HYDROGEN ATOM - ORIGINS OF QUANTUM THEORY

This article is a summary of the early history of quantum theory. It is a perspective of the beginnings of quantum theory as seen from the vantage point of Self-Field Theory (SFT). Before the new 20th century had reached the end of its first decade there arose a wide objective within science  to obtain a mathematics capable of giving accurate predictions of the quantum shifts of energy that were being measured using spectroscopic methods that were looking at the hydrogen atom since it was the simplest atom of all. Although the following precis of this effort shows the errors that were made and those that are still there, it is a story of triumph of the human intelligence and spirit in obtaining insight into the newly emerging atomic domain.

As all of us involved in present-day physics know, the hydrogen atom has  been solved since 1927 using the quantum theory (QT) that emerged after Planck in 1899 and Einstein in 1905 discovered experimental proof for the existence of the photon. Their concept from their experiments was of a regular particle that was discrete and could be physically counted.  They felt  this photon could be restricted in  space and time to a localized region in which the particle existed. In the subsequent years, after QT developed into a quantum field theory (QFT) the concept of the modern enigmatic photon emerged somewhat different to that envisaged by Planck and Einstein. It was found theoretically using the mathematics of QT that the photon could not be confined to a local region in space and time. This set up a historic and crucial debate within physics about the issue with Planck and Einstein on one side and Bohr, Heisenberg, and others on the other. For a history of the birth of quantum mechanics see the paper by Luca Nanni.

In his annus mirabilis (1905) Einstein had also pointed to an asymmetry in electrodynamics.  As a result any motions  from Maxwell’s theory were probably not fully trusted at that time. Bohr’s theory of the hydrogen atom had provided some correct frequencies using only the electric fields and currents within the atom modeled as two point charges, the electron and the proton. In reality and in hindsight the reason for the difficulty at this stage was due to the way the fields were being measured (see A Major Revision in Mathematical Physics).

Thus it was considered that the only way to solve the hydrogen atom at that early stage was via the Sturm Liouville (SL) eigenvalue theory.  The experimental value for Planck’s constant that Planck had determined in 1899 was simply substituted into this SL theory. (Note: It is important to realize that Planck’s constant did not belong with the SL theory from the start but was simply inserted into the preexisting SL theory - this is in stark contrast to SFT where Planck's constant comes about from the formulation using Maxwell's equations ab initio).  It is here the QT solution became probabilistic rather than deterministic as is the conventional case for solutions to differential equations including SFT.  At this point some solutions were found to be singular; but using probability densities gave solutions that were generally stable and found to be accurate; it was later thought by Feynman and many others that ‘atoms in reality work that way'.  Again in (mathematical) reality probabilities were needed due to the way the fields were being measured. The mathematics of solving over-constrained problems is discussed elsewhere (Arrivederci Uncertainty).

Seeking to match the number of unknowns with the number of equations the then unknown error ( the way the fields were being measured) was compounded by trying to solve both Maxwell’s equations and the equations of QT  by ignoring the magnetic fields and currents of each particle in the same way as the electric fields had been examined by Bohr in his model of the hydrogen atom but not the magnetic currents. An examination of the index of books on quantum theory at that time or even the present-day have no listing concerning magnetic field, magnetic current, etc. So Einstein was correct when he said quantum theory was incomplete. Only one scientist actually attempted to use both the electric and magnetic currents within quantum theory Herbert Fröhlich.

In hindsight knowing how SFT handled the hydrogen atom in 2005 we see there were two problems: (1) the fields were being measured incorrectly (2)  the magnetic currents of particles were omitted in the formulations (both by Bohr and in quantum mechanics).

After a while magnetic spin was added to the Hamiltonian for hydrogen atom and the lack of magnetic fields and currents in applications to EM and quantum theory was forgotten and ignored, along with the incorrect metric (see A Major Revision in Mathematical Physics). Within some of the halls of academia today, this whole story about the origins of quantum theory is treated by assuming Heisenberg and Bohr were 100% correct. The complete solution was found using SFT in 2005. Now the solution is no longer probabilistic but deterministic; there is no need for the Copenhagen or many-worlds, or other unworldly interpretations, only a straight-forward solution method.

The ‘weird’ quantum world supposedly ‘observed’ at the atomic level can finally be seen as nothing more than numerical error due to the incomplete theory on which the atomic solution was based. This is now obvious to those of us who use numerical methods and have experience of the way truncation errors, modeling errors etc due to finite element or finite difference methods appear as numerical noise in the overall solution. All these negative insights about quantum theory are more than outweighed by the positive effects that the evolution of computational methods across physics brought to science as a whole

Now once again the photon can be viewed as Bohr and Einstein originally envisaged it: as a localized particle, more correctly a composite particle consisting of many particles that move creating waves both inside the photon and outside. But this new mathematics is an insight into a new world of fields and particles. Particles can now be viewed as dynamic interactions between many internal particles. The concept of an infinite fractal emerges within the photon. The self-fields of particles can now be examined much more clearly by science; this appears to be a new analytic avenue for particle physicists to use in their hunt for new understanding at the nuclear level and beyond. Using this new insight into fields and particles new technologies may emerge including microscopy, telescopy and the development of medicinal drugs with reduced side-effects.