Note that the Born probabilities really obviously have something to do with the unitarity of QM, while no single-world interpretation is going to have this be anything but a random contingent fact.
Not so. If we insist that our predictions need to be probabilities (take the Born probabilities as fundamental/necessary), then unitarity becomes equivalent to the statement that probabilities have to sum to 1, and we can then try to piece together what our update equation should look like. This is the approach taken by the 'minimalist'/'ensemble' interpretation that Ballentine's textbook champions, he uses probabilities sum to 1 and some group theory (related to the Galilean symmetry group) to motivate the form of the Schroedinger equation. Edit to clarify: In some sense, its the reverse of many worlds- instead of taking the Schroedinger axioms as fundamental and attempting to derive Born, take the operator/probability axioms seriously and try to derive Schroedinger.
I believe the same consideration could be said of the consistent histories approach, but I'd have to think about it before I'd fully commit.
Edit to add: Also, what about "non-spooky" action at a distance? Something like the transactional interpretation, where we take relativity seriously and use both the forward and backward Green's function of the Dirac/Klein-Gordon equation? This integrates very nicely with Barbour's timeless physics, properly derives the Born rule, has a single world, BUT requires some stochastic modifications to the Schroedinger equation.
What surprises me in the QM interpretational world is that the interaction process itself is clearly more than just a unitary evolution of some wave function, given how the number of particles is not conserved, requiring the full QFT approach, and probably more, yet (nearly?) all interpretations stop at the QM level, without any attempt at some sort of second quantization. Am I missing something here?
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A list of some posts that are pretty awesome
I recommend the major sequences to everybody, but I realize how daunting they look at first. So for purposes of immediate gratification, the following posts are particularly interesting/illuminating/provocative and don't require any previous reading:
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Note from orthonormal: MBlume and other contributors wrote the original version of this welcome post, and I've edited it a fair bit. If there's anything I should add or update on this post (especially broken links), please send me a private message—I may not notice a comment on the post. Finally, once this gets past 500 comments, anyone is welcome to copy and edit this intro to start the next welcome thread.