Universal Journal of Physics and Application Vol. 12(3), pp. 31 - 40
DOI: 10.13189/ujpa.2018.120301
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A New Approach to Classical Electrodynamics: Covariant Second-Order Field Variations

William B. Maier II *
Department of Physics, Naval Postgraduate School (ret.), USA


This paper describes a formulation of classical electrodynamics without point charges and masses. Maxwell's equations are assumed to be valid at all scales, and the Lorentz force is replaced as a fundamental law of nature by equations derived by a second order variation on a covariant 'action' in which the usual term involving mass,, has been replaced by a covariant mass density associated with the fields. Fij and Tik are the usual field and energy-momentum tensors, and ui is the four-velocity associated with charge. Distributions having charge of a single sign are found to be stabilized by charge motion in the distribution's self-field, and they have finite extent, charge, and mass. The motion of these charged bodies in an imposed electromagnetic field is shown to obey the Lorentz force law, where the mass is equivalent to the total energy of the electromagnetic field integrated over all space. Ordinary classical electromagnetism is thus reproduced, and in addition, the classical structures of fundamental charged bodies are obtained. The singularities usual to dualistic theories disappear. Classical structures of the electron and proton are briefly discussed.

Electrodynamics, Classical Field Theory, Electromagnetism, Electron Structure, Particle Structure, Second-Order Field Variations, Self-field-stabilized Charged Bodies

Cite this paper
William B. Maier II . "A New Approach to Classical Electrodynamics: Covariant Second-Order Field Variations." Universal Journal of Physics and Application 12.3 (2018) 31 - 40. doi: 10.13189/ujpa.2018.120301.