Dear Edwin Eugene Klingman,
Well done! This is an excellent essay. Your argument is clear and well-written, and you've given me much to think about. I too think there must be something classical happening at the heart of quantum mechanics, and I think your essay describes a logically consistent way of accounting for the wave equation in that respect, although I'm not an expert and my ability to judge your derivation critically is limited. However, I really do agree with your approach, which I think meets the purpose of this contest right on the mark, and I find your results very intriguing, so I'll definitely be following up on the advice you've given in the final paragraph.
I was particularly interested in the way you've described superposition, although it's something that hasn't bothered me as much. In itself, I don't have an issue with the idea of a cat (one particle) that's both alive and dead while it's in the box. There is a problem, though, when it comes to looking in the box, because then the cat can only be alive or dead, and I'm not a fan of the act of measurement being something that causes the wave function to collapse. So, although I'm not immediately opposed to the idea of one particle that's also a superposition of multiple possibilities, I don't like the implication that the result of looking into the box should be probabilistic. This backs me into a small-ish corner, where I think my best option is along these lines: maybe the particle really is one such thing (the cat's either alive or dead), and the whether of that is the thing that's probabilistic, e.g. depending on a radioactive half-life; but more than that, the physical description of the thing that actually exists is also mathematically something like one root of a polynomial, although the root is more accurately a `superposition' of numbers. If that superposition is consistent with the probabilistic nature of what the particle actually is, then I think you'd have quantum mechanics. I think this is right in line with what you've written in `The Source of the Error', second paragraph, and therefore with your interesting result, that `Each possible solution has a probability yet only one physical solution occurs'.
Anyway, I have a result written up which I think you'd find interesting, and it would explain (more concisely than it does in my dissertation) where I'm coming from in mentioning polynomials here. The result is a long, long way from quantum theory, but I'd be happy to email you the paper that's in review if you thought you'd have time to read it.
Again, excellent work, and I truly wish you success in this contest!
Sincerely,
Daryl
P.S. I only noticed the comment you left about my essay and dissertation on J. C. N. Smith's blog a couple of days ago, which I see you've reproduced above. I can't begin to express the profound gratitude I continue to feel for the enthusiasm and support you've shown for my work.