There are lots of posts about EM wave model of photons, but I haven't read one that covers the more specific question I am focusing on here.
Here How does energy transfer between B and E in an EM standing wave? david was concerned about the presence of a zero $E$ & $B$ field point in the wave, close, but that is not my concern.
An electromagnetic waves is propagated by the oscillations of the electric and magnetic fields. A changing electric field produces a changing magnetic field and a changing magnetic field produces a changing electric field. An electromagnetic wave is self propagating and does not need a medium to travel through.
But I can't overcome the idea that in order to achieve propagation an $\dot E$ or $\dot B$ in one place must be capable of inducing a $\dot B$ or $\dot E$ in a different place.
How do we understand a change in position to occur?
In Maxwells Vacuum Equations (such as $\nabla \times E = -\dot B$ ) does not curl E result in a vector located in the same place as E, suggesting that it is only at that point a B field may be induced?
We know that two different EM waves interfere, rather than interacting - yet propagation seems to require that a decaying EM wave at one point interacts with and generates more of itself, that is, an EM wave at another point. Something's missing from the picture.
The rest of the post is just a list of dead ends I considered.
2) If a $\dot E$ resulted in a distant $\dot B$ (or vice versa), energy would need to be carried between the locations. I suppose this might be by a propagating EM wave. However I am trying to understand a propagating EM wave in the first place, and it is difficult (although not impossible) to work with a recursive or circular explaination.
3) if constant speed is assumed one can easily turn a time dependent wave equation to a (space) spatially dependent one. However, what I'm looking for is a mechanism from which to derrive or at least justify propagation, and the assumption of any speed essentially skips over that step.
4) Matter waves, such as on a string exhibit a clear coupling in the form of tension along the string. Although as they are a fundamentally different kind of wave looking for something very similar to that may be flawed. Is there some conceptual aspect of field waves I've managed to miss or forget, I wonder?
5) Maybe I got it backwards, and photon propagation is the evidence of E to B induction over a distance/ I haven't got very far with that line of reasoning
6) Special relativity "explains" magnetic fields as the relativistic effect of charge motion. I always felt this was one of the greatest insights, so I started to wonder if there is any way to make use of it to develop an argument for motion of energy in an E field. Must be googling the wrong keywords though.
7) Another approach is to imagine that $\dot E$ is equivalent to the motion of a charge, and then try to think about the B-field that moving charge would induce. However E fields being present omnidirectionally around the charge seems to make this impossible.