Charged particle in free fall

I would appreciate any insight into these questions; I have had a little EM but no general relativity. Maybe general relativity is not involved at all - just EM with an observer in an accelerated frame.

1. Suppose we have two charged particles Q1 and Q2. Q1 is sitting on our lab table. Q2 falls off the table. Which one does the lab technician see radiate?

The answer seems to depend on the frame of the technician? If he is sitting in his lab, I think it's clear that he does not see radiation from Q1 (even though Q1 is in a frame that is equivalent to an accelerated frame since it is in a grav field but not falling). The falling charge Q2 should emit radiation (even though that is locally a noninertial frame). So is it correct to say neither charge radiates in the eyes of an observer in the frame of that charge, and both charges are seen to radiate from the frame of the other charge? (I asked a physicist this and he said someone wrote a paper in the 1960s on this that showed there is no paradox and that 'the falling charge radiates but does not know it radiates' - if anyone could expound on that, it would help. My comment above is just my trying to make sense out of his statement.)

2. If this is true then where does energy conservation work? Is the energy of radiation produced by the falling charge come from the loss of gravitational potential energy? And if so, does that mean it falls at a slower acceleration than a neutral particle?

3. But where does the energy of radiation seen by a freely falling observer of the charge on the table come from? I can keep falling all day but can the charge on the table just keeping radiating energy? Since its gravitational potential energy is not changing, I don't see how energy can be conserved. Unless my drop in grav pot energy is more over a given time (so smaller acceleration) to feed the energy that goes into the radiation. So do I fall slower if I fall through an electric field than through space free of an electric field?

4. What if I run in a circle around the charge on the table - will I see it radiate then? I think so, but again, where does the energy flow come from? Is it from a reactive force on me so that it is harder to run around a charge than to run around an empty table? This seems to require that I have net charge (or be able to interact with the radiation somehow, say dipoles). If I am truly a neutral object then I suppose the there is no way the charge can get energy from me to radiate but then I wouldn't be able to `see' the radiation even if it were there! I am not sure of the proper way to think about EM where the observer is in accelerated frame.

Last edited: