Charged particle in free fall

[High Mass]

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.

 

[yuiop]

Your question may be related to the Unruh effect, where an observer accelerating in a vacuum detects radiation (and particles) that are not detectable by an inertial observer in the same vacuum. See http://en.wikipedia.org/wiki/Unruh_effect

 

[Entropia]

In this scenario, general relativity is not involved, as it is not necessary to explain the behavior of charged particles in free fall. The behavior can be explained using classical electromagnetism and the concept of an accelerated frame of reference.

1. From the frame of the lab technician, both charges will appear to radiate. This is because the lab technician is in an inertial frame and sees both charges accelerating, which will cause them to radiate. However, from the frame of either charge, no radiation will be observed because they are both in an equivalent accelerated frame and will not experience any radiation.

2. Energy conservation still holds in this scenario. The energy of the radiation emitted by the falling charge comes from its loss of gravitational potential energy. This does not affect its acceleration, as the electromagnetic force is much stronger than the gravitational force. As for the neutral particle, it will fall at the same rate as the charged particle because they are both in the same gravitational field.

3. The energy of radiation seen by a freely falling observer of the charge on the table also comes from the loss of gravitational potential energy of the charged particle. The observer's fall through an electric field may affect the rate at which they fall, but it does not change the fact that the charged particle is losing energy and thus emitting radiation.

4. If you run in a circle around the charge on the table, you will still see it radiate. This is because your acceleration around the charge will cause it to radiate, and the energy for this radiation still comes from the charge's loss of gravitational potential energy. Your neutral charge does not affect the radiation, as it is the acceleration of the charged particle that causes it to emit radiation. This scenario does not require a net charge on the observer.