Earman, John
(2022)
The Status of the Born Rule and the Role of Gleason's Theorem and Its Generalizations: How the Leopard Got Its Spots and Other Just-So Stories.
[Preprint]
Abstract
Approaching a hundred years since the publication of Born's epochal 1926 papers, the status of the Born rule is still the subject of lively discussion in the physics and philosophy literatures. Here I examine some approaches to justifying the Born rule within the mathematical framework that construes quantum probability theory as the study of probability measures on the projection lattices of von Neumann algebras. Of particular concern is the role of Gleason's theorem and its generalizations. A common line is to credit the Gleason theorems with providing a derivation of the Born rule, but then to complain that the theorems offer little physical insight into the emergence of quantum probabilities and the Born rule and/or that they commit the sin of "non-contextuality." It is argued that both the credit and the complaints are off the mark.
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