History shows us that classical EM with its ubiquitous fields could not solve for the motions of the electron inside the atom; perhaps more accurately, no solution could be found. In the hope of finding a way forward to very similar and related problems involving the discrete nature of various physical phenomena, Max Planck blackbody radiation and Albert Einstein photoelectric effect put forward a hypothesis of discrete radiation. The course of the next few decades saw the development of quantum mechanics. In 1926, Wolfgang Pauli used 'matrix mechanics' to solve for the spectrum of the hydrogen atom.

If one looks inside a text in an academic library concerning this important historical scientific turning point, an index listing will not be found for the magnetic, or cyclotron motion due to charged subatomic particles, even though such cyclotron effects were well known. The problem was always posed only in terms of the electric, or orbital motion due to charged subatomic particles. It was indeed this failure to see the coupled solution consisting of both an orbital AND a cyclotron motion, two orthogonal motions, that the EM path remained unsolved prior to 1926 and after. It has taken around 100 years to discover the EM self-field solution. Fortunately this failure led to the discovery of QFT. However, the fact remains that the much simpler approach of EMSFT based on pde's and not integro-differential equations offering a broad vision of unification across physics has remained hidden for the entire 20th century.

One interesting line of research now becomes apparent. There must be a form of potential theory that matches the pde approach of EMSFT. The standard model is an experimentally founded theory based entirely on the potential theory of the inhomogeneous wave equations. Yet this basis in potential theory, rather than the direct usage of Maxwell's equations, induces renormalization problems. We find with the vector and scalar potentials have reduced the overall number of equations to solve but we have introduced integrands into our formulation, i.e. integro-differential equations. Such a potential solution analogous to EMSFT must exist.

On the other hand if we approach our problem as if solving finite difference equations, a la numerical solutions, the headaches associated with integrands at singular points do not arise; we can solve the equations at hand to give us an analytic solution, the self-fields, We seek a special periodic solution, one that comes back to a point in space-time and is therefore a self-perpetuating motion. This is how we soive for the hydrogen atom via EMSFT

If the photon solutions obtained from EMSFT-photon chemistry-in exactly the same way as the spectrum of the hydrogen atom can be made to fit the W+, W-, and Z0, and gluon experiments, then we're really looking at a second method apart from quantum field theory that fits the facts but without the renormalization. This is akin to the similarities and differences in the two numerical methods of finite differences (FDM) and finite elements (FEM). The FEM has its variational methods based on energy densities applied over a mesh of small volume elements with boundary conditions inserted in the form of integrands, while FDM has its many points at which boundary conditions are applied as Dirichlet, Neumman, or radiation conditions. So there exist two different maths, and different, but maybe not dissimilar analytic solutions.