dipole said:
Interesting discussion so far, but my original question was regarding electromagnetic waves - if we take Jefimenko's equations, then how can we couple the E and B fields such that they propagate together as a wave? Was Maxwell wrong, do his equations in fact not imply the existence of electromagnetic waves?
There are two different ways of looking at electrodynamics, one based on the field interpretation of Faraday, Maxwell, Hertz, et al, and the other based on the retarded distant action interpretation of Weber, Lienard-Weichert, Tetrode-Fokker, et al. It was once thought that the phenomena of electromagnetic waves was unique to the field interpretation, so when Hertz discovered behavior that was interpreted as evidence of electromagnetic waves it was taken as a sign by many people that Maxwell was right and the action-at-a-distance theories were wrong. However, in later years it was realized that exactly the same phenomena that was interpreted as wave action also emerges from the action-at-a-distance interpretation - with suitable retarded action and boundary conditions. Ultimately all the observable effects are interactions between electric charges. (This of course is a hypothesis... it's conceivable in Maxwell's interpretation that there could be electromagnetic waves in the universe that never originated with any accelerating charges - but we have never observed any such thing.)
There are subtleties here, involving radiation reaction and the self-energy of a charged particle, that present difficulties for both the field interpretation and the distant-action interpretation. Wheeler-Feynman gave an account of radiation reaction within the context of distant action by making use of both the advanced and the retarded solutions, with an ideal absorber in the future. So, at least nominally, there is a viable distant-action interpretation of classical electrodynamics... at least as viable as the field interpretation.
It sometimes surprises students to learn that there is no fully self-consistent classical electrodynamics, either with fields or with distant-action, but see the last chapter of Jackson for why our classical theories work as well as they do, in spite of this.
PhilDSP said:
Jackson probably should have placed a footnote reference on the term "in this author's text". Notice that "(Jefimenko)" appears immediately after it. I'd interpret that to refer to Jefimenko's 1966 book on EM which is listed in the bibliography.
Yes, I interpret it that way too.
PhilDSP said:
Jefimenko brings further clarity to the question of what causes what and does not rest in complacency on his initial findings. He pursues that question and others very actively and deeply to arrive at at least new perspectives on older matters. He even has proposed experiments which potentially show different results from how the behavior of EM differs from common expectations.
Again, there is no new physics in writing down solutions to Maxwell's equations, so he should not be expecting experimental results to differ from what Maxwell's equations predict. You don't exactly say that he does... instead you say he predicts results that differ from "common expectations". Well, that's an odd thing to say. The common expectation is that experimental results will agree with Maxwell's equations, so if Jefimenko expects something different, his expectations are in conflict with Maxwell's equations - but he also claims to accept the validity of Maxwell's equations - so what you've described seems somewhat confused.
The Wikipedia article on Jefimenko suffers from the same confusion. It says it is commonly believed that a varying E field causes B, and a varying B field causes E, but it gives no reference that supports the claim that this is commonly believed (the one reference it cites actually says something very different), so it's really just a straw man - like your "common expectations".