Analysis of the Spectral Line Emissions of the Hydrogen Atom with Paraquantum Logic

Author(s)
João Inácio Da Silva Filho

ABSTRACT

In this work we presented a study of the obtaining of the spectral line emissions of the hydrogen atom using equations that are originated from the foundations of the Paraquantum Logic (PQL). Based on a class of logics called Paraconsistent Logics with annotation 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 Vertices where special equations transform these degrees into Paraquantum logical states ψ which propagate. This allows creating Paraquantum logical models of physical systems of the real world. Using the paraquantum equations, we investigated the hydrogen atom spectrum and his main series known. We performed a numerical comparative study that applies the Paraquantum Logical Model to calculate the wavelengths values. The values of wavelengths obtained by the Paraquantum Equations are compared by the results found by the Rydberg formula and are verified that the series of the spectral line emissions of the hydrogen atom can be identified with the representative Lattices of the Paraquantum Logic. Through the application of the Paraquantum equations it was found a numeric value relates the layers of Paraquantum model of the Hydrogen atom. This value represents a constant that relates the Lattices that compose the Paraquantum universe, and it was denominated Paraquantum Structure Constant, whose symbol is αψ. The obtained results of the comparison demonstrate that the Paraquantum Logic comes with good possibilities of being the ideal logic to model our physical reality.

In this work we presented a study of the obtaining of the spectral line emissions of the hydrogen atom using equations that are originated from the foundations of the Paraquantum Logic (PQL). Based on a class of logics called Paraconsistent Logics with annotation 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 Vertices where special equations transform these degrees into Paraquantum logical states ψ which propagate. This allows creating Paraquantum logical models of physical systems of the real world. Using the paraquantum equations, we investigated the hydrogen atom spectrum and his main series known. We performed a numerical comparative study that applies the Paraquantum Logical Model to calculate the wavelengths values. The values of wavelengths obtained by the Paraquantum Equations are compared by the results found by the Rydberg formula and are verified that the series of the spectral line emissions of the hydrogen atom can be identified with the representative Lattices of the Paraquantum Logic. Through the application of the Paraquantum equations it was found a numeric value relates the layers of Paraquantum model of the Hydrogen atom. This value represents a constant that relates the Lattices that compose the Paraquantum universe, and it was denominated Paraquantum Structure Constant, whose symbol is αψ. The obtained results of the comparison demonstrate that the Paraquantum Logic comes with good possibilities of being the ideal logic to model our physical reality.

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, "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.

J. Filho, "Analysis of the Spectral Line Emissions of the Hydrogen Atom with Paraquantum Logic,"

References

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[2] N. C. A. da Costa, “On the Theory of Inconsistent For- mal 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. Subrahmanian and C. Vago, “The Paraconsistent Logic PT,” Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, Vol. 37, 1991, pp. 139-148. doi:10.1002/malq.19910370903

[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, A. Rocco “Paraconsistent Algorithm Extractor of Contra- diction Effects—Paraextrctr”, Journal of Software Engi- neering and Applications, Vol. 4, No. 11, 2011, pp. 579- 584.

[7] J. I. Da Silva Filho, A. Rocco, A. S. Onuki, L. F. P Fer- rara and J. M. Camargo, “Electric Power Systems Con- tingencies Analysis by Paraconsistent Logic Application,” International Conference on Intelligent Systems Applica- tions to Power Systems, Niigata, 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, Prin- ceton, 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 Phys- ics, Vol. 2, No. 11, 2011, pp. 1397-1409.

[12] J. I. Da Silva Filho, “Analysis of Physical Systems with Paraconsistent Annotated Logic: Introducing the Paraq- uantum Gamma Factor γψ,” Journal of Modern Physics, Vol. 2, No. 12, 2011, pp. 1455-1469.

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

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

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

[1] S. Ja?kowski, “Propositional Calculus for Contradictory Deductive Systems,” Studia Logica, Vol. 24, No. 1, 1969, pp. 143-157. doi:10.1007/BF02134311

[2] N. C. A. da Costa, “On the Theory of Inconsistent For- mal 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. Subrahmanian and C. Vago, “The Paraconsistent Logic PT,” Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, Vol. 37, 1991, pp. 139-148. doi:10.1002/malq.19910370903

[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, A. Rocco “Paraconsistent Algorithm Extractor of Contra- diction Effects—Paraextrctr”, Journal of Software Engi- neering and Applications, Vol. 4, No. 11, 2011, pp. 579- 584.

[7] J. I. Da Silva Filho, A. Rocco, A. S. Onuki, L. F. P Fer- rara and J. M. Camargo, “Electric Power Systems Con- tingencies Analysis by Paraconsistent Logic Application,” International Conference on Intelligent Systems Applica- tions to Power Systems, Niigata, 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, Prin- ceton, 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 Phys- ics, Vol. 2, No. 11, 2011, pp. 1397-1409.

[12] J. I. Da Silva Filho, “Analysis of Physical Systems with Paraconsistent Annotated Logic: Introducing the Paraq- uantum Gamma Factor γψ,” Journal of Modern Physics, Vol. 2, No. 12, 2011, pp. 1455-1469.

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

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

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