Classical Wave Equation: A Gross Error in Mathematics and Physics

Authors

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

DOI:

https://doi.org/10.48165/bpas.2023.42D.2.7

Keywords:

Mathematical Physics, Foundations of Theoretical Physics, Foundations of Mathematics, Wave Equation, Formalisms in Classical Mechanics, Newtonian Mechanics, Mechanical and Elastic Waves, String Variations, History of Science, Philosophy Of Science, Formal Logic, Higher Education

Abstract

A detailed proof of the incorrectness of the classical wave equation is proposed. The correct  methodological basis for the proof is the unity of formal logic and rational dialectics. The proof  leads to the following irrefutable statement: the classical wave equation and the derivation of the  classical wave equation are a gross error in mathematics and physics. The proof of this statement  is based on the following irrefutable main results: (1) The first gross error is the following  approximate relationship: “sine of angle is approximately equal to tangent of angle; cosine of  angle is approximately equal to 1”. This relationship means (implies) that the quantity of the  angle and the right-angled triangle do not exist. Consequently, the relationship between the  tangent of the angle and the derivative of the displacement with respect to coordinate does not  exist; (2) The second gross error is that the second-order derivative of the displacement with  respect to coordinate does not exist, because the dimensions of displacement and coordinate are  “meter”, the first-order derivative of the displacement with respect to coordinate is  dimensionless quantity (i.e. the first-order derivative of the displacement respect to coordinate  has no the dimension “meter”); (3) The third gross error is that the first-order derivative of the  displacement with respect to coordinate cannot be expanded into the Taylor series, because the  second-order derivative of the displacement with respect to coordinate does not exist; (4) The  fourth gross error is as follows: (a) the left side of the wave equation contains the condition that  time is a variable quantity, and the coordinate is a constant quantity; (b) the right side of the  wave equation contains the condition that time is a constant, and the coordinate is a variable.  This means (implies) that the equation contains contradictory conditions (propositions).  Therefore, the equation represents a violation of the formal-logical law of the lack (absence) of  contradiction; (5) The fifth gross error is that the standard derivation of the equation relies on the  following false theories: negative number theory, complex numbers theory, trigonometry, vector  calculus, differential calculus, and Newton's second law. Thus, the classical wave equation does  not satisfy the criterion of truth and is not a scientific achievement. 

References

R. Courant, D. Hilbert. Methods of Mathematical Physics. Vol 2. Interscience (Wiley), New York, (1962).

G. Whitham. Linear and Nonlinear Waves. Wiley-Interscience, New York, (1974).

G. F. Wheeler, W. P. Crummelt. “The vibrating string controversy”. Am. J. Physics, Vol. 55, No. 1, (1987), pp. 33–37.

D. R. Bland. Wave Theory and Applications. Clarendon Press, Oxford, (1988).

K. F. Graff. Wave Motion in Elastic Solids. Dover, New York, (1991).

D. C. Amstead, M. A. Karls. “Does the wave equation really work?”. Primus, Vol. XVI, No. 2, (2006), 162–176.

Juri Engelbrecht. Estonian Journal of Engineering, 2013, 19, 4, 273–282.

F. S. Crawford, Jr. Waves: Berkeley Physics Course. Vol. 3. McGraw-Hill Book Company, 1968.

V.I. Smirnov. Higher Mathematics Course. Vol. 2. Moscow, Nauka, 1974. [10] T.Z. Kalanov, “Critical analysis of the foundations of differential and integral calculus”. MCMS (Ada Lovelace Publications), (2011), pp. 34-40.

T.Z. Kalanov, “Logical analysis of the foundations of differential and integral calculus”. Indian Journal of Science and Technology, Vol. 4, No. 12 (2011), pp. 1786-1789.

T.Z. Kalanov, “Logical analysis of the foundations of differential and integral calculus”. Bulletin of Pure and Applied Sciences, Vol. 30 E (Math.& Stat.), No. 2 (2011), pp. 327-334.

T.Z. Kalanov, “Critical analysis of the foundations of differential and integral calculus”. International Journal of Science and Technology, Vol. 1, No. 2 (2012), pp.80-84.

T.Z. Kalanov, “On rationalization of the foundations of differential calculus”. Bulletin of Pure and Applied Sciences, Vol. 31 E (Math. & Stat.), No. 1 (2012), pp. 1-7.

T.Z. Kalanov, “The critical analysis of the Pythagorean theorem and of the problem of irrational numbers”. Basic Research Journal of Education Research and Review, (ISSN 2315-6872, http//www.basicresearchjournals.org),

Vol. 2, No. 4 (2013), pp. 59-65.

T.Z. Kalanov, “The logical analysis of the Pythagorean theorem and of the problem of irrational numbers”. Asian Journal of Mathematics and Physics, (ISSN 2308-3131, http://scienceasia.asia), Vol. 2013 (2013), pp. 1-12.

T.Z. Kalanov, “The critical analysis of the Pythagorean theorem and of the problem of irrational numbers”. Bulletin of Pure and Applied Sciences, Vol. 32 (Math & Stat), No. 1 (2013), pp. 1-12.

T.Z. Kalanov, “On the logical analysis of the foundations of vector calculus”. International Journal of Scientific Knowledge. Computing and Information Technology, Vol. 3, No. 2 (2013), pp. 25-30.

T.Z. Kalanov, “On the logical analysis of the foundations of vector calculus”. International Journal of Multidisciplinary Academic Research, Vol. 1, No. 3 (2013).

T.Z. Kalanov, “On the logical analysis of the foundations of vector calculus”.

Journal of Computer and Mathematical Sciences, Vol. 4, No. 4 (2013), pp. 202- 321.

T.Z. Kalanov, “On the logical analysis of the foundations of vector calculus”. Journal of Research in Electrical and Electronics Engineering (ISTP-JREEE), (ISSN: 2321-2667), Vol. 2, No. 5 (2013), pp. 1-5.

T.Z. Kalanov, “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), Vol. 2, No. 2 (2013), pp. 59-68.

T.Z. Kalanov, “On the logical analysis of the foundations of vector calculus”. Research Desk, (ISSN: 2319-7315), Vol. 2, No. 3 (2013), pp. 249-259.

T.Z. Kalanov, “The foundations of vector calculus: The logical error in mathematics and theoretical physics”. Unique Journal of Educational Research, Vol. 1, No. 4 (2013), pp. 054-059.

T.Z. Kalanov, “On the logical analysis of the foundations of vector calculus”. Aryabhatta Journal of Mathematics & Informatics, (ISSN: 0975-7139), Vol. 5, No. 2 (2013), pp. 227-234.

T.Z. Kalanov, “Critical analysis of the mathematical formalism of theoretical physics. II. Foundations of vector calculus”. Bulletin of Pure and Applied Sciences, Vol. 32 E (Math & Stat), No. 2 (2013), pp.121-130.

T.Z. Kalanov, “On the system analysis of the foundations of trigonometry”. Journal of Physics & Astronomy, (www.mehtapress.com), Vol. 3, No. 1 (2014).

T.Z. Kalanov, “On the system analysis of the foundations of trigonometry”. International Journal of Informative & Futuristic Research, (IJIFR, www.ijifr.com), Vol. 1, No. 6 (2014), pp. 6-27.

T.Z. Kalanov, “On the system analysis of the foundations of trigonometry”. International Journal of Science Inventions Today, (IJSIT,

www.ijsit.com), Vol. 3, No. 2 (2014), pp. 119-147.

T.Z. Kalanov, “On the system analysis of the foundations of trigonometry”. Pure and Applied Mathematics Journal, Vol. 3, No. 2 (2014), pp. 26-39.

T.Z. Kalanov, “On the system analysis of the foundations of trigonometry”. Bulletin of Pure and Applied Sciences, Vol. 33E (Math & Stat), No. 1 (2014), pp. 1-27.

T.Z. Kalanov. “Critical analysis of the foundations of the theory of negative number”. International Journal of Informative & Futuristic Research (IJIFR, www.ijifr.com), Vol. 2, No. 4 (2014), pp. 1132-1143.

T.Z. Kalanov. “Critical analysis of the foundations of the theory of negative numbers”. International Journal of Current Research in Science and Technology, Vol. 1, No. 2 (2015), pp. 1-

T.Z. Kalanov. “Critical analysis of the foundations of the theory of negative numbers”. Aryabhatta Journal of Mathematics & Informatics, Vol. 7, No. 1 (2015), pp. 3-12.

T.Z. Kalanov. “On the formal–logical analysis of the foundations of mathematics applied to problems in physics”. Aryabhatta Journal of Mathematics & Informatics, Vol. 7, No. 1 (2015), pp. 1-2.

T.Z. Kalanov. “Critical analysis of the foundations of pure mathematics”. Mathematics and Statistics (CRESCO, http://crescopublications.org), Vol. 2, No. 1 (2016), pp. 2-14.

T.Z. Kalanov. “Critical analysis of the foundations of pure mathematics”. International Journal for Research in Mathematics and Mathematical Sciences, Vol. 2, No. 2 (2016), pp. 15-33.

T.Z. Kalanov. “Critical analysis of the foundations of pure mathematics”. Aryabhatta Journal of Mathematics & Informatics, Vol. 8, No. 1 (2016), pp. 1-14 (Article Number: MSOA-2-005).

T.Z. Kalanov. “On the formal–logical analysis of the foundations of mathematics applied to problems in

physics”. Asian Journal of Fuzzy and Applied Mathematics, Vol. 5, No. 2 (2017), pp. 48-49.

T.Z. Kalanov. “On the correct formulation of the starting point of classical mechanics”. International journal of Chemistry, Mathematics and Physics (IJCMP, AI Publications, www.aipublications.com), Vol. 1, No. 1 (2017), pp. 27-47.

T.Z. Kalanov. “On the correct formulation of the starting point of classical mechanics”. Advances in Physics Theories and Applications, Vol. 64, (2017), pp. 27-46.

T.Z. Kalanov. “On the correct formulation of the starting point of classical mechanics”. International Journal of Advanced Research in Physical Science. Vol. 4, No. 6 (2017), pp. 1-22.

T.Z. Kalanov. “On the correct formulation of the starting point of classical mechanics”. International educational scientific research journal. Vol. 3, No. 6 (2017), pp. 56-73.

T.Z. Kalanov. “The formal-logical analysis of the foundation of set theory”. Bulletin of Pure and Applied Sciences, Vol. 36E, No. 2 (2017), pp. 329 -343.

T.Z. Kalanov. The critical analysis of the foundations of mathematics. Mathematics: The Art of Scientific Delusion. LAP LAMBERT Academic Publishing (2017-12-05). ISBN-10: 620208099X.

T.Z. Kalanov. “On the correct formulation of the starting point of classical mechanics”. Physics & Astronomy (International Journal). Vol. 2, No. 2 (2018), pp. 79-92.

T.Z. Kalanov. “The formal-logical analysis of the foundation of set theory”. Scientific Review, Vol. 4, No. 6 (2018), pp. 53-63.

T.Z. Kalanov, “Definition of Derivative Function: Logical Error In Mathematics”. MathLAB Journal, Vol. 3, (2019), pp. 128-135.

T.Z. Kalanov, “Definition of Derivative Function: Logical Error in Mathematics”. Academic Journal of

Applied Mathematical Sciences, Vol. 5, No. 8, (2019), pp. 124-129.

T.Z. Kalanov, “Definition of Derivative Function: Logical Error in Mathematics”. Aryabhatta Journal of Mathematics & Informatics, Vol. 11, No. 2 (2019), pp. 173-180.

T.Z. Kalanov, “Vector Calculus and Maxwell’s Equations: Logic Errors in Mathematics and Electrodynamics”. Open Access Journal of Physics, Vol. 3, No. 4, (2019), pp. 9-26.

T.Z. Kalanov, “Vector Calculus and Maxwell’s Equations: Logic Errors in Mathematics and Electrodynamics”. Sumerianz Journal of Scientific

Research, Vol. 2, No. 11, (2019), pp. 133- 149. (ISSN(e): 2617-6955, ISSN(p): 2617- 765X. Website: https://www.sumerianz.com).

T.Z. Kalanov, “Formal-logical analysis of the starting point of mathematical logic”. Aryabhatta Journal of Mathematics & Informatics, Vol.13, No. 1, (2021), pp. 01-14.

T.Z. Kalanov, “On the problem of axiomatization of geometry”. Aryabatta Journal of Mathematics & Informatics, Vol.13, No.2, (2021), pp. 151-166. [55] T.Z. Kalanov, “On the problem of axiomatization of geometry”. Chemistry Biology and Physical Sciences Academic, 3(1), (2021), pp. 8–25.

T.Z. Kalanov, “Theory of Harmonic Oscillations: A Gross Error in Physics”. Bulletin of Pure and Applied Science: Physics, Vol. 41D, No.2, (2022), pp. 1-7 (Print version ISSN 0970 6569. Online version ISSN 2320 3218. DOI: 10.5958/2320-3218.2022.00001.X).

T.Z. Kalanov, “On fundamental errors in trigonometry”. Bulletin of Pure and Applied Sciences (Section - E - Mathematics & Statistics), Vol. 41E, No.1, (2022), pp. 16-33.

T.Z. Kalanov, “Theory of complex numbers: A gross error in mathematics and physics”. Bulletin of Pure and Applied Sciences (Section - E -

Mathematics & Statistics), Vol. 41E, No.1, (2022), pp. 61-68.

T.Z. Kalanov, “Differential calculus: A gross error in mathematics”. Bulletin of Pure and Applied Sciences (Section - E - Mathematics & Statistics), be published in 2023.

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Published

2023-12-22

Issue

Vol. 42 No. 2 (2023): Bulletin of Pure and Applied Science-Physics (Jul-Dec) 2023

Section

Articles

How to Cite

Classical Wave Equation: A Gross Error in Mathematics and Physics. (2023). Bulletin of Pure and Applied Sciences – Physics, 42(2), 98–107. https://doi.org/10.48165/bpas.2023.42D.2.7