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.

I’m 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. There is no radiation. You have just entered the Equivalence Principle Zone.

Whoa! Did you feel that? The pod thrusters are throttling back. The tension in the thread is tapering off. And look … 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. We’ve just been informed that we’re ascending at constant velocity in an elevator in the world’s tallest building. What gives? The charge is definitely radiating. Yet charges moving at a constant velocity don’t radiate, right?

Maybe there’s an exception to that rule. This building is so tall that the Earth’s gravity is measurably lessening as we ascend. So … 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. We’ll check that out when we return to street level.)

Good grief! The elevator cable broke! Ya-a-ah, we’re free falling. But look at that! The charge isn’t radiating after all. The tension in the thread has gone to zero. But now there’s a net force ---the force of gravity --- acting on the charge. And it’s varying in time, thanks to Earth’s 1/r² field. Why isn’t there any radiation?