The Born Rule in Quantum and Classical Mechanics

Abstract

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.

5 pages, no figures, to appear in Phys. Rev. A

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• From probabilistic mechanics to quantum theory
• Quantum/Classical Interface: Fermion Spin
• Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems
• Unitary representation of the Poincaré group for classical relativistic dynamics