My old "classical" understanding of how electromagnetic waves propagates is this: varying electric field generates a varying magnetic filed which in turns generates a varying electric field .. and so on the wave will travel by it's own.
But when thinking about it from Special Relativity point of view this description does not fit for me!
For instance in special relativity the magnetic force is a consequence of length contraction as observed in a different frames of reference, so there will be only an electric field and no magnetic filed in the travelling wave frame of reference (is that correct?).
So how exactly EM waves travel in SR from an observer frame of reference? and from the travelling wave frame of reference?