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

PhysicsNoob
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    They’re called “interpretations” rather than “different theories” because they all lead to the same results. – Ghoster Oct 28 '23 at 22:31
  • @Ghoster I do understand this. But I was led to believe that there were mathematical differences. Is this not the case? So for an electron orbital we have Hψ = Eψ, and we solve for ψ given a potential energy H, where |ψ|² gives the probability distribution. Does anything different happen mathematically after this, or is the only difference how the math is interpreted? – PhysicsNoob Oct 28 '23 at 22:36
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    All interpretations lead to the same orbitals. Pick any interpretation you like. It won’t matter. – Ghoster Oct 28 '23 at 22:38
  • Hartle histories formalism is a distinct form of calculation with a many worlds flavour. – Mitchell Porter Oct 29 '23 at 00:28
  • I talk about the difference toward the end of my answer to Does the collapse of the wave function happen immediately everywhere?. There is no mathematical difference, at least in this world. And this is the only one we can observe or even know exists. – mmesser314 Oct 29 '23 at 00:38

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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.

Maximal Ideal
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