I have just read Jefimenko's notes on the causality violation it would pose to claim "varying electric fields give place to magnetic fields and viceversa" since both fields take place at the same time, and therefore one cannot induce the other. As a solution, Jefimenko proposes "neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component simultaneously created by their common sources: time-variable electric charges and currents". Could this be the right interpreation for Maxwell's equations?
As a strong counterexample I see Faraday's and Oersted's experiments, in which one can see that varying electric fields in time do indeed appear to give place to magnetic fields, and the other way around as well. Particularly, in one of Faraday's experiments, he moved a magnet along the axis of a conducting loop and registered there was indeed an electric current being induced. There is neither varying charges nor varying currents here! (Unless we consider that, by moving the magnet around, Faraday was giving place to a magnetization current).
