Conclusions

The paraconsistent model of the atom proposed in this work is based on the foundations of the PAL and combines the concepts of the entropy of information theory with quantum mechanics. The proposed paraconsistent model of the atom, which applies the interlaced PqL bilattice, shows a convincing geometric aspect for the atomic particle. Thus, well-adjusted fundamentals for the phenomena of quantum physics could be demonstrated. Despite the impossibility of covering all quantum phenomena in this work, the equations obtained by the analyses provide the characteristics of symmetry, recurrence, and superposition of states. The entanglement concept can be expressed in the form of the division obtained through the distance factor dF

used in the equations of the degrees of certainty. The quantum phenomenon of the superposition of states is explicitly expressed through the equations and the representation in which two observers are active. This procedure, which was conducted through the simultaneous use of equations and the analysis of an observer in the vector of the base X and an observer in the vector of the base Y, is similar to the quantum theory. The model presented in this work is innovative and opens a field of in-depth investigations of different conditions and the effects originating from interpretations of the model under diverse conditions and dimensions. All the equations feature good computability and ensure that all the procedures can be presented in matrix and algorithmic forms. Notably, in the presented paraconsistent model of the atom, no equation results in a defined value. In general, all the equations used in the simulations are probabilistic functions that result in indefinite trajectories of paraquantum logical states. Even the direction and orientation of the orbital trajectories shown in the result graphics are indefinite because they are always opposite to one another. In the simulations, the paraconsistent model of the atom was represented by algorithms I and II that allowed showing the probabilistic trajectories of the paraquantum logical states that can be related to the probable orbits of the elementary particles. With the simulation applying the PqL equations, the energy functions, represented by the degrees of certainty and contradiction, therefore values generated in the quantum universe - Interlaced PqL Bilattice -, can to express the probabilities to be measured in the real world. These algorithms and equations have high significance for the beginning of new studies in computational applications of PqL. In its application to Raman spectroscopy data, the paraconsistent model showed versatility and a good representation of the energy variations at the atomic level of hydrogen. These results enable us to further explore the use of the proposed model with the presented concepts, such as the adjustment of the energy values in the lower layers of the hydrogen atom and for other atomic models. This work demonstrates that the use of the Shannon entropy in a paraconsistent model is an excellent method for modeling quantum systems. In the future, new simulation procedures will expand the application possibilities of the paraconsistent model of the atom in other areas, including computation, quantum logic gates, quantum systems for signal recognition, and quantum cryptography.

Supplementary Materials: The data that support the plots within this paper and other findings of this study are available in additional material and from the corresponding author.

Author Contributions: J.I. carried out the experiments, did the analysis of the results, wrote the paper and prepared the illustrations.

Acknowledgments:

The author acknowledges ISESC - Instituto Superior de Educação Santa Cecilia for the financial support for this research.

The author would like to acknowledge L. Silveira Jr. for Raman spectroscopy data obtained by FAPESP (São Paulo Research Foundation) process no. 2009/01788-5.

Conflicts of Interest: The author declares no competing interests.

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