Alright, good, I figured this idea is going to take several posts to get at the heart of the idea.
The idea is that EM , the Maxwell Equations are equations like none other in physics and that there is a deep mystery as to why they stand apart.
If you study gravity and then study EM, you quickly realize that the Coulomb law is contained in just one of the Maxwell Equations and the Coulomb law is the mirror image of the law of gravity. So that gravity is just one of the Maxwell Equations, and that is the whole of gravity, while EM still has three more Maxwell Equations to contend with.
Now thermodynamics has more laws than just one, but only one of those laws is dynamics-- the 2nd law, and the others are definitions or conservation.
So the richness of the EM laws is very much more expansive than either gravity or thermodynamics and that neither gravity nor thermodynamics is rich enough to derive EM. And only EM is rich enough to derive gravity and thermodynamics.
But the mystery of EM richness does not stop with deriving other branches of physics. The richness is to be admired in that EM are the axioms over all of physics. And that is what I tried to fetch out in my first post.
What I mean is that given a section of the Cosmos, a volume of Space of the Universe and in that volume you create a Faraday law where you take a closed loop of wire and move a bar magnet into that closed loop, and the reaction you get is to create a current in the loop. And that current tries to restore itself back to where the magnet was not in motion. So in a deep sense, the Maxwell Equations are a attempt by the Universe to restore itself to the situation it was before the magnet moved.
There is a very famous statement by Faraday, where he says, "light is a disturbance in the electromagnetic field".
Well, we can say that Faraday's law or all the Maxwell Equations are a disturbance in a volume of Space, for which that Space wants to return to the same situation before the disturbance.
We cannot say that of gravity, that gravity is a disturbance of the Cosmos for which the force of gravity tries to return the Cosmos to the same situation before the force of gravity took place. But we can say that of the Faraday law or Ampere law that they disturbed the Cosmos and the Cosmos is returning the order it was before.
We cannot say that of thermodynamics, but unlike gravity, thermodynamics in the 2nd law says that the Cosmos cannot return to a order that it was before the disturbance.
So EM is very mysterious and very rich.
Now another facet of that richness is the fact that in EM, the laws require a circle, or circuit. In gravity we need no circuit. In thermodynamics we need no circuit. In Quantum Mechanics, we need no circuit. But in Maxwell Equations, a circuit is essential. The circuit is the interface of the disturbance.
This is what I meant in the first post about Space and the Maxwell Equations seem to be a slice into space which wants to return to the conditions before the Space was sliced.
For a branch of physics to be the axioms over all of physics, that branch has to be these characteristics:
1) the richest branch so as to derive all the other branches 2) equations which take a volume of Space and interact and where the end result is for that Space to return to the order it was before the interaction. This is important because the branch that does that is what the entire Universe represents. The Maxwell Equations are a disturbance in the Cosmos, and because the Cosmos is the Maxwell Equations, the experiment returns to the same order it had before the experiment. 3) No other equation in physics is beyond the domain of the Maxwell Equations. An easy test of this, is that the Maxwell Equations when summed up together yield a equation that has the Dirac equation as a subset equation.
I keep wanting to go to poetry to emphasize what I am saying. As a metaphor, if we take Space in general that contains matter and space combined, there is a set of equations that uniquely talks of circuits which spill out forces and currents, in order to put that Space back together and return it as was before. It is that set of equations which is not only a branch of physics, but is the Universe itself.
Now this discussion leads me into the curiosity of how and why a photon would pair up with an electron in the Faraday law to move it along the wire to be a current. How would a photon zip along the wire and come in contact with a electron, how would that photon communicate to the electron where to move and guide it along the way? Faraday saw the photon as a disturbance in the field, here we see the photon as the pilot or guiding wave for the electron. Now photons are very complex and rich particles because a single photon can break apart into a electron and positron.
Google's archives are top-heavy in hate-spew from search-engine- bombing. Only Drexel's Math Forum has done a excellent, simple and fair archiving of AP posts for the past 15 years as seen here: