Fig. 1 shows a charged pith ball, hanging from the ceiling on a silk thread. The charge on the ball remains constant in time. The net force on the ball is zero. The ball remains at rest. There is no radiation.
Charge at Rest in Gravitational Field
Iím sorry. We have just been informed that our "room" is actually a space pod in intergalactic space. There is no gravity. The pod thrusters are firing. There is a net, constant force acting on the ball. The ball is accelerating (along with us). There is no radiation. You have just entered the Equivalence Principle Zone.
How can it be that the ball isnít radiating? Didnít I just read somewhere that accelerating charges always rad-i-ate? But wait! There was also an article showing that charges subject to a constant force donít radiate, even though theyíre accelerating.
Whoa! Did you feel that? The pod thrusters are throttling back. The tension in the thread is tapering off. And look Ö the ball is now radiating! Well, that might make sense. The force on the ball is no longer constant.
Oh no! Now we really must apologize. Weíve just been informed that weíre ascending at constant velocity in an elevator in the worldís tallest building. What gives? The charge is definitely radiating. Yet charges moving at a constant velocity donít radiate, right?
Maybe thereís an exception to that rule. This building is so tall that the Earthís gravity is measurably lessening as we ascend. So Ö a charge moving from stronger to weaker gravity radiates, even when it does so at a constant velocity! (The same can no doubt be claimed when the charge moves from weaker to stronger gravity. Weíll check that out when we return to street level.)
Good grief! The elevator cable broke! Ya-a-ah, weíre free falling! But look at that! The charge isnít radiating after all. The tension in the thread has gone to zero. But now thereís a net force ---the force of gravity --- acting on the charge. And itís varying in time, thanks to Earthís 1/r2 field. Why isnít there any radiation?
But is there a force? Einstein says that gravity isnít a force after all. Itís a matter of warped space-time! I really must think about this. But Ö so little time. Better perhaps if you work it out.