Undulatory Theory with Paraconsistent Logic (Part I): Quantum Logical Model with Two Wave Functions (original) (raw)
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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 probabil-istic 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.
Journal of Modern Physics, 2011
In this paper we use a non-classical logic called ParaQuantum Logic (PQL) which is based on the foundations of the Paraconsistent Annotated logic with annotation of two values (PAL2v). The formalizations of the PQL concepts, which is represented by a lattice with four vertices, leads us to consider Paraquantum logical states ψ which are propagated by means of variations of the evidence Degrees extracted from measurements performed on the Observable Variables of the physical world. In this work we introduce the Paraquantum Gamma Factor γ Pψ which is an expansion factor on the PQL lattice that act in the physical world and is correlated with the Paraquantum Factor of quantization h ψ whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. Our studies show that the behavior of the Paraquantum Gamma Factor γ Pψ , at the time of reading the evidence Degrees through measurements of the Observable Variables in the physical world, is identical to that one of the Lorentz Factor γ used in the relativity theory. In the final part of this paper we present results about studies of expansion and contraction of the Paraquantum Logical Model which correlate the factors γ Pψ and γ. By applying these correlation factors, the lattice of the PQL suitable for the universe understudy can be contracted or expanded, allowing the quantization model to cover the several study fields of physics.
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 entan-glement. 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.
2010
Current research in Logic is no longer confined to the traditional study of logical consequence or valid inference. As can be witnessed by the range of topics covered in this special issue, the subject matter of logic encompasses several kinds of informational processes ranging from proofs and inferences to dialogues, observations, measurements, communication and computation. What interests us here is its application to quantum physics: how does logic handle informational processes such as observations and measurements of quantum systems? What are the basic logical principles fit to handle and reason about quantum physical processes? These are the central questions in this paper. It is my aim to provide the reader with some food for thought and to give some pointers to the literature that provide an easy access to this field of research. In the next section I give a brief historical sketch of the origin of the quantum logic project. Next I will explain the theory of orthomodular lattices in section 2. Section 3 covers the syntax and semantics of traditional quantum logic. In section 4, I focus on the limits of quantum logic, dealing in particular with the implication problem. This paves the way to section 5 on modal quantum logic. I end with section 6 on dynamic quantum logic, giving the reader a taste of one of the latest new developments in the field.
In this paper we use a non-classical logic called ParaQuantum Logic (PQL) which is based on the foundations of the Paraconsistent Annotated logic with annotation of two values (PAL2v). The formalizations of the PQL concepts, which is represented by a lattice with four vertices, leads us to consider Paraquantum logical states ψ which are propagated by means of variations of the evidence Degrees extracted from measurements performed on the Observable Variables of the physical world. In this work we introduce the Paraquantum Gamma Factor γ Pψ which is an expansion factor on the PQL lattice that act in the physical world and is correlated with the Paraquantum Factor of quantization h ψ whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. Our studies show that the behavior of the Paraquantum Gamma Factor γ Pψ , at the time of reading the evidence Degrees through measurements of the Observable Variables in the physical world, is identical to that one of the Lorentz Factor γ used in the relativity theory. In the final part of this paper we present results about studies of expansion and contraction of the Paraquantum Logical Model which correlate the factors γ Pψ and γ. By applying these correlation factors, the lattice of the PQL suitable for the universe understudy can be contracted or expanded, allowing the quantization model to cover the several study fields of physics.
Study of the Interactions between Particles Based in Paraquantum Logic
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. J. I. DA SILVA FILHO 361 λ 1 Physical World ετ Figure 1. The lattice of the LPA2v and the Paraconsistent logical state ε τ .
Arxiv preprint quant-ph/0101028, 2001
We investigate some forms of quantum logic arising from the standard and the unsharp approach.
An Introductory Study of the Hydrogen Atom with Paraquantum Logic
Paraquantum Logics (P QL ) 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), P QL 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 P QL 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. 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 P QL 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.
Use of mathematical logical concepts in quantum mechanics: an example
Journal of Physics A: Mathematical and General, 2002
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple example of such a system, based on an example described by Smullyan, is studied here. Based on a path interpretation for some word states, definitions of truth, validity, consistency and completeness are given and their properties studied. It is also shown by means of examples that the relation between the potential meaning, if any, of word states and the quantum algorithmic complexity of the process generating the word states must be quite complex or nonexistent.
A proposal for a new approach to Quantum Logic
Article CITATIONS 0 READS 17 2 authors, including: Some of the authors of this publication are also working on these related projects: interpretation of analytical mechanics through the two dichotomies. Search of a new formualtion of quantum mechanics relying on the alternative choices of the Dirac-von Neumann's one A new View project Antonino Drago University of Naples Federico II 70 PUBLICATIONS 88 CITATIONS SEE PROFILE All content following this page was uploaded by Antonino Drago on 14 January 2015.