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From arXiv

The Born Rule in Quantum and Classical Mechanics

Considerable effort has been devoted to deriving the Born rule (e.g. that

|\psi(x)|^2 dx

is the probability of finding a system, described by

\psi

, 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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Published on April 24, 2006

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