Charged particle、neutral particle will hit the ground simultaneously？

[magnetar]

If we drop a charged particle and a neutral particle at the same time(same hight) in a uniform gravitaional field, they will hit the ground simultaneously?

on one hand：a freely falling charged particle will radiate according to a supported observer, so the radiation recoil (radiation damping) wil decelerate the charged particle,the neutral particle will hit ground first.

on the other hand : a freely falling charged particle will not radiate according to a freely falling observer,so the two particles will hit the ground simultaneously.

how to solve this paradox?

 

[WannabeNewton]

Well for starters, the back reaction on a charge involves the interaction of the charge with its own electromagnetic field so how could the charge be freely falling? In other words, a freely falling particle can only be under the influence of the "gravitational force" but the back reaction involves the Abraham-Lorentz force as well.

 

[Bill_K]

Same answer as for your previous thread, magnetar. The electromagnetic field surrounding a charged particle is extended. Although the particle itself falls freely in the gravitational field it sees locally, distant parts of it see a different gravitational field, in which they are not freely falling.

The charged object therefore does emit electromagnetic radiation. producing a back reaction and causing the charged object to fall more slowly than the neutral one.