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Undulatory Theory with paraconsistent logic (Part II): Schrödinger Equation and Probability Representation

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Journal of Quantum Information Science 2016年第3期6卷 181-213页

作者： João Inácio Da Silva Filho Laboratory of applied paraconsistent logic Santa Cecilia University Santos Brazil

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 SchrÖdinger’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.

关键词： paraconsistent logic Wave Theory Quantum Mechanics Paraquantum logic Schrödinger Equation

A Probabilistic paraconsistent logical Model for Non-Relativistic Quantum Mechanics Using Interlaced Bilattices with Conflation and Bernoulli Distribution

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Journal of Quantum Information Science 2017年第3期7卷 89-124页

作者： Joao Inacio Da Silva Filho Laboratory of applied paraconsistent logic Santa Cecilia University—UNISANTASantosBrazil

In this work, we make a representation of non-relativistic quantum theory based on foundations of paraconsistent annotated logic (PAL), a propositional and evidential logic with an associated lattice FOUR. We use the PAL version with annotation of two values (PAL2v), named paraquantum logic (PQL), where the evidence signals are normalized values and the intensities of the inconsistencies are represented by degrees of contradiction. Quantum mechanics is represented through mapping on the interlaced bilattices where this logical formalization allows annotation of two values in the format of degrees of evidence of probability. The Bernoulli probability distribution is used to establish probabilistic logical states that identify the superposition of states and quantum entanglement with the equations and determine the state vectors located inside the interlaced Bilattice. In the proposed logical probabilistic paraquantum logic model (pPQL Model), we introduce the operation of logical conflation into interlaced bilattice. We verify that in the pPQL Model, the operation of logical conflation is responsible for providing a suitable model for various phenomena of quantum mechanics, mainly the quantum entanglement. The results obtained from the entanglement equations demonstrate the formalization and completeness of paraquantum logic that allows for interpretations of similar phenomena of quantum mechanics, including EPR paradox and the wave-particle theory.

关键词： paraconsistent logic Interlaced Bilattice Probability Theory Quantum Mechanics Paraquantum logic Model

Study of the Interactions between Particles Based in Paraquantum logic

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Journal of Modern Physics 2012年第5期3卷 362-376页

作者： Joao Inacio Da Silva Filho group of applied paraconsistent logic Santa Cecilia UniversitySantosBrazil Institute for Advanced Studies University of Sao PauloSao PauloBrazil

Paraquantum logic (P QL ) has its origins in the fundamental concepts of the paraconsistent Annotated logic (PAL) whose main feature is to be capable of treating contradictory information. In this work we presented a study of application of the P QL in resolution of phenomena of physical systems that involves the interactions between physical bodies or particles. Initially is considered that each particle or physical body that is in the physical world has a representative Lattice in the Paraquantum world. From this consideration is made a study of the phenomena of Paraquantum Entanglement modeling the interaction between particles based in fundamental concepts of the Paraquantum logic. The mathematical relationships of representative Lattices of the Paraquantum logic originate models with values that are identified with some physical constants. In this work these paraquantum values are identified with the Universal constant of Gravity, proposed by Newton, and the constant K, that relates the Interaction Force in charged particles in the Coulomb’s Law. The results showed that the Paraquantum logical Model elaborated starting from the fundamental concepts of the Paraquantum logic (P QL ) is adequate to support theories based in a Paraquantum Universe built by an infinite amount of Lattices and forming a Paraquantum net of infinite dimensions.

关键词： paraconsistent logic Paraquantum logic Classical Physic Relativity Theory Quantum Mechanics

An Introduction to paraconsistent Integral Differential Calculus:With Application Examples

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applied Mathematics 2014年第6期5卷 949-962页

作者： Joao Inácio Da Silva Filho group of applied paraconsistent logic Santa Cecília UniversitySantosBrazil Institute for Advanced Studies University of Sao PauloSao PauloBrazil

In this paper we show that it is possible to integrate functions with concepts and fundamentals of paraconsistent logic (PL). The PL is a non-classical logic that tolerates the contradiction without trivializing its results. In several works the PL in his annotated form, called paraconsistent logic annotated with annotation of two values (PAL2v), has presented good results in analysis of information signals. Geometric interpretations based on PAL2v-Lattice associate were obtained forms of Differential Calculus to a paraconsistent Derivative of first and second-order functions. Now, in this paper we extend the calculations for a form of paraconsistent Integral Calculus that can be viewed through the analysis in the PAL2v-Lattice. Despite improvements that can develop calculations in complex functions, it is verified that the use of paraconsistent Mathematics in differential and Integral Calculus opens a promising path in researches developed for solving linear and nonlinear systems. Therefore the paraconsistent Integral Differential Calculus can be an important tool in systems by modeling and solving problems related to Physical Sciences.

关键词： paraconsistent logic paraconsistent Annotated logic paraconsistent Mathematics paraconsistent Integral Differential Calculus

Relativity Theory and Paraquantum logic—Part II:Fundamentals of an Unified Calculation

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Journal of Modern Physics 2012年第9期3卷 972-988页

作者： Joao Inacio Da Silva Filho group of applied paraconsistent logic-Santa Cecilia University SantosBrazil Institute for Advanced Studies of the University of Sao Paulo Cidade Universitaria Sao PauloBrazil

The studies of the PQL are based on propagation of Paraquantum logical states ψ in a representative Lattice of four vertices. Based in interpretations that consider resulting information of measurements in physical systems are found paraquantum equations for computation of the physical quantities in real physical systems. In the first part of this work we presented a study of Relativity theory which involved the time and the space with their characteristics as degrees of evidence applied in Paraquantum logical Model. Now, in this second Part we present a study of application of the PQL in resolution of phenomena of physical systems that involve concepts of the Relativity Theory and the correlation of these effects with the Newtonian Universe and Quantum Mechanics. Considering physical fundamental quantities varying periodically in amplitude, we introduce the paraquantum equations which consider frequency in the analysis. From of these mathematical relationships obtained in the PQL Lattice some main physical constants related to the studies of De Broglie appeared. With the equations of Energy obtained through the analyses is demonstrated that the Paraquantum logic is capable to correlate values and to unify the several study areas of the Physical Science.

关键词： paraconsistent logic Paraquantum logic Classical Physic Relativity Theory Quantum Mechanics

An Introductory Study of the Hydrogen Atom with Paraquantum logic

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Journal of Modern Physics 2012年第4期3卷 312-333页

作者： Joao Inacio Da Silva Filho group of applied paraconsistent logic Santa Cecilia UniversitySantosBrazil Institute for Advanced Studies University of Sao Paulo Cidade UniversitariaSao PauloBrazil

Paraquantum logics (PQL) has its origins in the fundamental concepts of the paraconsistent Annotated logics (PAL) whose main feature is to be capable of treating contradictory information. Based on a class of logics called paraconsistent logics with annotations of two values (PAL2v), PQL performs a logical treatment on signals obtained by measurements on physical quantities which are considered Observable Variables in the physical world. In the process of application of the PQL the obtained values are transformed in Evidence Degrees and represented on a Lattice of four Ver- tices where special equations transform these degrees into Paraquantum logical states ψ which propagate. The propagation of Paraquantum logical states provides us with results which can be interpreted and modeled through phenomena studied in physics. Using the paraquantum equations, we investigate the effects of balancing of Energies and the quantization and transience properties of the Paraquantum logical Model in real Physical Systems. As a demonstration of the usage of the paraquantum equations we perform a numerical comparative study that applies the PQL to the Bohr’s model to find the energy levels of the Hydrogen atom. It is verified that the values of energy in each level of the Paraquantum logical model of the Hydrogen atom are close to the values found by the conventional way. The results through the Paraquantum logic allow considering other important properties of the atom, as the forecast of number of electrons in each layer.

关键词： paraconsistent logic Paraquantum logic Classical Physic Relativity Theory Quantum Mechanics

Relativity Theory and Paraquantum logic—Part I:The Time and Space in the Paraquantum logical Model

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Journal of Modern Physics 2012年第9期3卷 957-971页

From fundamental concepts of the paraconsistent Annotated logic with annotation of two values (PAL2v), whose main feature is to be capable of treating contradictory information, was created the Paraquantum logic (PQL). The studies of the PQL are based on propagation of Paraquantum logical states ψ in a representative Lattice of four vertices. Based in interpretations that consider resulting information of measurements in physical systems, are found two Paraquantum factors: the Paraquantum Gamma Factor γPΨ, that has his action in the measurements of Observable Variables in the Physical world and the Paraquantum Factor of quantization hΨ, which has his action in the Paraquantum World represented by the PQL Lattice. Correlation between γPΨ and hΨ produces paraquantum equations for computation of the physical quantities in real physical systems. In this work we present a study of application of the PQL in resolution of phenomena of physical systems that involve concepts of the Relativity Theory. Initially the time t is considered like an Observable Variable and the paraquantum analysis is done with the same conditions assumed in the relativity theory for the study of the time dilatation. After the time considerations, paraquantum equations are involved with the space-time and velocity creating conditions for a relativistic/paraquantum analysis. In the part II of this work a new approaches of the relativistic phenomena in the Paraquantum logical Model will show the correlation of these effects with the Newtonian universe and with quantum mechanics.

关键词： paraconsistent logic Paraquantum logic Classical Physic Relativity Theory Quantum Mechanics

Analysis of the Spectral Line Emissions of the Hydrogen Atom with Paraquantum logic

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Journal of Modern Physics 2012年第3期3卷 233-254页

作者： Joao Inacio Da Silva Filho group of applied paraconsistent logic Santa Cecilia UniversitySantosBrazil Institute for Advanced Studies The University of Sao Paulo Cidade UniversitariaSao PauloBrazil

In this work we presented a study of the obtaining of the spectral line emissions of the hydrogen atom using equations that are originated from the foundations of the Paraquantum logic (PQL). Based on a class of logics called paraconsistent logics with annotation of two values (PAL2v), PQL performs a logical treatment on signals obtained by measurements on physical quantities which are considered Observable Variables in the physical world. In the process of application of the PQL the obtained values are transformed in Evidence Degrees and represented on a Lattice of four Vertices where special equations transform these degrees into Paraquantum logical states ψ which propagate. This allows creating Paraquantum logical models of physical systems of the real world. Using the paraquantum equations, we investigated the hydrogen atom spectrum and his main series known. We performed a numerical comparative study that applies the Paraquantum logical Model to calculate the wavelengths values. The values of wavelengths obtained by the Paraquantum Equations are compared by the results found by the Rydberg formula and are verified that the series of the spectral line emissions of the hydrogen atom can be identified with the representative Lattices of the Paraquantum logic. Through the application of the Paraquantum equations it was found a numeric value relates the layers of Paraquantum model of the Hydrogen atom. This value represents a constant that relates the Lattices that compose the Paraquantum universe, and it was denominated Paraquantum Structure Constant, whose symbol is αψ. The obtained results of the comparison demonstrate that the Paraquantum logic comes with good possibilities of being the ideal logic to model our physical reality.

关键词： paraconsistent logic Paraquantum logic Classical Physic Relativity Theory Quantum Mechanics

Dark Energy Calculations Using the Paraquantum Gamma Factor(γ_(Pψ)) on the Relativistic Energy Equation

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Journal of Modern Physics 2014年第6期5卷 319-334页

作者： Joao Inácio Da Silva Filho group of applied paraconsistent logic Santa Cecília University-UNISANTASantosBrazil Institute for Advanced Studies of the University of Sao Paulo-IEAUSP Sao PauloBrazil

A paraconsistent logic (PL) is a non-classical logic which revokes the principle of non-Contradiction and admits the treatment of contradictory information in its theoretical structure. Paraquantum logic (PQL) is based on a type of PL denominated paraconsistent Annotated logic with annotation of two values (PAL2v). The PAL2v have a representative Lattice of four vertices (Lattice FOUR) where are made interpretations with construction of Paraquantum logical Model and equations capable computation values extract of Observable Variable measurements. The studies of the PQL are based on propagation of Paraquantum logical states ψ in a Paraquantum Universe represented by PQL-Lattice of four vertices. These studies of PQL are based in two Paraquantum factors: the Paraquantum Gamma Factor (γPψ) that has his action in the measurements of Observable Variables in the Physical world and the Paraquantum Factor of quantization hψ, which has his action in the Paraquantum Universe. In this paper we analyze the application of Paraquantum Gamma Factor γPψ and its intrinsic characteristics that add important information into the equation of Einstein’s relativistic Energy (E = MC2). In this article were made several calculations to demonstrate the effects of applying the Paraquantum Gamma Factor (γPψ) in relativistic energy equation. It is found that the factors of using the Paraquantum logical Model make an adjustment in the equation of Einstein’s relativistic Energy and identify related values with recent results found for the Dark Energy and dark matter. In the Paraquantum/Relativistic Energy equation the γPψ appears as an important factor of transition between the relativistic universe and the Newtonian Universe. The results suggest that its use would be very important in the interpretation of the behavior of other astronomical factors as the cosmological constant and gravitation.

关键词： paraconsistent logic Paraquantum logic Dark Energy Dark Matter Relativity Theory