Tom, the paper I wrote and linked to is directly related to the discussion in this thread, and answers the questions I raised in it. I'll explain further but first I would like to respond directly to this statement by you:
tvf wrote: "The abstract makes some assertions of a possibly mathematical character with no hint of any plausible physics behind them."
The abstract is merely that and so there is only so much it can explain, but as it says that electromagnetic forces are being analyzed, I was hoping the reader would take it to mean that I am using standard tools of electromagnetism, which is indeed the case. The mathematics behind this is not terribly complicated, but it certainly is too complicated to post directly here. In any case, the point I want to get to is that I use entirely only completely standard electromagnetic theory, and arrive at what might seem quite paradoxical results. I expected you would be interested in this sort of thing.
After thinking about Carlip's response to your paper I got to thinking that even assuming everything he said about EM theory is true there were some interesting issues remaining. Supposing the propagation delay effects are canceled to first order, that could easily leave a residual effect that would be significant. Carlip in one of your online discussions I think hinted that the leftover energy might account for what is radiated. Well, I thought, if that were the case that would be pretty important because the radiation resistance force is quite mysterious as I think I cover in the thread above. A new way to understand it would be quite valuable. On the other hand, if aberrational forces could cancel radiation resistance that should be interesting as well as it might for the first time provide a non-ad hoc explanation for the stability of atomic systems.
So I analyzed the magnitude of the aberrational Coulomb force classically for the point charge hydrogen model. It turned out that the residual aberrational component after the correction as pointed out by Carlip is quite small, too small to cancel radiation resistance at typical atomic radii, although it has the proper sign to cancel. Also, adding in the time advanced action part (as proposed by Wheeler and Feynman and discussed above) does exactly cancel any non-conservatve force for a circular orbit, identically. For an elliptical orbit it is not zero everywhere but it appears to integrate to zero around the course of the orbit.
That was some substantial effort that didn't amount to anything of great import, but I found the answer to the questions I proposed here and so do feel at least duty-bound to report about it. No need for somebody else to repeat the exercise at this point. Then I went on thinking about the classical atomic model, and it occurred to me that there is another interesting force, simply another direct consequence of Maxwell's equations, due to the intrinsic magnetic moments of the electron and proton. As I show in the paper, the motion of the magnetic moments naturally leads to electric forces due to the time variation of the intrinsic magnetc fields. These forces are rather asymetrical though because the electron has a much larger intrinsic magnetic moment, and also because it is moving a lot faster. So, this force that is merely a consequence of Maxwell's theory would seem to break that old adage about for every action there is an equal and opposite reaction. I think that is worth knowing. I also think it's weird enough it could provide a basis for quantum behavior. It has Planck's constant attached to it via the spin. I have gotten the Bohr formula for the hydrogen ground state radius from it a couple of different ways. One of them is in the currently posted paper, and the other I hope to post pretty soon. I won't bother you with it though if you're uninterested.
The final wrinkle I will trouble you with is how when one takes into account propagation delay for this force due to motion of intrinsic moments, the aberrational component of it is quite large, larger than in the case of the Coulomb force. It's interesting because the Coulomb force is about a million times stronger to begin with, but the correction term Carlip points out integrates out in the case of the other, so that the aberrational force is enough to cancel radiation resistance. It has a different range dependency, though, so it doesn't happen at just any distance. Rather, as I show in the paper, it happens in the classical hydrogen atom at 9/16 times the Bohr ground-state radius. So, the radiative decay of the classical atom that is mentioned in so many physics textbooks simply doesn't happen according to Maxwell's elecftrodynamics. It stops at about the typical atomic dimension. Also, this newly-recognized (so far as I know, and I have now done quite a bit of searching through the APS online archives back to the 1800s) aberrational force does not cancel out when the time-advanced action is included.
Tom, we do disagree on what is the significance and interpretation of these kind of seemingly paradoxical phenomena, but in any case I believe you deserve great credit for raising the issues.
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