I haven’t gone through any of the supposed derivations, but I’m led to believe that the Born rule is convincingly derivable within many worlds. I have a book called “Many Worlds? Everett, quantum theory and reality”, which contains such a derivation, I’ve been meaning to read it for a while and will get around to it some day. It claims:
An agent who arranges his preferences among various branching scenarios—quantum games—in accordance with certain principles of rationality, must act as if maximizing his expected utilities, as computed from the Born rule.
Which I think is a nice angle to view it from. At any rate, the Born rule is a fairly natural result to have, since the probabilities are simply the vector product of the wavefunction with itself, which is how you normally define the sizes of vectors in vector spaces. So I’m expecting the argument in the book to be related to the criteria that mathematicians use to define inner products, and how those criteria map to assumptions about the universe (ie no preferred spatial direction, that sort of thing). Maybe if I understand it I’ll post something here about it for those who are interested — I’m yet to see a blog-style summary of where the Born rule comes from.
At any rate it doesn’t come from anywhere in the way we’re taught quantum mechanics at uni, it’s simply an axiom that one doesn’t question. So any derivation, however assumption laden and weak would be an improvement over standard Copenhagen.
I haven’t gone through any of the supposed derivations, but I’m led to believe that the Born rule is convincingly derivable within many worlds. I have a book called “Many Worlds? Everett, quantum theory and reality”, which contains such a derivation, I’ve been meaning to read it for a while and will get around to it some day. It claims:
Which I think is a nice angle to view it from. At any rate, the Born rule is a fairly natural result to have, since the probabilities are simply the vector product of the wavefunction with itself, which is how you normally define the sizes of vectors in vector spaces. So I’m expecting the argument in the book to be related to the criteria that mathematicians use to define inner products, and how those criteria map to assumptions about the universe (ie no preferred spatial direction, that sort of thing). Maybe if I understand it I’ll post something here about it for those who are interested — I’m yet to see a blog-style summary of where the Born rule comes from.
At any rate it doesn’t come from anywhere in the way we’re taught quantum mechanics at uni, it’s simply an axiom that one doesn’t question. So any derivation, however assumption laden and weak would be an improvement over standard Copenhagen.