An Introductory Study of the Hydrogen Atom with Paraquantum Logic

ABSTRACT

Paraquantum Logics (PQL) 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), PQL 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 PQL the obtained values are transformed in Evidence Degrees and represented on a Lattice of four Ver- tices 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 PQL 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.

Paraquantum Logics (PQL) 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), PQL 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 PQL the obtained values are transformed in Evidence Degrees and represented on a Lattice of four Ver- tices 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 PQL 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.

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. Silva Filho, "An Introductory Study of the Hydrogen Atom with Paraquantum Logic,"*Journal of Modern Physics*, Vol. 3 No. 4, 2012, pp. 312-333. doi: 10.4236/jmp.2012.34044.

J. Silva Filho, "An Introductory Study of the Hydrogen Atom with Paraquantum Logic,"

References

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[2] 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. doi:10.1305/ndjfl/1093891487

[3] 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.

[4] N. C. A. Da Costa, V. S. Subrahmaniane and C. Vago, “The Paraconsistent Logic PT,” Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, Vol. 37, 1991, pp. 139-148.

[5] J. I. Da Silva Filho, G. Lambert-Torres and J. M. Abe, “Uncertainty Treatment Using Paraconsistent Logic— Introducing Paraconsistent Artificial Neural Networks,” Vol. 21, IOS Press, Amsterdam, 2010, p. 328.

[6] J. I. Da Silva Filho, G. Lambert-Torres, L. F. P. Ferrara, A. M. C. Mário, M. R. Santos, A. S. Onuki, J. M. Camargo and A. Rocco, “Paraconsistent Algorithm Extractor of Contradiction Effects—Paraextrctr,” Journal of Software Engineering and Applications, Vol. 4, No. 10, 2011, pp. 579-584. doi:10.4236/jsea.2011.410067

[7] J. I. Da Silva Filho, A. Rocco, A. S. Onuki, L. F. P. Ferrara and J. M. Camargo, “Electric Power Systems Contingencies Analysis by Paraconsistent Logic Application,” The 14th International Conference on Intelligent System Applications to Power Systems, Kaohsiung, 5-8 November 2007, pp. 1-6.

[8] 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

[9] D. Krause and O. Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, Vol. 11, No. 2, 2007, pp. 187-201.

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

[11] 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. doi:10.4236/jmp.2011.211172

[12] J. I. Da Silva Filho, “Paraconsistent Annotated Logic in Analysis of Physical Systems: Introducing the Paraquantum Gamma Factor γψ,” Journal of Modern Physics, 2011, Vol. 2, No. 12, pp. 1455-1469. doi:10.4236/jmp.2011.212180

[13] Pl. A. Tipler, “Physics,” Worth Publishers Inc, New York, 1976.

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

[15] Pl. A. Tipler and R. A. Llewellyn, “Modern Physics,” 5th Edition, W. H. Freeman and Company, New York, 2007.

[16] J. I. Da Silva Filho, “Analysis of the Spectral Line Emissions of the Hydrogen Atom with Paraquantum Logic,” Journal of Modern Physics, Vol. 3 No. 3, 2012, pp. 233- 254. doi:10.4236/jmp.2012.33033

[1] S. Jas’kowski, “Propositional Calculus for Contradictory Deductive Systems,” Studia Logica, Vol. 24, 1969, pp. 143-157. doi:10.1007/BF02134311

[2] 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. doi:10.1305/ndjfl/1093891487

[3] 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.

[4] N. C. A. Da Costa, V. S. Subrahmaniane and C. Vago, “The Paraconsistent Logic PT,” Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, Vol. 37, 1991, pp. 139-148.

[5] J. I. Da Silva Filho, G. Lambert-Torres and J. M. Abe, “Uncertainty Treatment Using Paraconsistent Logic— Introducing Paraconsistent Artificial Neural Networks,” Vol. 21, IOS Press, Amsterdam, 2010, p. 328.

[6] J. I. Da Silva Filho, G. Lambert-Torres, L. F. P. Ferrara, A. M. C. Mário, M. R. Santos, A. S. Onuki, J. M. Camargo and A. Rocco, “Paraconsistent Algorithm Extractor of Contradiction Effects—Paraextrctr,” Journal of Software Engineering and Applications, Vol. 4, No. 10, 2011, pp. 579-584. doi:10.4236/jsea.2011.410067

[7] J. I. Da Silva Filho, A. Rocco, A. S. Onuki, L. F. P. Ferrara and J. M. Camargo, “Electric Power Systems Contingencies Analysis by Paraconsistent Logic Application,” The 14th International Conference on Intelligent System Applications to Power Systems, Kaohsiung, 5-8 November 2007, pp. 1-6.

[8] 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

[9] D. Krause and O. Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, Vol. 11, No. 2, 2007, pp. 187-201.

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

[11] 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. doi:10.4236/jmp.2011.211172

[12] J. I. Da Silva Filho, “Paraconsistent Annotated Logic in Analysis of Physical Systems: Introducing the Paraquantum Gamma Factor γψ,” Journal of Modern Physics, 2011, Vol. 2, No. 12, pp. 1455-1469. doi:10.4236/jmp.2011.212180

[13] Pl. A. Tipler, “Physics,” Worth Publishers Inc, New York, 1976.

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

[15] Pl. A. Tipler and R. A. Llewellyn, “Modern Physics,” 5th Edition, W. H. Freeman and Company, New York, 2007.

[16] J. I. Da Silva Filho, “Analysis of the Spectral Line Emissions of the Hydrogen Atom with Paraquantum Logic,” Journal of Modern Physics, Vol. 3 No. 3, 2012, pp. 233- 254. doi:10.4236/jmp.2012.33033