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The structure of classical extensions of quantum probability theory

By Paul Busch and Werner Stulpe

Abstract

On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed

Topics: 2610, 3100, 3109
Year: 2008
OAI identifier: oai:eprints.whiterose.ac.uk:3754

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