An analogue of the Heisenberg uncertainty relation in prequantum classical field theory
Abstract
Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility of representing 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 wave type. For example, 'electron' is described by electronic field. In contrast to quantum mechanics (QM), this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of , for example, an 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 analogue of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. The PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM.
- Publication:
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Physica Scripta
- Pub Date:
- February 2010
- DOI:
- 10.1088/0031-8949/81/06/065001
- arXiv:
- arXiv:0912.1565
- Bibcode:
- 2010PhyS...81f5001K
- Keywords:
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- Quantum Physics
- E-Print:
- Physica Scripta 81 (6), art. no. 065001 (2010)