[ExI] 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
<https://www.journals.uchicago.edu/doi/10.1093/bjps/axw004>*

*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
<https://arxiv.org/pdf/quant-ph/9906015>*


*Quantum Probability and Decision Theory, Revisited
<https://arxiv.org/pdf/quant-ph/0211104>*

John K Clark    See what's on my list at  Extropolis
<https://groups.google.com/g/extropolis>
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