Rydberg, Schrodinger, Mills and the Sausage Making of Mathematics

When I learned about it, I was initially not concerned at all about the theory of Dr. Mills.  I saw claims of high replication rates and high power gain in a light water electrolytic calorimetry experiment.  It was reproduced by several experimenters, some of whom, like Dr. Robert Bush, rejected the hydrino hypothesis, but confirmed that light water "cold fusion" excess heat was happening in his lab.  This was at a university and it attracted a lot of interest, so it seemed to me that it probably was real.  I just wanted to see something produce excess heat.

I read Dr. Mills' 1991 paper as far as I could, enough to grasp his novel physical conceptualization of the electron and claims that this held up well in mathematical physics modeling to produce behaviors in agreement with well established observations.  I dropped it in favor of other cold fusion work when I then went to work for Dr. Mallove.  My interest was jump-started when I met Dr. Phillips, as described elsewhere.

Physical theory is not my profession.  But, I studied it a great deal, and how it relates to science philosophy.  I began an effort to understand GUTCP, hoping that my rusty math mental machinery might permit some progress.  I discovered in the discussion group moderated by Dr. Mills' former physical chemistry professor, Dr. Farrell, that nobody there claimed to have re-derived the formulas that could be used to calculate ionization energies of elements.  This was troubling.  It was jet fuel for skeptics.

I discovered that the standard model of quantum mechanics deserves a lot of harsh criticism, but (at least prior to GUTCP) it is the best smelling dirty shirt in the hamper.  It turns out that physics is not Platonic.

I saw a lot of theoretical work around the Rydberg formula and I thought that meant that it was derived from something, but it is not.  There were naturally attempts to find mathematically correct relationships between Rydberg and classical physics models, like Bohr's.  It is definitely an "empirical relationship", i.e. curve fitting.  So, I thought maybe the standard model had a firm foundation in the Schrodinger Equation.  Well, Schrodinger didn't think so.  The standard model is like democracy.  "This is commonly called the most difficult form of government in the world; it has even been called the worst form of government, except for all others which have been tried." Guy Hensen

Dr. Raj Pal understands the situation well.  He has been teaching the standard model of quantum mechanics for quite a while.  He is not so critical of the standard model.  It is the best we have accepted and it works.  I hope that he is not upset with me when I compared it to epicycles of Ptolmaic celestial mechanics, which is the comparison that Schrodinger made.

Rydberg made a wild guess.  So did Schrodinger.  With enough corrections, these initial guesses worked well.  But, their foundation was not provided by Newton, who has proven to be the most far sighted and who embodies the first principles, which extend back to the Greeks and do not require interpretation and do not produce contradictory results, despite what college students may believe😆.  Newton was not guessing.  

It is hard to gain an adequate cultural context on Newton.  So many advancements trace directly to his theory, and those include Maxwell's equations, which are the theoretical basis for the modern age of technology.

I understand that a weak mathematical basis of a physical theory does not necessarily prevent the theory from getting accepted, not if a theory is needed.  As an engineer, this was a fact of life.  We were led to believe that someone established, somehow, somewhere, a link between practical engineering and pure theory in a virtual Platonic world, but don't think about it, or you'll hurt yourself.  Just "shut up and calculate".

The Riemann Hypothesis has stood as an unproved, but very useful mathematical tool in number theory, with possible huge implications in cryptography.  I do not pretend to understand it well.  At 4:16 in that video are famous similar examples.  How can we reject Mills because his math is not proven (although Dr. Phillips and Dr. Booker apparently find no problems with it)?  Of course, if you read this and you know of a problem with the math of GUTCP that derives formulas for ionization energies, please tell me.  I just want to focus on those formulas for now.

It is a weak defense of a theory to say that other theories have weaknesses.  What I am arguing here is that it is irrational to reject GUTCP because of imperfections (which Mills acknowledges), when the standard model seems ridiculously flawed in comparison.

What matters most is the empirical results.  What matters with theory is consistency with established knowledge and utility, but I have nothing against people striving to see the world through the eyes of  mathematical perfection.