Information dynamics and new geometric foundations of quantum theory

Details Information dynamics and new geometric foundations of quantum theory Information dynamics and new geometric foundations of quantum theory

2011-10-20

arxiv.org/abs/1110.4492v3

Physics

Quantum Physics

To appear in: Khrennikov A. (ed.), Proceedings of the Foundations of Probability and Physics 6 conference, Linneuniversitetet,

Scientific paper

We discuss new approach to mathematical foundations of quantum theory, which is completely independent of Hilbert spaces and measure spaces. New kinematics is defined by non-linear geometry of spaces of integrals on abstract non-commutative algebras. New dynamics is defined by constrained maximisation of quantum relative entropy. We recover Hilbert space based approach (including unitary evolution and the von Neumann--L\"{u}ders rule) and measure theoretic approach to probability theory (including Bayes' rule) as special cases of our approach.

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