But here is where it becomes very puzzling. Consider the following:
I have a charge sitting at some origin that I define. Now, at a distance r away, I can measure an electric field at that point. This is all simple electrostatics. How come you don't have an issue with this? After all, what is the origin of that field at that point, since technically, it requires NO medium for that field to exist? We have nothing oscillating here, no "wave" of any kind. You didn't ask about this, so I presume that you have no issue with such a thing.
But the question is, why not? You see, I can now take that charge, and then jiggle it up and down, and voila, I get your EM wave! No different than before other than, now, I have an oscillating E and B field, per Maxwell equation.
So how come you have a problem with the latter, but not the former?
Zz.