The “gap” referred to here is a communications gap. It lies between theoreticians and researchers—those apparantly in the know—and practitioners—those with an everyday need to know. The mathematics used to characterize electromagnetics, for example, are really an extensive shorthand code. And, that code is used not only by researchers, but also by teachers. As a result, to make real progress in EMC engineering, those mathematics need to be simplified as much as possible, decoded, and carefully explained. They need to be made easier to understand, both for practitioners and for students. Then, more of today’s students who later become teachers and researchers will be better able to communicate and better able to teach. And, that will make electromagnetics in general, and EMC engineering in particular, easier to understand and easier to practice.
The basic problem was described by Richard Courant and Herbert Robbins in their book entitled “What is Mathematics?” (Oxford University Press, 1941). They said:
“Without doubt, all mathematical development has its psychological roots in more or less practical requirements. But once started under the pressure of necessary applications, it inevitably gains momentum in itself and transcends the confines of immediate utility.”
In other words, mathematics is a very useful tool, but quite often its users get carried away and it becomes overused. That has created the need for EMC practitioners to understand both the physics of electromagnetics and the mathematical shorthand used to describe those physics. The result makes genuine understanding doubly difficult.
To further envision this gap, consider two comments made by Morris Kline in his book entitled “Mathematics and the Physical World” (Thomas Y. Crowell Company, 1959): “Science has become a collection of mathematical theories adorned with a few physical facts.” . . . “Unfortunately the relationship of mathematics to the study of nature is not presented in our dry and technique-soaked textbooks.”
At the time he wrote those comments Kline was a professor of mathematics, and the director of the Division of Electromagnetic Research at New York University as well! That clearly indicates the strength of the connection between mathematics and electromagnetics forty years ago. And, the two are no less connected today.
It certainly would seem that Morris Kline was saying exactly what I am saying—the physics and the mathematics of electromagnetics need to be more clearly related to one another. We need to back up, slow down, and think about how to rid electromagnetic theory of explanatory gaps due to unnecessarily abstract mathematics. Electromagnetic phenomena need to be characterized with more pictures and with simpler mathematics. Then, and only then, will the communications gap between theoreticians and practitioners become bridgeable. And, teachers will be better able to communicate with their students.