- #1

- 624

- 11

## Main Question or Discussion Point

Hello! Griffiths is deriving the Abraham-Lorentz formula, which calculates the force that the radiation puts on a charged, accelerating particle (i.e. the force that makes it harder to accelerate a charged particle than a neutral one). For the non-relativistic case, the formula is: $$F_{rad}=\frac{\mu_0 q^2}{6 \pi c}\dot{a}$$ He then mentions a paradox based on the fact that if the particle is subject to no external forces, based on Newton's second law you obtain: $$F_{rad}=\frac{\mu_0 q^2}{6 \pi c}\dot{a}=ma$$ and if you solve for ##a##, you obtain that the acceleration increases spontaneously with time (then he talks about certain attempts to solve this issue). I am a bit confused about what is the actual issue. If I understand the formula well, this ##F_{rad}## appears when you have a change in the acceleration. So it is the change in the acceleration that creates the force, not the force that creates the change in the acceleration. However, he assumes that you have no external forces, i.e. the particle moves at constant speed (or stands still). So with no external forces the acceleration would remain the same (which is zero). So the equation would reduce to $$F_{rad}=ma=0$$ He indeed mentions that if we ASSUME that the acceleration is zero we can avoid this problem (and have another one instead), but I am not sure why would we ASSUME it is zero. Isn't it obvious it is zero, as you have no external force, so nothing to change the acceleration? Thank you!