Theory of Electrodynamics of Media in Non-Inertial Frames and Applications

Citation

Mo, Tse Chin (1969) Theory of Electrodynamics of Media in Non-Inertial Frames and Applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1Z64-YS50. https://resolver.caltech.edu/CaltechTHESIS:03282017-111748813

Abstract

In the first half of this thesis a local electrodynamics of media in given non-inertial frames*, within Maxwell-Einstein classical field theory, is constructed in terms of observable EM fields and co-moving local physical media parameters. Localization of tensors to observables is introduced and justified, and a relation is obtained connecting tensor transforms to instantaneous Lorentz transforms for observers in different frames. A constitutive tensor, explicitly expressed by the four-velocity and the local properties in co-moving frame of a linear medium, is found for the first time. Previous mistakes in confusing the tensors, in which forms the physical quantities combine with the non- flatness of frames to be used in covariant equations and thus make geometrical quantities, with observables are cleared. Also a Lagrangian formulation for both lossless and lossy media is constructed, and boundary conditions, local conservation laws, and energy momentum tensor are obtained.

The second half concerns application to motions in SRT, such as uniform linear (hyperbolic) acceleration and steady rotation. For these local Maxwell equations in co-moving frames are obtained, and approximate solutions are found for special cases. 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 rotating medium case a plane wave scattered by a rotating sphere is solved by an integral iteration method in the laboratory frame. The scattered field purely associated to the rotation of the medium is separated from the Mie scattering. Its first order amplitudes are found and plotted for incidences perpendicular and parallel to the rotation axis. Particular synunetry and shapes of scattering amplitude in the results agree with intuition and resemble radiation patterns of appropriately induced traveling electric and magnetic dipole sheaths.

*The contribution of EM field to g_µv is neglected.

Thesis Files