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

  • #1
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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  • #2
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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1. What are point-like particles in classical electrodynamics?

Point-like particles in classical electrodynamics refer to particles that are considered to have no spatial extent, meaning they are treated as mathematical points with no volume or size. This simplification allows for easier mathematical calculations and analysis of the particles' interactions within the framework of classical electrodynamics.

2. What are some common problems encountered when dealing with point-like particles in classical electrodynamics?

Some common problems include the divergence of the electromagnetic field at the location of the point-like particle, leading to infinite self-energy and infinite electromagnetic radiation. These issues arise due to the assumption of point-like particles, which do not have a finite size to contain the field.

3. How do physicists address the issues with point-like particles in classical electrodynamics?

Physicists often introduce regularization techniques to handle the divergences associated with point-like particles. By introducing cutoff parameters or modifying the equations to account for the finite size of particles, physicists can avoid infinite self-energy and radiation and obtain physically meaningful results in their calculations.

4. Can classical electrodynamics accurately describe the behavior of point-like particles?

Classical electrodynamics struggles to accurately describe the behavior of point-like particles due to the inherent issues with infinite self-energy and radiation. Quantum mechanics provides a more suitable framework for understanding the behavior of particles at the quantum level, where the concept of point-like particles is replaced by wave functions and probabilistic interpretations.

5. Are there any experimental observations that support the existence of point-like particles in classical electrodynamics?

While classical electrodynamics assumes point-like particles for theoretical simplicity, experimental observations at the quantum level reveal the particle-wave duality of matter. This duality suggests that particles do not behave as point-like entities but exhibit wave-like properties, challenging the classical notion of point-like particles in electrodynamics.

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