Date of Award
5-12-2015
Document Type
Thesis
Degree Name
Mathematics, MS
First Advisor
Brandon Kemp
Committee Members
Jeongho Ahn; Jie Miao; William Paulsen
Call Number
LD 251 .A566t 2015 S35
Abstract
Optical momentum within material media has been studied for a century. Although great strides have been made towards understanding photon momenta, there is still a question regarding the correct momentum of light. This is due to the many mathematical interpretations of Maxwell's unification of electromagnetism, yielding many independent views of classical electrodynamic quantities. Within this correspondence, the optical momentum controversy is studied via mathematical principles of continuum relativistic electrodynamics. The electromagnetic wave momentum is studied via moving contribution, where a framework for moving media is developed. Application of the framework with respect to independent formulations of electrodynamics are shown to be consistent with conservation of energy and momentum. In doing this, thought experiments are employed to test each approach and demonstrate the electrodynamic forces with respect to each formulation. This is first applied to two moving perfect reflector submerged in a dielectric medium such that both Abraham and Minkowski momenta are derived. Second, a moving slab of moving magneto-dielectric material is studied expanding the arguments into time average and time varying calculations. Each approach is consistent with electromagnetic wave theory and demonstrates the mathematical methods for deriving the both Abraham and Minkowski momentum models. The kinetic subsystem is studied by use of established physical principles, namely the Lagrangian. The field energy density and momentum density are used to derive the force expressions of electromagnetic fields. This formulates the respective system of equations, forming Maxwell's equations in terms of the field energy and momentum density. By use of the relativistic principle of virtual power, the Maxwell field stress tensor and kinetic momentum density are derived uniquely, disproving specific electrodynamic formulations as the kinetic formulation.
Rights Management
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Sheppard, Cheyenne Jack, "Mathematical Analysis of Continuum Electrodynamics: Implications for the Kinetic Formulation of Light" (2015). Student Theses and Dissertations. 708.
https://arch.astate.edu/all-etd/708
