Rob,
I am very happy that you found time for my essay. As I noted in my first comment to you, I view your essay as one of the very best, and I'm glad to see others have given you high ranking.
As for your (and John's) remark that "it does not go far enough towards giving a conceptually understandable physical interpretation to the wave function", let me say that I was in process of writing a 300-plus page book on this when the FQXi topic was announced. I then decided to try to condense the book to a nine-page essay. Clearly I did not fully succeed.
Yet I do believe there is more to the essay than can be absorbed in one reading. For example you state that "It is my belief, that wave-functions and de Broglie frequencies/waves do not exist at all "in reality", but only as ... mathematical abstractions." I think we largely agree, except that I do believe the induced C-field circulation is physically real and is always associated with the inducing particles. The question is how this non-normalizable local energy is then represented (in Hilbert space) as a normalized wave function.
You focus on a specific situation, detectors in a two-slit experiment, that, while important, is only a small portion of quantum physics. In this experiment, the wave function is typically used to compute the 'probability of being found at a given position'. As noted in my essay, I believe that the link between the physical reality and the probability representation is best understood in terms of energy. The position representation, you rightly note, is then derived by Fourier transformation on momentum space. The process of squaring is to get rid of the unknown 'phase'.
I also agree, in principle, with you that "instead of viewing the Fourier superposition of orthogonal basis functions as a "wave-function", one" should instead analyze the setup in terms of filters. In fact, I have gotten my copy of Goodman's "Introduction to Fourier Optics" down off the shelf to review these principles. But since quantum mechanics since 1927 has been formulated in terms of wave functions, and since there is considerable recent focus on the 'meaning' or 'reality' of wave functions, my focus was on describing [what I understand to be] the underlying physics. I definitely plan to spend more time looking at it from the perspective you present.
What I have failed to do, it seems quite clear, is to sufficiently distinguish the nature of a physically circulating field (which is the "wave") from the oscillating up and down sine wave that is the usual interpretation of de Broglie waves. In fact, since the essay was submitted, I've been made aware of certain differences that I had not seen at the time. 'Vortex' is probably a better mental image than 'wave'.
You disagree that "They were confused about physical waves and probability waves," and suggest the confusion was between a necessary and sufficient description. I'll give this some thought. As I noted to John, this essay deals only with the quantum mechanics of the C-field. The theory also details the genesis of the elementary particles: neutrino, electron, up and down quarks, their three families, the meson and baryon combinations, and the W and Z bosons, with the potential of calculating the mass spectrum. Thus, based on Tajmar's measurements and my own theory I consider the field to be physically real and to produce particles in a manner not at all like QED 'particle creation'.
My question to you Rob is whether you reject the idea of actual physically real particles plus induced field circulation/disturbance or whether you simply reject the Fourier based analysis that has led to such confusion?
Just as I could not condense 300-plus pages into 9 pages, I cannot 'clarify' what is missing in a comment or two, but I would ask you to look again at the new relation, "lambda (dot) del (cross) C ~ h" as a volume form that represents a conservation that is not based on Fourier analysis but still yields quantized energy levels.
Thanks again for reading my essay and commenting. I always enjoy your perspective and will continue to try to incorporate more of it in my thinking.
Edwin Eugene Klingman