I suppose I should confess up front that I'm not one of the folks who understands all of QM. I tend to follow Einstein and he was unable to effectively make his case.
As far as the math goes, all advanced math is tedious. It's the results it gives that are interesting.
I congratulate you on your efforts to cope with QM without the math background. It's hard enough with the math background. Good luck.
I was going to let this go by without comment but have changed my mind. It is too arrogant.
I respect mathematicians for their ability just as I respect Pele's ability to play world-class soccer. Watching clips of some of his moves while playing are so eloquent and precise and beautiful and unique as to defy description. I am moved. I respect able mathematicians in the same way.
But facility with the math does not necessarily correlate with understanding and can result in lack of perspective and hubris. So I respect the ability but I look with a very critical eye at the implications and the conclusions drawn by the the mathematician. I find them ofttimes to be unwarranted and the certainty with which they are propounded often also seems to be likewise unwarranted.
It is astounding that reality so closely corresponds to underlaying mathematical rules and is so reflective of symmetry. How or why this is so no mortal can say. And the best of the mathematicians acknowledge that the beauty of some newly discovered mathematical structure at least sometimes leads to breakthroughs in our understanding of the universe. Beauty? This is amazing.
The point is of course that understanding is a "thing apart", available somehow to those with the capacity and without regard to their technical abilities with math. Or so I believe.
I'm now reading Modern Physics and Ancient Faith by Stephen M. Barr, professor of physics at the Bartol Research Institute, University of Delaware. It is a marvelous book and not math-intensive. The following begins at page 184:
If free will, as it is traditionally understood, is real, then scientific materialism is certainly wrong. The reason is simple. Scientific materialism is the view that (a) only matter exists, and (b) matter is governed by the laws of physics and nothing else. However, after four hundred years of experience, we can say something rather definite about what a "law of physics" is. A law of physics is either deterministic or stochastic. That is, it is based on a rule or on randomness -- or a combination of the two.
Physics is quantitative. If human behavior is reduced to quantities, two things only can be found. To the extent that the behavior is predictable, it falls under some deterministic rule. The the extent that it is unpredictable, it appears to mathematical analysis as merely random. There is nothing else that a quantitative analysis can yield.
However, according to the traditional view of free will, an act is "free" only to the extent that it is neither random nor determined by rule. Like random behavior, it is not predictable, but unlike random behavior it is the product of rational choice rather than chance. Free behavior is a tertium quid, a third kind of thing. And therefore there is no way that it can be fully explained by a mathematical theory of physics. This is almost a matter of definition.
Since free will is fatal scientific materialism, the materialist is forced to deny its reality. This is done in two ways. Some simply assert that free will is altogether an illusion. It is a "naive" idea, a myth, and there is simply nothing in the real world that corresponds to it.
The other materialists admit that we mean something real when we talk about free will, but not what we think we mean. What free will really means, according to them, is that our choices are not coerced by causes outside ourselves ...