Yubal M said:
... I don't get why the fields can't stand still and alternate at the same point. ...
I'm not an expert like your earlier respondants, so don't rely on my ideas, but I don't understand why you say this. At least in the context of radio waves, which is what springs to my mind when someone says "electromagnetic waves", you can.
If I stand still near an oscillating tuned circuit, then I can "see" (or detect, measure, observe on an oscilloscope, etc) an alternating electric field and an alternating magnetic field. The fields oscillate at a fixed point - indeed, at any fixed point, though their strength will be lower, the further away from the source I am.
If by some magic power I were able to travel along with the radiating radio wave at the speed of light, then I think I would not observe any oscillation in the fields at all! I would see constant phase, though monotonically diminishing amplitude..If there is a constant current flowing in a wire near me, I expect to observe a constant magnetic field at my position. I also expect everyone else to observe the same constant magnetic field at their position - weaker if they are further away, stronger if they are nearer. Similarly if there is an electrically charged object.
If that current now varies periodically, as I first said, I expect to observe a varying field. And I expect everyone else to now observe a varying field.
So is your thought that they should not observe this varying field? That only I at some special position can observe it, but nowhere else can it be observed?
Or is your question more subtle, about why they can't observe the variations at the same time as I do,? Is the problem not that they see the same field as I do, but that they apparently see it later than I depending on how much further away they are?
So could you clarify a bit, what you mean by a field "standing still"? And perhaps whether you consider non-oscillating fields to be moving or standing still.Although I can't really imagine the situation you speak of, if we did have an oscillating magnetic field in some fixed region and nowhere else, would that not give rise to an electric field, just as a changing magnetic field causes an emf in a wire? And since a wire loop could be anywhere where the magnetic field passes through the closed surface defined by the wire, would not that electric field have to exist, if not everywhere, at least in places going away to an indefinite distance? So even if the oscillating field could be trapped, the electric field would inevitably escape.
And I think maybe there is a similar argument for the electric field letting a magnetic field escape (though I don't understand that one, even in my naive way!).