Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random var...

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Veröffentlicht in:Journal of mathematical physics 2010-08, Vol.51 (8), p.082106-082106-20
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description One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.
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subjects BANACH SPACE
CALCULATION METHODS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CORRELATIONS
Exact sciences and technology
FIELD THEORIES
HILBERT SPACE
MATEMATIK
Mathematical methods in physics
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
PHASE SPACE
Physics
PROBABILISTIC ESTIMATION
Probability
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
Quantum physics
RANDOMNESS
Sciences and techniques of general use
SPACE
STATISTICAL MECHANICS
Statistical methods
TENSORS
title Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces
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