Generalized Lévy Distributions and the Principle of Complementarity

Elliot W. Montroll

Alexander Klimets

The article formulates and substantiates the philosophical epistemological principle, which generalizes the principle of complementarity of Bohr to all phenomena of reality. The general complementarity principle is formulated as follows: the rational side of reality and its cognition and its associated irrational side of reality and its cognition are complementary to each other. The general principle of complementarity allows one to search for phenomena of duality in various fields, grouping them according to rational and irrational signs.

Klimets Alexander

We show that Bohr's complementarity principle can be generalized to all the phenomena of reality. The generalized principle of complementarity Bohr can be formulated as follows: the rational side of reality and conjugate irrational side of reality are complementary to each other. This raises the question of relations between science and mysticism.

Yuh-Jia Lee, Hsin-Hung Shih

Eric Jakobsson

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.