The bizarre and intriguing story of Oleg Jefimenko and the solutions to Maxwell's Equations
Jefimenko’s tiny bit of fame comes from Jefimenko’s Equations, which are the general solution to Maxwell’s equations expressed solely in terms of sources, that is charge and current distributions. The equations are messy and difficult to work with, and aren’t used much in practice. But they do reveal certain bits of physics (such as the applicability of the quasistatic approximation (the link goes to a thermodynamics page, but the idea is the same) and that fields must be created by sources), and it’s always nice to have the general solution to a problem available.
These equations weren’t written down until 1966, about a century after Maxwell’s Equations were known. Some people will claim (as the Wikipedia article cited does) that Jefimenko’s Equations were written down earlier, but those earlier versions are always slightly different and not quite complete. What’s really funny is that Jefimenko wrote them down in an attempt to formulate an alternative to Maxwell’s equations.
When my current Professor, David Griffiths, was in the process of writing a paper on the subject, he independently derived Jefimenko’s equations, and tried to figure out if anyone had done it before. Other than some slightly tricky and annoying math, they’re not hard to derive, so someone must have done it. He found that Jefimenko had written them in a book that was published by a company that had only published one other work, also by Jefimenko (apparently regular publishers wouldn’t take his books, so he went to a prestige press). He contacted Jefimenko, and Jefimenko didn’t believe that he had solved Maxwell’s equations, but that he had created an electromagnetic theory separate from (and doubtless better than) Maxwell’s. Of course he had done no such thing, his formulation is exactly equivalent to Maxwell’s, but he wasn’t buying it.
According to Griffiths, Jefimenko currently submits one or two papers a week to American journals, gets denied, then publishes them in Europe (where review is apparently not as stringent). I don’t know what they’re about, the Wikipedia article says he focuses on overthrowing Einstein’s General Relativity and Maxwell.
I found this story behind some esoteric equations to be pretty amusing, and thought others might agree. I hope you’ve enjoyed the convoluted and intriguing story behind Jefimenko’s equations.
[Most of my information comes from a lecture with Griffiths, and as such could not be found online. Anything that is available online has been referenced.]