Introducing the Paraquantum Equations and Applications

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 Paraquantum 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

KEYWORDS

Paraconsistent Logic; Paraquantum Logic; Classical Physic; Relativity Theory; Quantum Mechanics

Paraconsistent Logic; Paraquantum Logic; Classical Physic; Relativity Theory; Quantum Mechanics

Cite this paper

J. Filho, "Introducing the Paraquantum Equations and Applications,"*Journal of Modern Physics*, Vol. 4 No. 6, 2013, pp. 712-733. doi: 10.4236/jmp.2013.46098.

J. Filho, "Introducing the Paraquantum Equations and Applications,"

References

[1] D. Krause and O. Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, NEL—Epistemology and Logic Research Group, Federal University of Santa Catarina (UFSC), Brazil, 2007, pp. 187-201.

[2] N. C. A. Da Costa, V. S. Subrahmanian and C. Vago, Mathematical Logic Quarterly, Vol. 37, 1991, pp. 139-148. doi:10.1002/malq.19910370903

[3] J. I. Da Silva Fiho, G. Lambert-Torres and J. M. Abe, “Uncertainty Treatment Using Paraconsistent Logic: Introducing Paraconsistent Artificial Neural Networks,” IOS Press, Amsterdam, 2010, p. 328.

[4] J. M. Abe and J. I. Da Silva Filho, “Inconsistency and Electronic Circuits,” In: E. Alpaydin, Ed., Proceedings of EIS’98 International ICSC Symposium on Engineering of Intelligent Systems, Vol. 3, Artificial Intelligence, ICSC Academic Press, Rochester, 1998, pp. 191-197.

[5] N. C. A. Da Costa, Notre Dame Journal of Formal Logic, Vol. 15, 1974, pp. 497-510. doi:10.1305/ndjfl/1093891487

[6] N. C. A. Da Costa and D. Marconi, The Journal of Non-Classical Logic, Vol. 6, 1989, pp. 5-32.

[7] H. Reichenbach, “Philosophic Foundations of Quantum Mechanics,” University of California Press, Berkeley, 1944.

[8] J. A. Wheeler and H. Z. Wojciech, “Quantum Theory and Measurement,” Princeton University Press, Princeton, 1983.

[9] J. I. Da Silva Filho and A. Rocco, “Power systems Outage possibilities analysis by Paraconsistent Logic,” Power and Energy Society General Meeting on Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, 20-24 July 2008, pp. 1-6.

[10] H. A. Blair and V. S. Subrahmanian, “Paraconsistent Logic Programming,” 7th Conference on Foundations of Software Technology and Theoretical Computer Science, Pune, 17-19 December 1987. doi:10.1007/3-540-18625-5_59

[11] N. C. A. da Costa, D. Krause and O. Bueno, “Paraconsistent Logics and Paraconsistency,” In: D. Jacquette, D. M. Gabbay, P. Thagard and J. Woods, Eds., Philosophy of Logic, Elsevier, Series Handbook of the Philosophy of Science, Vol. 5, 2006, pp. 655-781.

[12] J. I. Da Silva Filho, Journal of Modern Physics, Vol. 2, 2011, pp. 1397-1409. doi:10.4236/jmp.2011.211172

[13] J. I. Da Silva Filho, Journal of Modern Physics, Vol. 2, 2011, pp. 1455-1469. doi:10.4236/jmp.2011.212180

[14] J. I. Da Silva Filho, Journal of Modern Physics, Vol. 3, 2012, pp. 233-254. doi:10.4236/jmp.2012.33033

[15] J. I. Da Silva Filho, Journal of Modern Physics, Vol. 3, 2012, pp. 312-333. doi:10.4236/jmp.2012.34044

[16] P. A Tipler,. and. A. Llewellyn “Modern Physics,” 5th Edition, W. H. Freeman and Company, 978-0-7167-7550-8, 2007.

[17] J. P. Mckelvey and H. Grotch, “Physics for Science and Engineering,” Harper and Row, Publisher, Inc., New York/ London, 1978, 426 pages.

[18] P. A Tipler, “Physics,” Worth Publishers, Inc., New York, 1976.

[19] P. A Tipler and G. M. Tosca “Physics for Scientists,” 6th Edition, W. H. Freeman and Company, New York, 2007.

[20] M. Ference Jr., H. B. Lemon and R. J. Stephenson, “Analytical Experimental Physics,” 2nd Edition, University of Chicago Press, Chicago, 1956.

[21] F. Gross, “Relativistic Quantum Mechanics and Field Theory,” John Wiley & Sons, Inc., Hoboken, 1993, p. 97.

[22] D. Kleppner and R. K. Binding, “An Introduction to Mechanics,” Mcgraw-Hill, Columbus, 1973.

[23] J. Bernstein, P. M. Fishbane and S. G. Gasiorowicz, “Modern Physics,” Prentice-Hall, New York, 2000.

[1] D. Krause and O. Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, NEL—Epistemology and Logic Research Group, Federal University of Santa Catarina (UFSC), Brazil, 2007, pp. 187-201.

[2] N. C. A. Da Costa, V. S. Subrahmanian and C. Vago, Mathematical Logic Quarterly, Vol. 37, 1991, pp. 139-148. doi:10.1002/malq.19910370903

[3] J. I. Da Silva Fiho, G. Lambert-Torres and J. M. Abe, “Uncertainty Treatment Using Paraconsistent Logic: Introducing Paraconsistent Artificial Neural Networks,” IOS Press, Amsterdam, 2010, p. 328.

[4] J. M. Abe and J. I. Da Silva Filho, “Inconsistency and Electronic Circuits,” In: E. Alpaydin, Ed., Proceedings of EIS’98 International ICSC Symposium on Engineering of Intelligent Systems, Vol. 3, Artificial Intelligence, ICSC Academic Press, Rochester, 1998, pp. 191-197.

[5] N. C. A. Da Costa, Notre Dame Journal of Formal Logic, Vol. 15, 1974, pp. 497-510. doi:10.1305/ndjfl/1093891487

[6] N. C. A. Da Costa and D. Marconi, The Journal of Non-Classical Logic, Vol. 6, 1989, pp. 5-32.

[7] H. Reichenbach, “Philosophic Foundations of Quantum Mechanics,” University of California Press, Berkeley, 1944.

[8] J. A. Wheeler and H. Z. Wojciech, “Quantum Theory and Measurement,” Princeton University Press, Princeton, 1983.

[9] J. I. Da Silva Filho and A. Rocco, “Power systems Outage possibilities analysis by Paraconsistent Logic,” Power and Energy Society General Meeting on Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, 20-24 July 2008, pp. 1-6.

[10] H. A. Blair and V. S. Subrahmanian, “Paraconsistent Logic Programming,” 7th Conference on Foundations of Software Technology and Theoretical Computer Science, Pune, 17-19 December 1987. doi:10.1007/3-540-18625-5_59

[11] N. C. A. da Costa, D. Krause and O. Bueno, “Paraconsistent Logics and Paraconsistency,” In: D. Jacquette, D. M. Gabbay, P. Thagard and J. Woods, Eds., Philosophy of Logic, Elsevier, Series Handbook of the Philosophy of Science, Vol. 5, 2006, pp. 655-781.

[12] J. I. Da Silva Filho, Journal of Modern Physics, Vol. 2, 2011, pp. 1397-1409. doi:10.4236/jmp.2011.211172

[13] J. I. Da Silva Filho, Journal of Modern Physics, Vol. 2, 2011, pp. 1455-1469. doi:10.4236/jmp.2011.212180

[14] J. I. Da Silva Filho, Journal of Modern Physics, Vol. 3, 2012, pp. 233-254. doi:10.4236/jmp.2012.33033

[15] J. I. Da Silva Filho, Journal of Modern Physics, Vol. 3, 2012, pp. 312-333. doi:10.4236/jmp.2012.34044

[16] P. A Tipler,. and. A. Llewellyn “Modern Physics,” 5th Edition, W. H. Freeman and Company, 978-0-7167-7550-8, 2007.

[17] J. P. Mckelvey and H. Grotch, “Physics for Science and Engineering,” Harper and Row, Publisher, Inc., New York/ London, 1978, 426 pages.

[18] P. A Tipler, “Physics,” Worth Publishers, Inc., New York, 1976.

[19] P. A Tipler and G. M. Tosca “Physics for Scientists,” 6th Edition, W. H. Freeman and Company, New York, 2007.

[20] M. Ference Jr., H. B. Lemon and R. J. Stephenson, “Analytical Experimental Physics,” 2nd Edition, University of Chicago Press, Chicago, 1956.

[21] F. Gross, “Relativistic Quantum Mechanics and Field Theory,” John Wiley & Sons, Inc., Hoboken, 1993, p. 97.

[22] D. Kleppner and R. K. Binding, “An Introduction to Mechanics,” Mcgraw-Hill, Columbus, 1973.

[23] J. Bernstein, P. M. Fishbane and S. G. Gasiorowicz, “Modern Physics,” Prentice-Hall, New York, 2000.