order propagation shows a frequency shift and amplitude change which have very simple physical significances of instantaneous Doppler shift and photon density in media and which agree with familiar results in the vacuum limit. A particle model for this wave shows that the ``mass-dressed'' photon is dragged by the medium and does not follow a geodesic path. In the case of a rotating medium, a plane wave scattered by a rotating sphere is solved by an integral iteration method in the laboratory frame. The scattered field which is associated only with the rotation of the medium is separated from the Mie scattering. Its first-order amplitudes are found for incidences perpendicular and parallel to the rotation axis. Particular symmetry and shapes of scattering amplitude in the results agree with intuition and resemble radiation patterns of appropriately induced traveling electric and magnetic dipole sheaths.