[hansen]

> Sure, but regular quantum mechanics does the same thing. It's > under-constrained and allows for too many possibilities.

No it doesn’t. There are a few good guiding principles that make it possible to build models that turn out to be an accurate description of nature. These guiding principles don’t manifest themselves in a set of axioms of a mathematical theory nevertheless they are there. And they are part of the theory, just not set in stone like the underlying mathematical structure. But that doesn’t matter at all as long as you are doing science and not math.

Take classical EM, measure the masses of the electron and atomic nuclei, and write down a suitable Hamiltonians. Viola, you have an explanation of almost every phenomena that’s relevant in our daily life and way beyond. Similar principles exist in elementary particle physics and lead to standard model.