The system of axioms for probability theory laid in 1933 by
Andrey Nikolaevich Kolmogorov can be extended to encompass the imaginary set of
numbers and this by adding to his original five axioms an additional three
axioms. Therefore, we create the complex probability set C, which is the sum of
the real set R with its corresponding real probability, and the imaginary set M
with its corresponding imaginary probability. Hence, all stochastic experiments
are performed now in the complex set C instead of the real set R. The objective
is then to evaluate the complex probabilities by considering supplementary new
imaginary dimensions to the event occurring in the ‘real’ laboratory.
Consequently, the corresponding probability in the whole set C is always equal
to one and the outcome of the random experiments that follow any probability
distribution in R is now predicted totally in C. Subsequently, it follows that,
chance and luck in R is replaced by total determinism in C. Consequently, by
subtracting the chaotic factor from the degree of our knowledge of the
stochastic system, we evaluate the probability of any random phenomenon in C.
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
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/13437
