Abstract
Part I of this study proved that the Paraconsistent Annotated Logic using two values (PAL2v), known as the Paraquantum Logic (PQL), can represent the quantum by a model comprising two wave functions obtained from interference phenomena in the 2W (two-wave) region of Young’s experiment (double slit). With this model represented in one spatial dimension, we studied in the Lattice of the PQL, with their values represented in the set of complex numbers, the state vector of unitary module and its correspondence with the two wave functions. Based on these considerations, we applied the PQL model for obtaining Paraquantum logical states ψ related to energy levels, following the principles of the wave theory through SchrOdinger’s equation. We also applied the probability theory and Bonferroni’s inequality for demonstrating that quantum wave functions, represented by evidence degrees, are probabilistic functions studied in the PQL Lattice, confirming that the final Paraquantum Logic Model is well suited to studies involving aspects of the wave-particle theory. This approach of quantum theory using Paraconsistent logic allows the interpretation of various phenomena of Quantum Mechanics, so it is quite promising for creating efficient models in the physical analysis and quantum computing processes.
Highlights
IntroductionThis paper assumes that it is possible to model phenomena occurring in classical quantum mechanics experiments through a non-classical logic, whose main foundation is its tolerance to contradiction
Around the 17th century, several scientists supported the wave theory of light
These procedures involving Paraquantum Logic (PQL) concepts demonstrated that values found by Schrödinger equation exist within the Paraquantum Universe, as well as wave functions in this context that define quantum mechanics theories
Summary
This paper assumes that it is possible to model phenomena occurring in classical quantum mechanics experiments through a non-classical logic, whose main foundation is its tolerance to contradiction To this end, we used Paraconsistent Annotated Logic with annotation of two values (PAL2v), named the Paraquantum Logic (PQL) [5]-[8], to model and solidify wave theory concepts. In this part, we give continuity to studies conducted in Part I, which focused on the fundamentals of Paraconsistent Logic (PL) and quantum mechanics to create a model based on the wave theory of the particle. In order to advance in the study of the logical quantum model with two wave functions, a few concepts previously defined in Part I will be briefly presented
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