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The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum Mechanics

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Abstract

We presented a contextual statistical model of the probabilistic description of physical reality. Here contexts (complexes of physical conditions) are considered as basic elements of reality. There is discussed the relation with QM. We propose a realistic analogue of Bohr’s principle of complementarity. In the opposite to the Bohr’s principle, our principle has no direct relation with mutual exclusivity for observables. To distinguish our principle from the Bohr’s principle and to give better characterization, we change the terminology and speak about supplementarity, instead of complementarity. Supplementarity is based on the interference of probabilities. It has quantitative expression trough a coefficient which can be easily calculated from experimental statistical data. We need not appeal to the Hilbert space formalism and noncommutativity of operators representing observables. Moreover, in our model there exists pairs of supplementary observables which cannot be represented in the complex Hilbert space. There are discussed applications of the principle of supplementarity outside quantum physics.

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  1. International Center for Mathematical Modeling in Physics and Cognitive Sciences, University of Växjö, S-35195, Sweden

    Andrei Khrennikov

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Khrennikov, A. The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum Mechanics. Found Phys 35, 1655–1693 (2005). https://doi.org/10.1007/s10701-005-6511-z

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