Unified Field Theory of Matter + Light Without Quantum

The unfinished revolution of modern physics as quantum physics is unification with classical continuum physics expressed as Newton-Maxwell differential equations in terms of gravitational and electromagnetic fields as functions of 3d space coordinates and a time coordinate as real numbers forming a space-time continuum without smallest scale. 

Classical physics describes a macroscopic world of matter separated from a microscopic world of light as a Newton-Maxwell deterministic Field Theory covering a change of scale of $10^{35}$ from gravitation on billions of light-years down to nanometers of visible light. 

This seemed to be the end of physics, but with the start of the 20th century of modernity a discovered new world of atoms required something new beyond Newton-Maxwell. In 1915 Danish physicist Niels Bohr presented a model of the electron of the Hydrogen atom with energies restricted to the observed discrete spectrum of Hydrogen as a form quantisation, however without convincing physics.    

In 1926 Austrian physicist Erwin Schrödinger presented a model of the Hydrogen atom as an eigenvalue problem of classical form with the eigenvalues representing energies exactly corresponding to the observed spectrum of Hydrogen. This saved classical Field Theory in the case of only one electron, but the world of atoms with more than one electron remained to be modeled to maintain credibility of the new atomic physics.  

This is where history of physics took a turn which became the leading principle of modern physics through the 20th century into our time as a break with classical deterministic physics in 3 space dimensions into a new form of probabilistic physics in $3N$ space dimensions for an atom with $N>1$ electrons without clear physicality. This became the story of Standard Quantum Mechanics StdQM as the fundamental theory of modern physics. It came with the stroke of a pen by a purely formal extension by adding a new set of space variables for each new electron. An easy catch which however came with severe side effects of leaving classical deterministic continuum physics in 3d for a new world of probabilities instead of actualities. 

StdQM thus split physics into classical Newton-Maxwell continuum theory for macroscopic matter and microscopic light into new physics with main objective to describe the interaction between microscopic atoms and light. Physicists claimed to be forced to take this step by a Nature refusing to be described within classical continuum physics, in a heroic or rather desperate act of giving up classical ideals of rationality in the words of Max Planck, who took the first step in his 1900 analysis of blackbody radiation starting from a proclaimed ultra-violet catastrophe. 

To avoid catastrophe Planck introduced a concept of smallest quantum of energy $h\nu$ connected to light of frequency $\nu$ and $h$ a small constant, which was picked up by the young Einstein in 1905 in a "heuristic" explanation of the photoelectric effect returning to Newton's since long abandoned idea of light as a stream of light particles each carrying an energy $h\nu$. From these acts of desperation was then  StdQM born 20 years later as a Schrödinger equation in terms of a multi-d wave-function carrying probabilities of distributions of quanta of energy.   

So was modern physics as StdQM formed by modern physicists under the condition that blackbody radiation and the photoelectric effect cannot be explained within classical continuum physics.

If this condition would show to not be binding, then the premises for modern physics would change. RealQM offers an explanation of both blackbody radiation and the photoelectric effect which is based on a threshold condition on wave frequency $\nu$ as a condition on spatial resolution instead of any quanta of energy. RealQM thus offers a Unified Field Theory within classical continuum mechanics of matter+light over all scales, which was the unfinished dream of both Einstein and Schrödinger,   

PS. I checked with chatGPT what could have happened if blackbody radiation, photoelectric effect and atomic spectra had been resolved within classical continuum mechanics, as suggested by RealQM, and got this counterfactual answer:

• ✅ Yes: Up through ~1920, a clever deterministic continuum model could plausibly have “explained away” choseblackbody, photoelectric, and spectra. Physics might have developed as a wave-resonance continuum theory instead of quantum mechanics.
• ❌ But: Once Compton scattering and single-particle double-slit came in, the cracks would show. The particle-like momentum transfer and the self-interference of single quanta are incompatible with any local classical continuum.
• So your hunch is right: a classical deterministic continuum could have survived if physics stopped before Compton + double-slit. But with those experiments, and later Bell tests, the “classical-only” path would collapse.   

We see that modern physics was not really forced to follow the track chosen by Bohr-Born-Heisenberg under protests from Schrödinger...