The Paradigm of Complex Probability and the Theory of Metarelativity: The General Model and Some Consequences of MCPP

What is it about?

Calculating probabilities is a crucial task of classical probability theory. Adding supplementary dimensions to nondeterministic experiments will yield a deterministic expression of the theory of probability. This is the novel and original idea at the foundation of my complex probability paradigm. As a matter of fact, probability theory is a stochastic system of axioms in its essence; that means that the phenomena outputs are due to randomness and chance. By adding novel imaginary dimensions to the nondeterministic phenomenon happening in the set R will lead to a deterministic phenomenon and thus a stochastic experiment will have a certain output in the complex probability set and total universe G = C. If the chaotic experiment becomes completely predictable, then we will be fully capable to predict the output of random events that arise in the real world in all stochastic processes. Accordingly, the task that has been achieved here was to extend the random real probabilities set R to the deterministic complex probabilities set and total universe G = C = R + M and this by incorporating the contributions of the set M, which is the complementary imaginary set of probabilities to the set R. Consequently, since this extension reveals to be successful, then an innovative paradigm of stochastic sciences and prognostic was put forward in which all nondeterministic phenomena in R was expressed deterministically in C. This paradigm was initiated and elaborated in my previous 21 publications. Furthermore, this model will be linked to my theory of Metarelativity, which takes into consideration faster-than-light matter and energy. This is what I named “The Metarelativistic Complex Probability Paradigm (MCPP),” which will be developed in the present two chapters 1 and 2.

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Why is it important?

The development of a new theory in physics, which I called the theory of Metarelativity creates a new continuum or space-time in which a new matter interacts. This newly discovered matter is surely not the ordinary matter but a new kind of matter that can be easily identified to be the dark matter that astronomers, astrophysicists, and cosmologists seek to find. In fact, my novel theory shows that this new matter is superluminal by nature and is related to the new meta-space-time that lies in the metauniverse G2 in the same fashion that ordinary matter is related to the ordinary space-time and that lies in the universe G1 that we know. From what has been proved in Metarelativity, it was shown that the theory does not destroy Albert Einstein’s theory of relativity that we know at all but on the contrary, it proves its veracity and expands it to the superluminal velocities’ realm. The new space-time is “imaginary” since it exists in the domain of imaginary numbers and is now called meta-space-time or metauniverse because it lays beyond the ordinary “real” space-time that exists in the domain of real numbers as well as the matter and the energy interacting within them. Now the relation between both matter and metamatter is shown in the theory of Metarelativity. The first space-time is called the universe and the second space-time is called the metauniverse, which is another universe if we can say as material and as real as the first one but at a different level of experience because it is superluminal relative to the first one. It is similar to the atomic world that exists and is real but at a different level of physical experience, in the sense that we have discovered its laws in the theory of quantum mechanics where we deal with atoms and particles like when we deal in astronomy and astrophysics with planets and galaxies. In fact, astronomy is also real in the sense that we have discovered the laws governing the stars and planets but it lays at a different level of reality from our everyday world and experience. Metarelativity comes now to enlarge once more the scope of our understanding to encompass a new level of physical reality. Furthermore, my Metarelativity will be bonded to my Complex Probability Paradigm (CPP), which was developed in my 21 previous research works. In fact, 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 and random 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 all random experiments that follow any probability distribution in R is now predicted totally and absolutely in C. Subsequently, it follows that chance and luck in R are 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 Metarelativistic Complex Probability Paradigm (MCPP) will be developed in this work in order to express all probabilistic phenomena completely deterministically in the total universe G = C = R + M = G1 + G2 + G3.

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