In vol. I, chapter 32, of The Feynman Lectures, Feynman says:

If we take a charged body and accelerate it up and down it radiates energy; if it were not charged it would not radiate energy. It is one thing to calculate from the conservation of energy that energy is lost, but another thing to answer the question, against what force are we doing the work?

Then he says:

this problem has never been solved.

Has this problem been solved since?

  • $\begingroup$ Quantum revolution: Qed: the jewel of physics, Volume 2 $\endgroup$ – Jimmy360 May 6 '15 at 11:51
  • $\begingroup$ the link is broken $\endgroup$ – nir May 6 '15 at 11:52
  • $\begingroup$ I edited it. There is some information on the subject there. Just do ctrl + F, then type in "Against what force are we doing work when we accelerate an electron?" $\endgroup$ – Jimmy360 May 6 '15 at 11:56
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    $\begingroup$ @CuriousOne, please don't patronize me; from my experience 9 out of 10 books are a waste of time so just sending one to the library doesn't seem helpful. also I humbly disagree with your opinion on feynman's lectures. $\endgroup$ – nir May 6 '15 at 14:27
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    $\begingroup$ @curiousone: the Force might be fictitious - but it's still useful. $\endgroup$ – Mozibur Ullah May 6 '15 at 18:22

Has this problem been solved since?

Not in the sense Feynman meant.

Approximate way to describe action of one charged part of body on another is known since Lorentz - the so-called Lorentz-Abraham-Dirac term.

What Feynman is getting at is this term works somewhat, but leads to contradictions when pushed to its consequences.

The problem of self-action of charged sphere on itself was not completely solved, because it involves modelling charged sphere in a way consistent with theory of relativity. Since in theory of relativity the sphere cannot be rigid but has internal degrees of freedom, the model gets very complicated very soon.

There are only approximate theories of charged sphere, search the works of Arthur Yaghjian and Rodrigo Medina.

Feynman and others thought there should be similar self-action term even for point particles, but this is not necessary.

Consistent theories of charged point particles were described many times long time ago, e.g. by Frenkel:

J. Frenkel, Zur Elektrodynamik punktfoermiger Elektronen, Zeits. f. Phys., 32, (1925), p. 518-534. http://dx.doi.org/10.1007/BF01331692

In English, this article also explains it concisely:

R. C. Stabler, A Possible Modification of Classical Electrodynamics, Physics Let- ters, 8, 3, (1964), p. 185-187. http://dx.doi.org/10.1016/S0031-9163(64)91989-4

There is no self-action in this kind of theory.

  • $\begingroup$ According to Google scholar the paper by stabler was cited 3 times since 1964; is this correct? why was it ignored? $\endgroup$ – nir May 6 '15 at 20:01
  • $\begingroup$ The paper is fine I think. I do not have any other information about the number of citations, but I expect it to be low. The theory these papers (and others, there were many more published with the same main idea) propose is very different from what one learns in the established textbooks. It solves the old problems but beyond that to derive further consequences from it requires quite hard calculations (numerical simulations for many-particle system with retarded interactions). $\endgroup$ – Ján Lalinský May 6 '15 at 20:23
  • $\begingroup$ Also, the paper is about non-quantum theory, which largely explains why it was ignored. Lots of good ideas get marginalized and forgotten. $\endgroup$ – Ján Lalinský May 6 '15 at 22:34

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