|MadSci Network: Physics|
This question is posed quite often. But the `charge in free fall' paradox is only a paradox because the equivalence principle is usually not stated in its full, correct form. An accelerated reference frame is indistinguishable from a frame in a gravitational field only locally! If large extensions (like the Coulomb field of a point charge) are involved, there is no problem in detecting gravitation, because there is no such thing as a totally homogeneous graviational field. And that is why the freely falling charge will indeed radiate! (There is, of course, also the related question of why a charge at rest in a gravitational field should not radiate, and what happens if an observer accelerates and passes by a charge at rest. All theses so-called paradoxes rest on the mentioned misunderstanding.)
It is, of course, not a trivial task to establish this insight microscopically, i.e. by looking at the Poynting vector of the electromagnetic field in both reference frames. I am actually not sure whether it can be done at all - one would have to look at the Maxwell equations in gravitational fields. But that the charge will radiate is out of the question.
Hope that helps,
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