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The Born Rule in Quantum and Classical Mechanics

Paul Brumer·Jiangbin Gong
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Abstract

Considerable effort has been devoted to deriving the Born rule (e.g. that $|ψ(x)|^2 dx$ is the probability of finding a system, described by $ψ$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

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Paul Brumer, Jiangbin Gong. 2006-04-24. The Born Rule in Quantum and Classical Mechanics. https://doi.org/10.1103/physreva.73.052109

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