Does anyone have a book they can recommend that explains the actual math of quantum mechanics?
You could try “The structure and interpretation of quantum mechanics” by R I G Hughes or “The Interpretation of quantum mechanics” by Roland Omnes. Either has enough math to articulate the problem.
I also really liked “Quantum mechanics and experience” by David Z Albert—it was this book that led me to realize that many-worlds is obviously true (as it now seems to me). Albert himself does not believe in many-worlds but he explains it really well.
I’m now working through the university physics texts because none of the above cover relativistic QM. They physics texts though are—to a man—in the “shut up and calculate” school of thought. It is claimed that many a promising physicist has disappeared down the rat-hole of the philosophical interpretation of QM.
You may also enjoy “A Different Universe: Reinventing Physics from the Bottom Down” by Robert Laughlin. He argues that so-called fundamental physics is just the lowest layer of emergent froth that we are able to see. Quantum Field Theory shows that “empty space” is full of stuff for example.
W Edwards Deming pointed out in the 1950s, in his books about quality management, the folly of combining measuring for the purpose of improvement with measurement for the purpose of remunerating people. If you do this, the whole measurement process is corrupted—“you get what you measure”. Almost invariably however the two forms of measurement are combined because it seems more efficient. As I speak, ambulances are waiting for many hours idle outside my local hospital for a spare bed for their patients, because if the hospital tells them to go to another hospital the hospital gets demerits for failing to have a bed available. If they make them wait, no such demerits are given.
Later, psychologists found that when you externally reward and punish people for doing things, any other intrinsic rewards from the activity tend to be extinguished. Thus (in part) the contrast between the 5 year old who is brimming with enthusiasm for learning and the resentful 14 year old who does as little at possible at school.
Maria Montessori found that if you place children consistently at the sweet spot of learning, where they have to make some effort but it is not discouragingly difficult, they remain enthusiastic and learn rapidly. Micro-tests occur all the time in Montessori classrooms to assess progress. Mainly the tests involve a self-assessment that this activity is boring now so I will move to the next one.