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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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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