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Book Publisher International (a part of SCIENCEDOMAIN International)

The Paradigm of Complex Probability and Quantum Mechanics

Abdo Abou Jaoudé

Published Feb 15, 2024• 0 citations
Publisher
DOI
10.9734/bpi/mono/978-81-970122-5-9

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The Paradigm of Complex Probability and Quantum Mechanics: The Quantum Harmonic Oscillator with Gaussian Initial Condition – The Position Wavefunction

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In the current work, we extend and incorporate 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 are replaced now by absolute and total determinism in C as a result of subtracting from the degree of our knowledge of 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.

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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.

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The Physics of Complex Probability

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The Paradigm of Complex Probability and Quantum Mechanics

Abdo Abou Jaoudé

The concept of mathematical probability was established in 1933 by Andrey Nikolaevich Kolmogorov by defining a system of five axioms. This system can be enhanced to encompass the imaginary numbers set after the addition of three novel axioms. As a result, any random experiment can be executed in the complex probabilities set C which is the sum of the real probabilities set R and the imaginary probabilities set M. We aim here to incorporate supplementary imaginary dimensions to the random experiment occurring in the “real” laboratory in R and therefore to compute all the probabilities in the sets R, M, and C. Accordingly, the probability in the whole set C = R + M is constantly equivalent to one independently of the distribution of the input random variable in R, and subsequently the output of the stochastic experiment in R can be determined absolutely in C. This is the consequence of the fact that the probability in C is computed after the subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic experiment. 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.

Book Publisher International (a part of SCIENCEDOMAIN International)•Feb 15, 2024•0 citations
In the current work, we extend and incorporate 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 are replaced now by absolute and total determinism in C as a result of subtracting from the degree of our knowledge of 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.
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.
The concept of mathematical probability was established in 1933 by Andrey Nikolaevich Kolmogorov by defining a system of five axioms. This system can be enhanced to encompass the imaginary numbers set after the addition of three novel axioms. As a result, any random experiment can be executed in the complex probabilities set C which is the sum of the real probabilities set R and the imaginary probabilities set M. We aim here to incorporate supplementary imaginary dimensions to the random experiment occurring in the “real” laboratory in R and therefore to compute all the probabilities in the sets R, M, and C. Accordingly, the probability in the whole set C = R + M is constantly equivalent to one independently of the distribution of the input random variable in R, and subsequently the output of the stochastic experiment in R can be determined absolutely in C. This is the consequence of the fact that the probability in C is computed after the subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic experiment. 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.