Workshop on: QUANTUM INFORMATION AND FOUNDATIONS OF QUANTUM MECHANICS

Workshop on: QUANTUM INFORMATION AND FOUNDATIONS OF QUANTUM MECHANICS
Quantum Mechanics: Axiomatics and connections with Computing and Information Theory Quantum correlation from classical waves and random background field
aula INFN - 4 luglio ore 11.00
	Andrei Khrennikov, nternational Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science Linnaeus University, Växjö-Kalmar, Sweden
>PRESENTATION:Andrei Khrennikov, born 06.08.1958 in Volgograd, USSR; graduated from Dpt. of Mechanics and Mathematics of Moscow State University - 1980, PhD from the same dept - 1983 (math physics), doctor of science degree of Steklov Math Institute of Russian Academy of Science (math problems of quantum field theory), since 1997 prof. of applied math at Linnaeus University (Vaxjoe-Kalmar, Sweden) and the director of International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science. Andrei Khrennikov is the author of 16 monographs (in particular 4 by Springer) and about 350 articles in internationally recognaized journals in quantum foundations, foundations of classical and quantum probability, math, physics, econophysics and finances, psychology, genetics and cognitive science. He organized in small town Vaxjo (South-East Sweden) a series of annual conferences in quantum foundations (Foundations of Probability and Physics 1 -- 6, Qunatum theory: Reconsideration of Foundations 1 -- 6, Advances in Quantum Theory); these conferences attracted best experts in quantum theory and foundations as well as information theory from the whole world; Vaxjo becomes of of world's centers for quantum foundations.
Abstract
	Prequantum classical statistical field theory (PCSFT) is a model which provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of the wave type. For example, ``electron'' is described by electronic field. In contrast to QM, this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of e.g. electron contains the irreducible contribution of the background field, vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper we derive a classical analog of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM. The quantum dispersion corresponds to the difference between e.g. the electron field dispersion and the dispersion of vacuum fluctuations. Classical Robertson-like inequality contains these differences. Hence, it does not imply such a rigid estimate from below for dispersions as it was done in QM.