Deriving The Born Rule

[John Clark]

I've heard it said that we know from quantum mechanical experiments that The Born Rule works but nobody has ever been able to derive it from first principles, however I'm not sure that's exactly true. Gleason's Theorem proves that if you have 3 or more Hilbert space dimensions and if things are "non-contextual" (a particular property has the same predetermined probability measure regardless of what other measurements are performed) and if you want all the probabilities to be positive and to always add up to exactly 1, then the Born Rule MUST have the form that it has. But Schrodinger's Equation is 100% deterministic, so the only real mystery is why we need to resort to probability at all because Gleason's Theorem says nothing about that. I think Many Worlds elegantly answers that question with the idea of self location uncertainty.

Self-locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics

In addition Deutsch and Wallace show that if we live in a branching universe as Everett described then a rational agent who wants to win as many bets as possible should assume that the square of the absolute value of the quantum wave function (a.k.a. The Born Rule) is true.

Quantum Theory of Probability and Decisions

Quantum Probability and Decision Theory, Revisited

John K Clark    See what's on my list at  Extropolis

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