Theory of Complex Numbers: Gross error in Mathematics and Physics

Temur Z Kalanov

doi:10.48165/

Authors

Temur Z Kalanov Home of Physical Problems, Yozuvchilar (Pisatelskaya) 6a, 100128 Tashkent, Uzbekistan

DOI:

https://doi.org/10.48165/

Keywords:

general mathematics, complex numbers, geometry, methodology of mathematics, mathematical physics, physics, special relativity, electromagnetism, quantum mechanics, general relativity, engineering, formal logic, dialectics, philosophy of mathematics, philosophy of science, education

Abstract

The critical analysis of the starting point of the theory of complex numbers is proposed. The unity of formal logic and rational dialectics is methodological basis of the analysis. The analysis leads to the following main results: (1) the definition of a complex number contradicts to the laws of formal logic, because this definition is the union of two contradictory concepts: the concept of a real number and the concept of a non-real (imaginary) number - an image. The concepts of a real number and a non-real (imaginary) number are in logical relation of contradiction: the essential feature of one concept completely negates the essential feature of another concept. These concepts have no common feature (i.e. these concepts have nothing in common with each other), therefore one cannot compare these concepts with each other. Consequently, the concepts of a real number and a non-real (imaginary) number cannot be united and contained in the definition of a complex number. The concept of a complex number is a gross formal-logical error; (2) the real part of a complex number is the result of a measurement. But the non-real (imaginary) part of a complex number is not the result of a measurement. The non-real (imaginary) part is a meaningless symbol, because the mathematical (quantitative) operation of multiplication of a real number by a meaningless symbol is a meaningless operation. This means that the theory of complex number is not a correct method of calculation. Consequently, mathematical (quantitative) operations on meaningless symbols are a gross formal-logical error; (3) a complex number cannot be represented (interpreted) in the Cartesian geometric coordinate system, because the Cartesian coordinate system is a system of two identical scales (rulers). The standard geometric representation (interpretation) of a complex number leads to the logical contradictions if the scales (rulers) are not identical. This means that the scale of non-real (imaginary) numbers cannot exist in the Cartesian geometric coordinate system. Consequently, the theory of complex numbers and the use of the theory of complex numbers in mathematics and physics (electromagnetism and electrical engineering, fluid dynamics, quantum mechanics, relativity) represent a gross methodological error and lead to gross errors in mathematics and physics.

References

Boyer C.B. (1991). A history of mathematics (Second ed.). John Wiley & Sons, Inc. ISBN 0-471-54397-7. 2. Nagel R. (2002). Encyclopedia of Science, 2nd Ed., The Gale Group.

Solomentsev E.D. (2001). Complex number, Encyclopedia of Mathematics.

Bourbaki N. (1998). Foundations of Mathematics. Springer.

Spiegel M.R., Lipschutz S., Schiller J.J., Spellman D. (2009). Complex Variables, Schaum's Outline Series (2nd ed.). McGraw Hill. ISBN 978-0-07-161569-3.

Brown J.W., Churchill R.V. (1996). Complex variables and applications (6th ed.). New York: McGraw Hill. ISBN 978-0-07-912147-9. (1996).

Weisstein E.W. (2020). Complex Number. (Mathworld.wolfram.com).

Ewald W.B. (2008). From Kant to Hilbert: a source book in the foundations of mathematics”. Oxford University Press US. ISBN 0-19-850535-3.

Caparrini S. (2000). On the Common Origin of Some of the Works on the Geometrical Interpretation of Complex Numbers. In Kim Williams (ed.). Two Cultures. Birkhäuser. ISBN 978-3-7643-7186-9. 10. Grant I.S., Phillips W.R. (2008). Electromagnetism. (2 ed.). Manchester Physics Series. ISBN 978-0-471- 92712-9.

Ahlfors L. (1979). Complex analysis. (3rd ed.). McGraw-Hill. ISBN 978-0-07-000657-7. 12. Madelung E. (1957). Die Mathematischen Hilfsmittel Des Physikers. Berlin, Gottingen, Heidelberg: Springer-Verlag.

Smirnov V.I. (1974). Course of Higher Mathematics, Vol. 1. Moscow.

Kalanov T.Z. (2010).The critical analysis of the foundations of theoretical physics. Crisis in theoretical physics: The problem of scientific truth. Lambert Academic Publishing. ISBN 978-3-8433-6367-9. 15. Kalanov T.Z. (2010). Analysis of the problem of relation between geometry and natural sciences”. Prespacetime Journal, 1(5), 75-87.

Kalanov T.Z. (2011). Logical analysis of the foundations of differential and integral calculus. Bulletin of Pure and Applied Sciences, (Math.& Stat.), 30E(2), 327-334.

T.Z. Kalanov. (2012), Critical analysis of the foundations of differential and integral calculus. International Journal of Science and Technology, 1(2), 80-84.

Kalanov T.Z. (2012). On rationalization of the foundations of differential calculus. Bulletin of Pure and Applied Sciences, (Math.& Stat.), 31E(1), 1-7.

Kalanov T.Z. (2013). The logical analysis of the Pythagorean theorem and of the problem of irrational numbers. Asian Journal of Mathematics and Physics. ISSN: 2308-3131. 2013, 1-12.

Kalanov T.Z. (2013). The critical analysis of the Pythagorean theorem and of the problem of irrational numbers. Global Journal of Advanced Research on Classical and Modern Geometries. ISSN: 2284-5569. 2(2), 59-68.

Kalanov T.Z. (2013). On the logical analysis of the foundations of vector calculus. Journal of Computer and Mathematical Sciences, 4(4), 202-321.

Kalanov T.Z. (2013). The foundations of vector calculus: The logical error in mathematics and theoretical physics”. Unique Journal of Educational Research, 1(4), 054-059.

Kalanov T.Z. (2013). On the logical analysis of the foundations of vector calculus. Aryabhatta Journal of Mathematics & Informatics, (ISSN: 0975-7139), 5(2), 227-234.

Kalanov T.Z. (2014). On the system analysis of the foundations of trigonometry. Journal of Physics & Astronomy, (www.mehtapress.com), 3(1).

Kalanov T.Z. (2014). On the system analysis of the foundations of trigonometry. International Journal of Informative & Futuristic Research, (IJIFR, www.ijifr.com), 1(6), 6-27.

Kalanov T.Z. (2014). On the system analysis of the foundations of trigonometry. International Journal of Science Inventions Today, (IJSIT, www.ijsit.com), 3(2), 119-147.

Kalanov T.Z. (2014). On the system analysis of the foundations of trigonometry. Pure and Applied Mathematics Journal, 3(2), 26-39.

Kalanov T.Z. (2014). On the system analysis of the foundations of trigonometry. Bulletin of Pure and Applied Sciences, (Math & Stat), 33E(1), 1-27.

Kalanov T.Z. (2014). Critical analysis of the foundations of the theory of negative number. International Journal of Informative & Futuristic Research (IJIFR, www.ijifr.com), 2(4), 1132-1143. 30. Kalanov T.Z. (2015). Critical analysis of the foundations of the theory of negative numbers. International Journal of Current Research in Science and Technology, 1(2), 1-12.

Kalanov T.Z. (2015). Critical analysis of the foundations of the theory of negative numbers. Aryabhatta Journal of Mathematics & Informatics, 7(1), 3-12.

Kalanov T.Z. (2015). On the formal–logical analysis of the foundations of mathematics applied to problems in physics”. Aryabhatta Journal of Mathematics & Informatics, 7(1), 1-2.

Kalanov T.Z. (2016). Critical analysis of the foundations of pure mathematics. Mathematics and Statistics (CRESCO, http://crescopublications.org), 2(1), 2-14.

Kalanov T.Z. (2016). Critical analysis of the foundations of pure mathematics. International Journal for Research in Mathematics and Mathematical Sciences, 2(2), 15-33.

Kalanov T.Z. (2016). Critical analysis of the foundations of pure mathematics. Aryabhatta Journal of Mathematics & Informatics, 8(1), 1-14 (Article Number: MSOA-2-005).

Kalanov T.Z. (2016). Critical Analysis of the Foundations of Pure Mathematics. Philosophy of Mathematics Education Journal, ISSN 1465-2978 (Online). Editor: Paul Ernest), No. 30 (October 2016). 37. Kalanov T.Z. (2017). On the formal–logical analysis of the foundations of mathematics applied to problems in physics. Asian Journal of Fuzzy and Applied Mathematics, 5(2), 48-49.

Kalanov T.Z. (2017). The formal-logical analysis of the foundation of set theory. Bulletin of Pure and Applied Sciences, 36E(2), 329 -343.

Kalanov T.Z. (2017). The critical analysis of the foundations of mathematics. Mathematics: The Art of Scientific Delusion. LAP LAMBERT Academic Publishing (2017-12-05). ISBN-10: 620208099X. 40. Kalanov T.Z. (2018). The formal-logical analysis of the foundation of set theory. Scientific Review, 4(6), 53-63.

Kalanov T.Z. (2019) Definition of Derivative Function: Logical Error in Mathematics. MathLAB Journal, 3, 128-135.

Kalanov T.Z. (2019). Definition of Derivative Function: Logical Error in Mathematics. Academic Journal of Applied Mathematical Sciences, 5(8), 124-129.

Kalanov T.Z. (2019). Definition of Derivative Function: Logical Error in Mathematics. Aryabhatta Journal of Mathematics & Informatics, 11(2), 173-180.

Kalanov T.Z. (2019). Vector Calculus and Maxwell’s Equations: Logic Errors in Mathematics and Electrodynamics. Sumerianz Journal of Scientific Research, 2(11), 133-149. (ISSN(e): 2617-6955, ISSN(p): 2617-765X. Website: https://www.sumerianz.com).

Kalanov T.Z. (2021). Formal-logical analysis of the starting point of mathematical logic. Aryabhatta Journal of Mathematics & Informatics, 13(1), 01-14.

Kalanov T.Z. (2021). On the problem of axiomatization of geometry. Aryabhatta Journal of Mathematics & Informatics, 13(2), 151-166.

Kalanov T.Z. (2021). On the problem of axiomatization of geometry. Chemistry Biology and Physical Sciences Academic, 3(1), 8–25.