Ironic that he confines his theory to classical EM. When a continuous band of charge goes around in a loop so that at all times there is the same amount of charge at any particular point, there is no radiation.
Ironic that he confines his theory to classical EM. When a continuous band of charge goes around in a loop so that at all times there is the same amount of charge at any particular point, there is no radiation.
This isn't true. For example, at the bending magnets in a particle accelerator there is a constant current of electrons moving through the bend but those electrons still radiate. From far away the charge density at the turn is constant, but the current density is not constant. You cannot eliminate current density by squinting - classically accelerating charge radiates.
If we have a classical scale beam of electrons released into a constant magnetic field it radiates as it moves in a circle, even if the instantaneous charge density at any point on the circle is constant. In fact, speaking purely classically, the current density is instantaneously constant at a given point on the circle but it still radiates because in order to maintain itself on a circular path the charge must accelerate, even if the speed stays the same.
Of course as the action of the system approaches hbar (as it must as the energy radiates away) the system begins to have quantized energy levels, as quantum mechanics correctly predicts.
Aren't you literally describing the conditions that create synchrotron radiation?
Discrete electrons accelerating radiate, but a single electron that is spread out around a spherical orbitsphere so that there is continuous charge flow in all great circle direction but no net movement of charge over time, does not.