Mills asserts that his theory, which he terms "Classical Quantum Mechanics", unifies Maxwell's Equations, Newton's Laws, and Einstein's General and Special Relativity, and that it is founded on the principle that physical laws hold over all scales—from that of subatomic particles to that of the cosmos—thus overturning conventional quantum field theory. Mills first put forth his proposition of the hydrino in 1991 to explain the disputed reports of cold fusion experimentalists of excess heat in certain electrolytic cells.
Andreas Rathke of the European Space Agency has pointed out that the existence of a hydrino is unlikely in the environment proposed by Mills. A 2005 evaluation by Rathke, found "severe inconsistencies" in Mills' theory, including a lack of "solutions that predict the existence of hydrinos". Rathke also stated that Mills' equations were not Lorentz invariant, a requirement of any theory that explains the behavior of particles moving close to the speed of light.
Mills' company (BlackLight Power, Inc.) has raised over fifty million dollars in venture capital. It has also given rise to a subsidiary company (Millsian Inc.) which has developed and released a molecular modeling program based on Mills' models.
According to Mills, a specific chemical process he calls "The BlackLight Process" allows the bound electron to fall to an energy state below that of currently accepted quantum theory, at 1/integer that of the ground state radius. These below-ground hydrogen atoms are called 'hydrinos'. The mechanism consists of a non-radiative energy transfer between a hydrogen atom and a catalyst that is capable of absorbing a certain amount of energy. The total energy Mills says is released for hydrino transitions is large compared to the chemical burning of hydrogen but less than nuclear reactions. Mills reports that limitations on confinement and terrestrial conditions have prevented the achievement of hydrino states below 1/30, which would correspond to an energy release of approximately 15 keV per hydrogen atom.
In addition to the BlackLight Power website, Mills and his team have published papers in peer reviewed journals, reporting experimental results such as these:
Mills and collaborators say that only hydrino theory can adequately explain their results.
Šišović et al have reported line broadening that contradicts Mills's models.
[Mills] may be creating compounds with unusual properties. This is obviously a rather clever guy, and he may be onto something, but he seems to think it's more fundamental than it really is.
Furthermore, Osheroff remained certain that hydrinos were a "crackpot idea".
On October 27 2002, Bob Park, a professor at the University of Maryland, wrote a follow-up:
Mills has written a 1000 page tome, entitled The Grand Unified Theory of Classical Quantum Mechanics, that takes the reader all the way from hydrinos to antigravity (WN 9 May 97). Fortunately, Aaron Barth (not to be confused with Erik Baard, the Randy Mills apologist), has taken upon himself to look through it, checking for accuracy. Barth is a post doctoral researcher at the Harvard-Smithsonian Institute, and holds a PhD in Astronomy, 1998, from UC, Berkeley. What he found initially were mathematical blunders and unjustified assumptions. To his surprise, however, portions of the book seemed well organized. These, it now turns out, were lifted verbatim from various texts. This has been the object of a great deal of discussion from Mills's Hydrino Study Group. Mills seems not to understand what the fuss is all about.
We found that CQM is inconsistent and has several serious deficiencies. Amongst these are the failure to reproduce the energy levels of the excited states of the hydrogen atom, and the absence of Lorentz invariance. Most importantly, we found that CQM does not predict the existence of hydrino states!
Rathke's questioning of the compatibility of hydrino states with standard quantum mechanics is contested by other scientists, including those who do not accept Mills' broader theory. One such scientist is Jan Naudts of the University of Antwerp, a supporter of standard quantum theory rather than Mills' theory, whose paper nonetheless states:
A. Rathke has questioned the existence of [the hydrino], claiming that it is incompatible with standard quantum mechanics. All Rathke’s arguments relate to nonrelativistic quantum mechanics. The present paper discusses the problem in the context of relativistic quantum mechanics... The present paper shows that one can find arguments in favour of the hydrino state also in the standard theory of relativistic quantum mechanics.
In June, the subsidiary Molegos, Inc. was formed to market a molecular-modeling software application based on CQM theory. In October 2006, Molegos was renamed to Millsian. On June 14, 2007, Millsian made the beta-version of their molecular modeling software available for download.
In 2007, Edmund Storms, a cold fusion researcher, said that the hydrino model provides a possible explanation to cold fusion. Another scientist disputing Rathke's analysis, Ronald C. Bourgoin, of the Edgecombe Community College, published a peer-reviewed paper in the journal Advanced Studies in Theoretical Physics, not only supporting the theoretical possibility of hydrino states, but further stating that the general wave equation of quantum mechanics predicts the very same reciprocal energy states as does Mills' theory.
In March and April 2008, Blacklight Power had four UK patent applications relating to models and apparatus based on hydrino theory refused by the UK Intellectual Property Office, partly on the grounds that the hydrino theory was objectively wrong.
In a press release issued May 28, 2008, BlackLight Power, Inc. said that they have developed a prototype power system generating 50,000 watts of thermal power on demand.