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 (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.
Cite this paper
nullJ. Filho, "Relativity Theory and Paraquantum Logic—Part I: The Time and Space in the Paraquantum Logical Model," Journal of Modern Physics, Vol. 3 No. 9, 2012, pp. 957-971. doi: 10.4236/jmp.2012.39126.
 N. C. A. Da Costa and D. Marconi, “An Overview of Paraconsistent Logic in the 80’s,” The Journal of Non-Classical Logic, Vol. 6, No. 1, 1989, pp. 5-31.
 N. C. A. Da Costa, “On the Theory of Inconsistent Formal Systems,” Notre Dame Journal of Formal Logic, Vol. 15, No. 4, 1974, pp. 497-510.
 S. Jas’kowski, “Propositional Calculus for Contradictory Deductive Systems,” Studia Logica, Vol. 24, No. 1, 1969, pp. 143-157. doi:10.1007/BF02134311
 J. I. Da Silva Filho, G. Lambert-Torres and J. M. Abe “Uncertainty Treatment Using Paraconsistent Logic—Introducing Paraconsistent Artificial Neural Networks,” IOS Press, Amsterdam, 2010.
 J. I. Da Silva Filho, “Paraconsistent Annotated Logic in analysis of Physical Systems: Introducing the Paraquantum Factor of Quantization hψ,” Journal of Modern Physics, Vol. 2, No. 11, 2011, pp. 1397-1409.
 C. A. Fuchs and A. Peres, “Quantum Theory Needs no ‘Interpretation’,” Physics Today, Vol. 53, No. 3, 2000, pp. 70-71. doi:10.1063/1.883004
 D. Krause and O. Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, Vol. 11 No. 2, 2007, pp. 187-201.
 J. I. Da Silva Filho, “Analysis of Physical Systems with Paraconsistent Annotated Logic: Introducing the Paraquantum Gamma Factor γψ,” Journal of Modern Physics, Vol. 2, No. 12, 2011, pp. 1455-1469.
 J. I. Da Silva Filho, “Study of the Interactions between Particles Based in Paraquantum Logic,” Journal of Modern Physics, Vol. 3, No. 5, 2012, pp. 362-376.
 Pl. A. Tipler and R. A. Llewellyn, “Modern Physics,” 5th Edition, W. H. Freeman and Company, New York, 2007.
 J. P. Mckelvey and H. Grotch, “Physics for Science and Engineering,” Harper and Row Publisher Inc, New York, London, 1978.
 Pl. A. Tipler, “Physics,” Worth Publishers Inc, New York, 1976.
 A. Einstein, “Relativity the Special and the General Theory,” Methuen & Co. Ltd., London, 1955.
 J. I. Da Silva Filho, “Analysis of the Spectral Line Emissions of the Hydrogen Atom with Paraquantum,” Journal of Modern Physics, Vol. 3, No. 3, 2012, pp. 233-254.
 J. I. Da Silva Filho, “An Introductory Study of the Hydrogen Atom with Paraquantum Logic,” Journal of Modern Physics, Vol. 3, No. 4, 2012, pp. 312-333.