Relativity Theory and Paraquantum Logic—Part I: The Time and Space in the Paraquantum Logical Model

Abstract

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 (P<sub>QL</sub>). The studies of the P<sub>QL</sub> are based on propagation of Paraquantum logical states <i>ψ</i> 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 <i>γ<sub>PΨ</sub></i>, that has his action in the measurements of Observable Variables in the Physical world and the Paraquantum Factor of quantization <i>hΨ</i>, which has his action in the Paraquantum World represented by the <i>P<sub>QL</sub></i> Lattice. Correlation between <i>γ<sub>PΨ</sub></i> and <i>hΨ</i> produces paraquantum equations for computation of the physical quantities in real physical systems. In this work we present a study of application of the <i>P<sub>QL</sub></i> in resolution of phenomena of physical systems that involve concepts of the Relativity Theory. Initially the <i>time t </i>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 <i>time dilatation</i>. After the time considerations, paraquantum equations are involved with the <i>space-time</i> and <i>velocity</i> 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

Dark Energy Calculations Using the Paraquantum Gamma Factor (<i>γ<sub>Pψ</sub></i>) on the Relativistic Energy Equation

“…Doing such comparisons and analogies between the International unit Systems (SI) and the British System we obtain for the proportionality factor k in the equation which expresses Newton's second law (see [9] [10]). Given the importance of the Factor br k , which will be largely used in the equations of the PQL, its value is called Newton Gamma Factor whose symbol is N γ [11] [12]. Therefore, in order to apply classical logics in the Paraquantum Logical model, the Newton Gamma Factor is 2 N γ = .…”

“…The Lorentz Factor γ can be identified in the infinite Power Series of the binomial expansion [13] [14] related to the series obtained from consecutively applying the Newton Gamma Factor N γ (see [11]). In the Paraquantum analysis [8] we define a correlation value called Paraquantum Gamma Factor Pψ γ such that:…”

“…The quantitative analysis on the PQL-Lattice defines a quantitative value (Q Value ) of any physical quantity, which can be represented on the PQL-Lattice horizontal axis of the certainty Degrees and on the vertical axis of the contradiction degrees. Since the maximum value is normalized on the PQL Fundamental Lattice [6] Equation (11) shows that the maximum amount of any quantity in the physical environment is composed by two quantized fractions where: one is determined on the Paraquantum Logical state of Quantization ψ hψ by the Paraquantum Factor of quantization h ψ and the other is determined by its complement (1 − h ψ ). When the Paraquantum Gamma Factor Pψ γ is applied on the paraquantum quantities, besides correlating the paraquantum values to the physical environment, it also works as a factor of expansion or contraction of the PQL-Lattice [11] [12].…”

“…As it was seen in [11] [12], on the Paraquantum analysis of the Physical Systems in the Newtonian universe the For the unitary value of the Discourse Universe (or Interest Interval), in the Newtonian universe the Paraquantum Gamma Factor acting in the time correlates in the equilibrium point the three greatness physics [8] [13], such that:…”

“…The average velocity in the Paraquantum Logical Model has a value computed according to the laws of physics [11]:…”