I ask this question again in a simpler, shorter form.
Maxwell's equations can be derived with Special relativity starting from the Coulomb's law. Therefore all the phenomena of classical electrodynamics can, in principle, be explained by relativistic considerations.
A simple example of the kind of explanation I am looking for: Why does the electric field of a moving particle look like the field of a stationary particle but ''flattened'' in the direction of velocity? Answer: Because by special relativity the field lines of the stationary charge can be imagined to experience a Lorentz contraction when view from a moving frame.
Now, a more challenging question is to explain radiation with relativistic arguments. This has partly been answered in multiple topics here (see this , or this one), at least in the case of instantaneous impulse and acceleration, accompanied by some pretty pictures. However, these post fail to explain, in relativistic terms, why the field lines behave in such a peculiar way at the radiation front. I think "Hey guys, the boss is moving, readjust" could be elaborated further. ''Hey guys, the boss is accelerating, how the hell should we readjust?''
What exactly happens when the charged particle accelerates, and, after acceleration, why the radiation front behaves in such a peculiar manner, continuing to distort more and more the further it propagates. Here is a nice applet for studying the phenomenon: Field of a moving particle. And here is a snapshot from that applet where the particle has been moving, has decelerated, and is now stationary: . Note the weird shape of the field lines in the region where the news ''boss is moving'' is received.
I'm looking for a heuristic explanation by Special Relativity. There has to be one, since the Maxwell's equations can be derived by Special relativity and Coulomb's law. If it make's things easier, change the particle to an infinite charged wall. It will radiate in a more simple manner.
This is the best I can do, but I must resort to General relativity: Say a charged wall starts to accelerate parallel to itself. It will ''think it is in a gravitational field'', and thus will see the field lines curve, since gravity is bending of spacetime. As soon as it stops accelerating it must see the field lines going straight again. But the news about interval of acceleration will continue to ripple further in space, as a warp in space time. Something wrong with this argument? Can you come up with better?
Please help me, I'd be extremely grateful. If you do not understand please ask me and I will do my best to clarify. Thank you.