Journal of Modern Physics, 2013, 4, 712-733 doi:10.4236/jmp.2013.46098 Published Online June 2013 (http://www.scirp.org/journal/jmp) Introducing the Paraquantum Equations and Applications João Inácio Da Silva Filho 1,2 1 Santa Cecília University, Group of Applied Paraconsistent Logic, Santos-SP, Brazil 2 Institute for Advanced Studies of the University of São Paulo, São Paulo-SP, Brazil Email: inacio@unisanta.br Received February 21, 2013; revised April 13, 2013; accepted May 13, 2013 Copyright © 2013 João Inácio Da Silva Filho. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT In this paper, we present an equationing method based on non-classical logics applied to resolution of problems which involves phenomena of physical science. A non-classical logic denominated of the Paraquantum Logic (PQL), which is based on the fundamental concepts of the Paraconsistent Annotated logic with annotation of two values (PAL2v), is used. The formalizations of the PQL concepts, which are represented by a lattice with four vertices, lead 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. The studies on the lattice of PQL give us equations that quantify values of physical largenesses from where we obtain the effects of the propagation of the Paraquantum logical states ψ. The PQL lattice with such features can be extensively studied and we obtain a Paraquan- tum Logical Model with the capacity of contraction or expansion which can represent any physical universe. In this paper the Paraquantum Logical Model is applied to the Newton Laws where we obtain equations and verify the action of an expansion factor the PQL lattice called Paraquantum Gamma Factor γ Pψ and its correlation with another important factor called Paraquantum Factor of quantization h ψ . We present numerical examples applied to real physical systems through the equations which deal with paraquantum physical largenesses and how these values are transmitted to the physical world. With the results of these studies we can verify that the Paraquantum Logical Model has the property of interconnect several fields of the Physical Science. Keywords: Paraconsistent Logic; Paraquantum Logic; Classical Physic; Relativity Theory; Quantum Mechanics 1. Introduction The science that we used to study nature is the Physics and has their main concepts based on laws of the classic logic [1]. In some cases, mainly in conditions limits, the classic logic is inoperative due to their binary fundamen- tal laws. Those fundamental binary concepts of the clas- sic logic generate incapacity of treating situations in the real world, as the ones that they bring contradiction and uncertainties [2]. The conception of physical system models that are more efficient to respond to analysis in extreme conditions becomes necessary when we verify inconsistencies in results obtained from models which represent the same natural phenomenon but belong to different areas of physics [3]. In [4,5] we presented a model based on the concepts of non-classical logics called Paraconsistent Logic where the main feature is the abolishment of the principle of non-contradiction. Its theoretical structure is able to deal contradictory signals with valid conclusions [3,5], so that these are not an- nulled because of the information conflicts. The proposed Paraconsistent models to solve questions related to physical phenomena are based on a non-clas- sical logics called Paraconsistent Annotated Logic with annotation of two values (PAL2v) [3,4,6]. Later in re- searches based on models of PAL2v we verified that the applications of its concepts offered results which could be identified with the ones found in the modeling of phenomena studied in quantum mechanics [4,7,8]. An overview of the theoretical foundations of the Paracon- sistent logics is presented in [3,5,6,9-11]. 1.1. The Paraquantum Logic (PQL) Based on the previous considerations about the PAL2v [3,4] and in [12,13], we present the foundations of the Paraquantum Logics-PQL as follows: A Paraquantum logical state ψ is created on the lattice of the PQL as the tuple formed by the certainty degree D C and the contradiction degree D ct . Both values depend on Copyright © 2013 SciRes. JMP