Radiation from an accelerated charge as seen by an inertial vs an accelerated observer

Question

According to this answer Will accelerated observer see radiation from the charge that is at rest in observers's frame? an accelerated observer does not observe radiation from a charge at rest relative to him. But if we have a photodetector attached to a bomb, in an inertial system, the detector will perceive the charge as radiating, and the bomb will explode. How does the non-inertial observer explains the explosion if in his frame there is no radiation entering the detector?

Answer 1

The confusion comes from the fact that we only use words as inertial and non-inertial. In reality, we need to use co-moving too.

Now you are not saying it specifically, but you are talking about a inertial frame with a bomb and a photodetector on the bomb, and separately from this, you have a non-inertial frame, with an observer, and a charge, where the observer is co-moving with the charge.

Now in the accelerating frame, the observer is aware of the acceleration, because it is absolute. Speed is relative, but acceleration is absolute and the observer can detect that the frame of the observer is accelerating and co-moving with the charge.

The observer can detect too, that the frame of the observer is accelerating relative to the non-inertial frame of the bomb and the photodetector.

Thus, the observer, knowing the laws of physics, knows, that although the observer is co-moving with the charge, and thus cannot detect the radiation itself, but the observer knows too that according to the laws of physics, the charge is accelerating relative to the non-inertial frame of the bomb and the photodetector.

Thus, the observer knows that the photodetector could detect radiation. And thus the observer knows that the bomb could explode.

This is not a paradox contrary to popular belief. To see a a similar example, look at magnetic and electric fields. If you are co-moving with a charge, you will see the static electric field of the charge. If you are not co-moving with the charge, that is, you are moving relative to the charge, you will see this as a static magnetic field. From different frames, you can detect different kind of fields (actually the same EM field viewed from different frames).

Now similarly in your case, the co-moving observer only sees the static electric field of the charge, but the non-comoving photodetector and bomb, that is moving relative to the charge, the photodetector and bomb will see the charge as radiating EM waves. This is the same charge, same EM field, just viewed from different frames.

The paradox is resolved as follows: the number of photons changes when you switch between non-inertial frames. This is actually a remarkable fact and it holds also for quantum particles, which can be created in pairs of particles and antiparticles, and whose number depends on the frame of reference. Now, a step back. Forget about gravity for a moment, as it is irrelevant here (we are still in GR, though). Imagine a point charge, which is accelerating with respect to a flat empty space. If you switch to the rest frame of the charge, you observe a constant electric field. When you switch back to the inertial frame, you see the field changing with time at each point and carrying away radiation from the charge. In the presence of gravity the case is absolutely similar. To conclude, switching between non-inertial frames makes a static electric field variable and corresponds to a radiation flow.

Does a charged particle accelerating in a gravitational field radiate?