Epistemology of Power Theory

The many mathematical “guises and disguises” under which the electrical power concept has been presented in the vast power engineering literature are summarized. These representations recapitulate the historical development of the concepts of number and space in mathematics. The author stresses that both classical electromagnetic theory and classical power theory are gauge theories of the Abelian (commutative) type. Their gauge symmetry is a global symmetry that in the case of power theory corresponds to the conservation of the electrical charge. However, and this is one of the main contributions of the author, the power theory should include a deeper symmetry – a local, non-Abelian (non-commutative) symmetry. This local mathematical symmetry is equivalent to the introduction of a new field: the bosonic field of photons. The speed of power transmission is related to the fact that massless photons transport electromagnetic force with subluminal speed. While electrons are carriers of electromagnetic matter, photons are carrier of electromagnetic momentum.