The most general form of the vector potential in electrodynamics

The most general form of the vector potential is deduced in curved spacetime using general relativity. It is shown that the longitudinal and timelike components of the vector potential exist in general and are richly structured. Electromagnetic energy from the vacuum is given by the quaternion valued canonical energy-momentum. It is argued that a dipole intercepts such energy and uses it for the generation of electromotive force. Whittaker’sU(l) decomposition of the scalar potential applied to the potential between the poles of a dipole, shows that the dipole continuously receives electromagnetic energy from the complex plane and emits it in real space. The known broken 3-symmetry of the dipole results in a relaxation from 3-flow symmetry to 4-flow symmetry. Considered with its clustering virtual charges of opposite sign, an isolated charge becomes a set of composite dipoles, each having a potential between its poles that, inU(1) electrodynamics, is composed of the Whittaker structure and dynamics. Thus the source charge continuously emits energy in all directions in 3-space while obeying 4-space energy conservation. This resolves the long-vexing problem of the association of the “source” charge and its fields and potentials. In initiating 4-flow symmetry while breaking 3-flow symmetry, the charge, as a set of dipoles, initiates a reordering of a fraction of the surrounding vacuum energy, with the reordering spreading in all directions at the speed of light and involving canonical determinism between time currents and spacial energy currents. This constitutes a giant, spreading negentropy which continues as long as the dipole (or charge) is intact. Some implications of this previously unsuspected giant negentropy are pointed out for the Poynting energy flow theory, and as to how electrical circuits and loads are powered.