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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: [decelarating particle]. 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.

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AnssiM
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    "Maxwell's equations can be derived with Special relativity starting from the Coulomb's law." This is misleading. The laws of electromagnetism are much more general than special relativity and electrostatics can imply, they are inferred generalized from experience. You cannot derive validity of the Gauss law for general electric field just from special relativity and Coulomb's law.

     – Ján Lalinský Apr 30 '17 at 14:31
  • , this user is not active since 2015, I just want to stress : when looking at the consequences of a physics theoretical model, one has to understand that "laws" are distillates of observations and are axioms , necessary to choose from the general solutions of wave equations those that describe data and are predictive of new data. The law of induction , which the OP in a comment wants explained, cannot be explained it is a chosen axiom for the mathematical model used in deriving maxwell's equations. https://en.wikipedia.org/wiki/Maxwell%27s_equations#Formulation_in_Gaussian_units_convention – anna v Jul 08 '18 at 06:04
  • Special relativity is already a part of EM! Einstein merely (!) transported that symmetry into classical mechanics. – Mozibur Ullah Jul 08 '18 at 06:18
  • Related : Electric field associated with moving charge. – Frobenius Sep 14 '18 at 21:06
  • 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. I don't think this argument really works. Lorentz contraction holds for a physical object, and is expressed in comparison to the object's rest frame. An electric field is not a physical object, and it doesn't necessarily have a rest frame, although there may be a frame where $B=0$. –  Nov 21 '18 at 01:58

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However, these post fail to explain, in relativistic terms, why the field lines behave in such a peculiar way at the radiation front.

This is just Gauss's law. Gauss's law says that field lines only begin and end on charges. Since there are no charges at the radiation front, the field lines can't begin or end there; they have to connect up.

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Let's study this animation

Let's say everything there happens in a large pool of water.

Let's especially look at the area left to the charge, where field lines move apart from each other. Water molecules are oriented in a certain way, and as the field strength decreases the molecules turn in a certain way, which means the charges of the molecules accelerate in a certain way.

When one plus charge accelerates to the west, nearby plus charges tend to accelerate to the east. That is the phenomenon called induction, or at least the basic idea is that.

Why is there a twist on a field line? There are accelerating charges near that area where the twist is. Those accelerating charges induce an electric field in that area.

If we are interested about the mechanism of the induction phenomenon, that can also be seen in the animation.

So now I hope we have explained everything that is happening in the animation, which includes radiation, as there was a charge that accelerated.

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  • link of animation missing – anna v Dec 06 '15 at 15:00
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    @user7072 Thank you. But... induction is part of the phenomenon what I am asking to explain here. It also depends on understanding what happens when charges accelerate. Second, water molecules will turn the way they do BECAUSE the accelerated particle produces a certain electric field. I am therefore afraid this answer is circular. But, thank you anyway! – AnssiM Dec 07 '15 at 07:49
  • Maybe ask question: "how is induction explained by relativity". I might answer. The answer might be: "an accelerating field line points into such direction that there is an induction effect". OK, that's not a good answer, as I don't know how induction follows from relativity. – stuffu Dec 07 '15 at 15:24
  • @stuffu induction is an observational law, an axiom for electrodynamics – anna v Jul 08 '18 at 06:12