A charged particle fixed to a frame $S^\prime$ is accelerating w.r.t an inertial frame $S$. For an observer A in the $S$ frame, the charged particle is accelerating (being attached to frame $S^\prime$) and therefore, he observes it to radiate. However, for the non-inertial observer B standing on the non-inertial frame $S^\prime$, the charged particle is at rest, and therefore, does not radiate at all.
A infers that the charged particle radiates but B infers it doesn't. Can both inferences (mutually contradictory) be correct simultaneously? If yes, how?
Answer
First, I'll note that unless the non-inertial frame has a changing acceleration, there is some doubt as to whether it radiates at all. https://en.wikipedia.org/wiki/Paradox_of_a_charge_in_a_gravitational_field
Assuming there is changing acceleration, yes the particle radiates, and this can be observed in both frames. Seeing it radiate would be a way of determining that you are in fact in a non-inertial frame, assuming your inner-ear was not already telling you that.
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