Invariant Form of the Maxwell-Lorentz Field Equations for Accelerated Systems

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Abstract
It is shown that the invariant field equations of Maxwell for stationary bodies are also valid for accelerated bodies, if all ordinary differentiations are replaced by absolute differentiation. The affine connection Γγαβ appearing in the absolute derivatives refers to a general non‐Riemannian metric space, with a holonomic or nonholonomic reference frame. The field equations are in a more general form than those used in the five‐dimensional unified field theory and reduce to the latter as a special case. However, the presence of an electrostatic field is not assumed in this paper. The motion of an accelerated body possessing mass, electric current and magnetic flux is given by an extended form of the dynamical equations of Lagrange containing the same general affine connection as the field equations. The material terms of the dynamical equations are expressed by a mechanical impulse‐energy tensor and the resultant motion of the material body under the influence of an electromagnetic field and a mechanical force is expressed by a combined impulse‐energy equation. The equations are calculated for a representative rotating electrical machine used in industry.

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