What is the mathematical difference between many worlds interpretation and Copenhagen interpretation?

Question

For instance, how would a many worlds theorist calculate an electron orbital differently than someone that prefers the Copenhagen interpretation?

Answer 1

Most interpretations strive to produce the same experimental results known up until today, but they start with different axioms (and postulates of "what exists"). Some modify predictions of QM (e.g. objective-collapse theories) making them experimentally distinguishable from other interpretations, while others (e.g. Bohmian mechanics, MWI) are claimed to produce the same predictions as standard QM for all possible cases (at least as far as non-relativistic QM goes).

Since the MWI falls into the latter camp, it leaves all predictions of standard QM the same, and the mathematics used is also the same, except for the starting axioms. In this case, most proponents of the MWI claim that the Born rule can be derived either from other existing axioms of QM or other more palatable postulates that avoid any use of probability.

For the MWI, the math used ends up the same, but there is a debate about how the Born rule can be derived by assuming some kind of "wavefunction ontology" and only "unitary evolution." Whether or not this has been successfully achieved is in debate.