I spend this Christmas, reading Simon Sings Big Bang. And as Simon pretty much says, I say as well, what a wonderful world.

I'm mentally affected by my education that I constantly ask myself if the things that is presented in a popularizing book is really what is true. Did he mean that. Sure people turn things int a better daylight when asked about it afterwords and so on. There is a constant flow on my mentally left margain. Anyhow I'm now really impressed by the puzzle that scientist made to achieve such a solid ground for the Big Bang theory.

There is always weak spots in an arguments but the core argument is really solid in my view.

I like the formulation that uses the potential formulation under the Lorenz gauge if I remember everything correctly. Then all components follow a wave equation and there is one linear first order constraints that look close to a simple continuity equations. Now I wanted to understand what this actually meant and searched for some example that would reveal that to me. And there is one telling partial solution. You could have a solution where you make the constraint a continuity equation. You will have a sort of "magnitude of disturbance field" in the scalar potential and the vector potential will be a sort of momentum potential e.g. the scalar potential times a velocity field of constant velocity c. It's a really trivial and very particular solution. But you can modify it. You can assume that if along a direction you have the same disturbance, then you can choose any velocity you like.

Now, in my view this captures some essential features of electromagnetism. A constant stream of light is not dependent of the speed of the stream and it is information that is constrained to the speed of light. Not necessary the actual physical or disturbance transport.

Note that if we have just one stream the transversal direction has to be transported with the speed of light and indicate plane waves.

Even if this is a simple particular solution. One would probably be able to deduce Maxwell's equations after closing the space using Lorenz transforms

Ok this is just a mathematical play, but it poses from my position of knowledge very interesting question. It's just some speculation from a guy that is not an expert. But I still hope that I've teased your imagination so please have fun, play with the mathematics, enjoy the stars and have a very happy hacking new year.