How to (Not) Create a Model of (Atom) Physics

The classical method to formulate a mathematical model of some physical phenomena used since ancient time through the 19th century is to combine a set of laws of physics describing some real (or imagined) physical reality. And then use the model to find consequences of the laws of physics and learn about the World.

A prime success example is Newton's model of a system of bodies interacting by Newton's Law of gravitational attraction. Another is Maxwell's equations expressing the Laws of Ampere, Faraday, Gauss and Coulomb.  Both models capture a very wide range of physics. 

In 1913 Bohr together with Rutherford formulated a model for the Hydrogen atom as an electron orbiting a kernel in the spirit of a Newtonian planetary system. But the model was not satisfactory since it ad hoc postulated that only certain electron orbits were allowed without convincing physical rationale. In addition it could not explain why an atom in ground state was stable. In short the model contained ad hoc elements without physics and did not fit with the observation of stable atoms without radiation. 

In 1925 Schrödinger formulated a new model for the Hydrogen atom as an electronic charge density attracted by a kernel according to Coulomb's Law. The model was greeted as an enormous success because it could explain both the stability of ground state and radiation spectrum. The model did not contain any ad hoc non-physics. 

Schrödinger's Hydrogen model opened the new era of atom physics, but the generalisation to atoms with more than one electron was not at all obvious, and so Schrödinger resorted to a formal generalisation into an equation in formal configuration space without physical meaning. This was another ad hoc model formed by a purely formal mathematical procedure without physics, but lacking any alternative it became Schrödinger's equation (S) as the foundation of quantum mechanics of atoms. 

But since (S) was not formed from a physical law, only from mathematical formality, the tasks to give solutions to (S) a physical meaning remained. But that showed to be far from easy troubling the minds of physicists for 100 years until it was agreed that this was not necessary: It was enough to "Shut up and calculate" and not ask about any physical meaning. 

RealQM offers a new atomic model based on laws of physics. This brings atom physics into the classical methodology of forming mathematical models of physics from laws of physics, not from formalities without physical meaning. 

A mathematical model based on laws of physics can say something about physics. This is Wigner's

•  Unreasonable Effectiveness of Mathematics in the Natural Sciences.

which should rather read: 

• Reasonable Effectiveness of Computational Mathematics in the Natural Sciences. 

It is further unreasonable to expect that a mathematical model based on ad hoc laws without physics, can say something about physics.