Preacceleration in radiation reaction solutions

[zlasner]

Hi,

I have been studying the radiation reaction problem and I see a weakness in the derivation that hopefully someone might illuminate for me. In the textbooks by Griffiths and Jackson, as well as some journal articles I have found, the radiation reaction seems to be "derived" by a suggestion from conservation of energy, and also derived more rigorously from the self-force of a charge distribution. When the charge distribution becomes smaller than a critical limit, we get "unphysical" behavior like preacceleration.

It seems to me that the reason preacceleration occurs is that the acceleration is required to be continuous when the radiation reaction is included in the equation of motion (ma = F + tau*a'). But in the derivations of the self-force, it most authors Taylor expand the velocity, which hides an ASSUMPTION that acceleration is continuous (so that it's differentiable).

I'm wondering if one can avoid the requirement that acceleration is continuous, and therefore avoid preacceleration solutions, by deriving the self-force without Taylor expanding velocity (and therefore without implicitly ASSUMING that acceleration is continuous).

Does anyone have thoughts about this, or references wherein this has been attempted?

Thanks :)

 

[Petr Mugver]

The problems here - the one you said about preacceleration but also others like runaway solutions or negative non-electromagnetic mass - arise from the fact that classical electromagnetism is a continuous-media theory, so it tends to fail when you try to use point-particles. Fortunately we have QM...

Anyway, try googling "Lorentz-Dirac equation". You can find old articles by Dirac on this topic. There is another article I read some time ago, I only remember one of the authors: Teitelboim.

 

[zlasner]

I'm not sure one should expect a continuous-media theory to give incorrect results when the limit is taken as the size of a distribution goes to zero. To me, that is analogous to saying that general relativity shouldn't give the correct results in the limit of flat spacetime because it is a curved-spacetime theory. Of course, as you mentioned, the truly correct theory to use here is QED, but I don't think the problems arise because there is anything wrong with taking a limit in an otherwise consistent, reasonable theory. (We do this all the time with other limits and other theories, after all.)

Thanks for those suggestions. I found something else that might address the problem of analyticity in the solution of the radiation reaction:

http://books.google.com/books?id=bZ...q=yaghjian lorentz&pg=PP1#v=onepage&q&f=false

I'm not sure yet whether its solution is satisfying to me, but I'll try to get hold of it and see.