Problems in classical electrodynamics: Only for point-like particles?

[greypilgrim]

Hi.

I was surprised when I first read that there's quite a couple of unsolved problems in classical electrodynamics, such as the Abraham–Lorentz force. I have a couple of questions about that:

1. Do those difficulties only appear for exact point-like particles? Do they all vanish with continuous charge densities (even if they might be localized around a very small, yet finite, region in space)?
2. If yes: Isn't the assumption of point-like particles or also quantized charge already quantum, so why would we even expect classical electrodynamics to hold?

 

[Dale]

Do those difficulties only appear for exact point-like particles? Do they all vanish with continuous charge densities (even if they might be localized around a very small, yet finite, region in space)?

As far as I know, yes. All of the mathematical inconsistencies stem from classical point charges.

Isn't the assumption of point-like particles or also quantized charge already quantum, so why would we even expect classical electrodynamics to hold?

I agree. To me these issues speak more to the non-existence of classical point particles than anything else.