Unified Field Theory: Newton + Maxwell + RealQM

Schrödinger created Quantum Mechanics by formulating in 1926 a mathematical model within classical continuum mechanics in terms of a wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ satisfying a wave equation named Schrödinger's Equation SE: 

• $i\frac{\partial\psi}{\partial t}+H\psi =0$     (SE)

with 

• $H=-\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$ a Hamiltonian differential operator.

The eigenvalues of SE showed to exactly fit with the observed spectrum of a Hydrogen atom and so was the answer to a search begun by Bohr 15 years before. The success was complete: SE revealed the secret of the Hydrogen atom as an eigenvalue problem for a Hamiltonian with time-independent normalised real-valued eigenfunctions $\Psi (x)$ with energies as sum of kinetic and potential energies appearing as eigenvalues:

• $E = E_{kin}+E_{pot}=\frac{1}{2}\int\vert\nabla\Psi\vert^2dx-\int\frac{\Psi^2(x)}{\vert x\vert}dx.$ 

The ground state of a Hydrogen atom took the physical form of a charge density $\Psi^2(x)$ with minimal energy appearing as a compromise of negative $E_{pot}$ by concentration near $x=0$ balanced by a positive $E_{kin}=-\frac{1}{2}E_{pot}$ appearing as a form of "compression energy".

SE took the form of classical continuum mechanics with a clear physical interpretation as charge density and so represented a complete success of classical mathematical physics suddenly expanding its excellent service from macroscopics into atomic microscopics. 

SE combines perfectly with Newtonian gravitation giving $\Psi^2(x)$ a double role as both charge density and mass density, as well as with Maxwell's electro-magnetics. The resulting Newton-Maxwell Schrödinger NMS model was a Unified-Field-Theory covering all of Hydrogen physics from galactic to atomic scales. A tremendous success of mathematical modelling of real physics! Since Hydrogen accounts for 74% of the mass of the Universe NMS captured nearly everything.

But 25% is Helium and 1% all the other atoms, and so SE had to be extended to atoms with more than one electron like Helium with two electrons to qualify as UFT. But how?

A quick formal resolution lay on the table: Give each new electron a whole set of 3d coordinates and trivially extend (SE) to any atom with a stroke of a pen. That gave a wave function depending on $3N$ space coordinates for an atom $N$ electrons. Easy to do but without clear physical meaning. 

Schrödinger refused to take this step, but Bohr-Born-Heisenberg jumped on the band wagon of Standard Quantum Mechanics StdQM based on a multi-d Schrödinger equation forming the foundation of modern physics under heavy protests from Schrödinger because it replaced causality and physicality by non-physical probabilities of observer measurement outcomes. 

In short StdQM is viewed to be the result of a process of quantisation preventing unification with the classical continuum physics of Newton and Maxwell, which has grown out into the deep crisis of modern physics of today.

Since Maxwell and Newton represent perfect theories, without any need of quantification, the natural idea to form a UFT is to search for a form of QM without quantification. But this has been prevented for 100 years by the very strong domination of the Copenhagen Interpretation of Bohr-Born-Heisenberg. Efforts have been made of  "dequantisation" of StdQM bringing it back to classic continuum physics (e g Bohmian mechanics), but without success because quantification cannot be reversed. 

RealQM offers a generalisation of SE for Hydrogen to atoms with more than one electrons, which stays within the realm of classical continuum physics, and so combines perfectly with Newton and Maxwell into a UFT.