Dear Alan Kadin,
Does math hinder or help physics? The title of your essay says math hindered the development of QM, and is followed by an articulate express argument. (Some other essays seem to argue implicitly that math is a sub-optimal intermediary medium for physics.) I hope you will not mind some comments despite my knowing little about QM.
Math is helpful (and sometimes indispensable) when it describes, explains, summarizes, condenses, provides insight, predicts, etc. Math is unhelpful when it obscures, is irrelevant, inapplicable, makes the conceptual thread hard to follow etc. An example would be 20 pages of equations of no discernible meaning, that no one will have the strength or interest to check. Another example would be A L = P, meaning actors with lines create a play; plus and minus signs do not of themselves invest ordinary words with insight.
Let's take your title now. Your diagnosis and cure may be right. I propose another possibility (which does not exclude your approach). The complexities and seeming incongruities of the mathematics of QM (such as the many worlds hypothesis, entanglement and the two slits experiment) might not be a failure of mathematics. Rather, apparent shortcomings might be a clue that a crucial postulate, assumption, theory, picture (as you say), conceptual reference frame or unknown unknown is missing. This suggests looking not outside mathematics but for better mathematics.
A paradigm example is Ptolemy's Almagest, a stupendous mathematical and astronomical achievement. Ptolemy wrote summarily that obviously the earth does not rotate on its axis, as some other astronomers had suggested, because clouds would appear to move at high speeds in the sky in a direction opposite that of the spinning earth, and birds, unable to keep up, would fall out of the sky. If he had the concept of inertia he might have come to a different conclusion.
Perhaps a question raised by your interesting essay is: are we missing something?
Regards,
Bob Shour