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.
Author(s) Details:
Abdo Abou Jaoudé,
Department of Mathematics and Statistics, Faculty of Natural and
Applied Sciences, Notre Dame University-Louaize, Lebanon.
Please see the link here: https://stm.bookpi.org/TPCPQM/article/view/13438
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