I recently reviewed Mills' book on Amazon. (revised 3/27)
A Transformational Scientific Monograph Describing A New Theory of Nature
This work is a highly-technical scientific monograph that marches through calculations with minimal exposition, but it may represent a landmark in the history of knowledge. It is the result of 25 years of work, during which it has been expanded and republished many times, growing from a slim volume in 1990 to well over two thousand pages. The reader should approach it as an encyclopedia of solutions rather than a cover-to-cover read; rather like Newton's Principia.
In the early twentieth century, physicists struggled to understand the nature of the atom. If the electron were, as the Bohr model suggested, a point, orbiting the proton like a planet orbits the sun, then according to the laws of electrodynamics the electron ought to radiate energy and spiral into the nucleus within a fraction of a second. When quantum theory came along in 1924, it was unanimously seen as an end to the pursuit of a "classical" theory of the behavior of the electron, but many of its problems were merely swept under the rug.
Following quantum theory, very little work was done on the nature of the classical electron. Most important was the discovery that whereas point-particles must radiate while accelerating, extended distributions (membranes) of charge may accelerate without radiating under some conditions. In 1964, a general condition was proposed by George Goedecke. Later, Herman Haus at MIT re-derived this condition, apparently unaware of Goedecke's work. Although the Goedecke-Haus condition held the promise of revitalizing classical electron models, it was relatively unknown.
Randell Mills was a medical student at Harvard in the 1980's and primarily interested in inventing medical technology. He took a year of graduate courses at MIT under Herman Haus, and later realized the importance of Haus's discovery. Mills continued where the early atomic theorists left off, proposing a new, extended electron model that (unlike the Bohr model) could remain stable and could absorb and emit light in a straightforward manner.
Mills's solution (described in Volume 1 of this work) is a spherical shell of charge completely surrounding the nucleus, with complex superconducting currents on its surface. It is the foundation from which Mills rebuilds quantum theory from the ground up, starting first with the hydrogen atom and its properties, then multi-electron atoms, then molecules. It is noteworthy that Mills' theory produces calculations for many well-known experimental parameters that quantum theory has been historically poor at calculating, such as the excited states of helium, the state lifetimes and line intensities of the hydrogen excited states; the ionization energies of all atoms and ions for the first twenty atoms in the periodic table, and so forth.
Mills's theory succeeds because the interactions between electrons boil down to simple force-balance equations that are easily solvable and match experiment to very high accuracy. By contrast, even the simplest systems described by quantum theory produce absurdly complex equations that are virtually unsolvable.
This work is not for beginners, and my advice is to grasp the forest before you grasp the trees. Begin with my highly-accessible introduction, Randell Mills and the Search for Hydrino Energy, then page through Mills's entire monograph before attempting to walk through the math in any particular subject.
Despite the profound nature of Mills's proposal, there has been very little discussion of this text in the scientific community. It is unfair to assume that this is a rejection of his work. In fact, there are enormous biases in the physics community; I have found it almost impossible to get quantum theoreticians to look at it. Such a major revision to knowledge often comes with profound psychological, sociological, and language barriers.
Among all of this work, Mills makes perhaps the most important new prediction of his new theory, that a mechanism may exist that allows the electron in a hydrogen atom to resonantly give energy to a catalyst and drop to fractional-integer electron orbit, with a subsequent release of high-energy continuum light. Mills has backed up this prediction with decades of experimental research.
Of course, the rabbit hole continues to run deeper. Mills theory allows the calculation of the masses of fundamental particles with a new model, and proposes a small modification to the Schwartzchild Metric that revises Einstein's theory of gravity on a quantum scale. All of this may represent, at long last, a unified theory of physics - not a single equation, but a constellation of laws that are internally consistent and explain all known physical phenomena.
In Volume 3, Mills walks through his particle theory, as well as cosmological ramifications; A 1995 edition of this book predicted an oscillating universe, and thus that our universe should be accelerating in its expansion - discovered in 1997 by astrophysicists. Mills's theory that matter-to-energy conversion produces spacetime expansion and contraction is the only convincing mechanism I have ever seen.
Finally, almost as an afterthought, Mills explains those paradigmatic quantum puzzles such as the double-slit experiments and entanglement experiments. After nearly a century of arguing over the meaning of quantum mechanics, it is refreshing to see simple, clear, and enlightened resolutions to these vexing problems, and to realize that all the confusion over the quantum world was really the artifice of a bad theory. Quantum mechanics was never really understood, never any good at making calculations, and it led us to toss out nearly every philosophical supposition of our modern, scientific enlightenment.
Can we believe that new ideas can change the world? Can we believe that almost our entire apparatus of physical theory can be refreshed and replaced by essentially one man? Society has been shaken by such individuals before.
History will be the judge of Mills's work, but history starts now.