Electrical and magnetic ﬁelds have been known in mathematical

form since the laws of Coulomb and Ampere were discovered in

the late 17th and early 18th centuries. Applying to macroscopic

domains, modern atomic physics was in its infancy at that time.

Both laws assume charge separation in a single nonlinear function,

the square root of the sum of the squares of orthogonal distances

involved in their separation.Within atomic andmolecular theory the

Pythagorean concept of distance has been utilized by both classical

electromagnetics and quantum theory. Einstein’s relativity gave

the ﬁrst hint that in some phenomena, separations in orthogonal

directions do not couple but stay separate. Thus electromagnetic

ﬁelds in atoms consist of two ﬁelds each causing the atomic

particles to rotate in orthogonal planes. If charge separation

includes both centres of rotation, electromagnetics can analytically

solve for the motions. In this chapter we examine how classical

electromagnetics failed at the atomic level and quantum theories

were deemed necessary, thus dominating 20th-century physics. The

classical ﬁelds were responsible for this historical failure. A selective

sweep across scientiﬁc knowledge provides a preview of self-ﬁeld

theory.