The Paradigm of Complex Probability and the Quantum Entropic Uncertainty Principle - Abdo Abou Jaoudé (The Paradigm of Complex Probability and Quantum Mechanics, 2024)
The mathematical probability concept was set forth by Andrey Nikolaevich Kolmogorov in 1933 by laying down a five-axioms system. This scheme can be improved to embody the set of imaginary numbers after adding three new axioms. Accordingly, any stochastic phenomenon can be performed in the set C of complex probabilities which is the summation of the set R of real probabilities and the set M of imaginary probabilities. Our objective now is to encompass complementary imaginary dimensions to the stochastic phenomenon taking place in the “real” laboratory in R and as a consequence to calculate in the sets R, M, and C all the corresponding probabilities. Hence, the probability is permanently equal to one in the entire set C = R + M independently of all the probabilities of the input stochastic variable distribution in R, and subsequently the output of the random phenomenon in R can be determined perfectly in C. This is due to the fact that the probability in C is calculated after the elimination and subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic phenomenon. My innovative ‘Complex Probability Paradigm’ (CPP) will be applied to the established theory of quantum mechanics in order to express it completely deterministically in the universe C = R + M as well as to the quantum entropic uncertainty principle in order to verify it and to extend it to the universes M and C.