In the current work, we extend and incorporate in the
five-axioms probability system of Andrey Nikolaevich Kolmogorov set up in 1933
the imaginary set of numbers and this by adding three supplementary axioms.
Consequently, any stochastic experiment can thus be achieved in the extended
complex probabilities set C which is the sum of the real probabilities set R
and the imaginary probabilities set M. The purpose here is to evaluate the
complex probabilities by considering additional novel imaginary dimensions to
the experiment occurring in the “real” laboratory. Therefore, the random
phenomenon outcome and result in C = R + M can be predicted absolutely and
perfectly no matter what the random distribution of the input variable in R is
since the associated probability in the entire set C is constantly and
permanently equal to one. Thus, the following consequence indicates that chance
and randomness in R is replaced now by absolute and total determinism in C as a
result of subtracting from the degree of our knowledge the chaotic factor in
the probabilistic experiment. Moreover, I will apply to the established theory
of quantum mechanics my original Complex Probability Paradigm (CPP) in order to
express the quantum mechanics problem considered here completely deterministically
in the universe of probabilities C = R + M.
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/13435
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