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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

Andrei Yu. Khrennikov

Foundations of PhysicsOct 1, 200577 citations

Complementarity, quantization, and uncertainty: An analytical perspective of set theory and probability

Aalok Pandya

Physics EssaysJun 2, 20140 citations

Contextual Quantization and the Principle of Complementarity of Probabilities

Andrei Yu. Khrennikov, Sergei Vladimirovich Kozyrev

The contextual probabilistic quantization procedure is formulated. This approach to quantization has much broader field of applications, compared with the canonical quantization. The contextual probabilistic quantization procedure is based on the notions of probability context and the principle of complementarity of probabilities. The general definition of probability context is given. The principle of complementarity of probabilities, which combines the ideas of the Bohr complementarity principle and the technique of noncommutative probability, is introduced. The principle of complementarity of probabilities is the criterion of possibility of the contextual quantization.The contextual probabilistic quantization procedure is formulated. This approach to quantization has much broader field of applications, compared with the canonical quantization. The contextual probabilistic quantization procedure is based on the notions of probability context and the principle of complementarity of probabilities. The general definition of probability context is given. The principle of complementarity of probabilities, which combines the ideas of the Bohr complementarity principle and the technique of noncommutative probability, is introduced. The principle of complementarity of probabilities is the criterion of possibility of the contextual quantization.

Open Systems & Information DynamicsAug 24, 20056 citations

I. Complementarity in Quantum Physics and its Philosophical Generalization

Adolf Grünbaum

The Journal of PhilosophyJan 1, 195716 citations

Principle of supplementarity: contextual probabilistic viewpoint to interference, complementarity and incompatibility

Andrei Yu. Khrennikov

There is 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 can not be represented in the complex Hilbert space. There are discussed applications of the principle of supplementarity outside quantum physics.There is 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 can not be represented in the complex Hilbert space. There are discussed applications of the principle of supplementarity outside quantum physics.

arXiv:quant-ph/0408187Aug 31, 20041 citation

An Epistemic Interpretation of Quantum Probability via Contextuality

Claudio Garola

arXiv:1806.09125Foundations of ScienceJul 23, 20187 citations

The Contextual Quantization and the Principle of Complementarity of Probabilities

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The Contextual Quantization and the Principle of Complementarity of Probabilities

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