Can the Born rule be derived from unitary quantum mechanics alone?
In plain words
The Born rule says the chance of an outcome is the squared size of its amplitude (the complex number attached to that outcome). Some argue it follows from symmetry or from rational betting in a universe that never collapses; others argue these derivations assume what they set out to prove.
Precise statement
Within unitary, no-collapse quantum theory (Everett), determine whether $p_{k} = \mid c_{k}\mid^2$ follows from explicitly stated assumptions (Deutsch-Wallace decision-theoretic axioms, Zurek envariance, Sebens-Carroll self-locating uncertainty) with no assumption equivalent to the rule itself. An answer is a proof of necessity and non-circularity, or an explicit model obeying all stated assumptions while violating $p_{k} = \mid c_{k}\mid^2$.
What would settle it
A rigorous derivation accepted as non-circular, or a counter-model that satisfies the stated axioms with a different probability rule.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Derivations by Deutsch (1999), Zurek (2005) and Wallace (2012) remain disputed on circularity grounds as of 2026.
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