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

AI Thread Summary
The discussion highlights unresolved issues in classical electrodynamics, particularly concerning the Abraham–Lorentz force and its relation to point-like particles. It suggests that these difficulties primarily arise from the assumption of exact point charges, while continuous charge densities may not exhibit the same problems. Participants agree that the notion of point-like particles leans towards quantum mechanics, questioning the validity of classical electrodynamics in this context. The consensus points to the non-existence of classical point particles as a significant factor in these inconsistencies. Overall, the conversation emphasizes the limitations of classical theories when applied to fundamental particle behavior.
greypilgrim
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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?
 
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greypilgrim said:
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.

greypilgrim said:
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.
 
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