Critical Analysis of Field Theory
DOI:
https://doi.org/10.64137/31082637/IJMAR-V1I2P104Keywords:
Foundations of mathematics, Vector and tensor analysis, Field theory, Foundations of theoretical physics, Mathematical physics, Philosophy of mathematicsAbstract
A detailed proof of the incorrectness of standard field theory (vector analysis) is proposed. The correct methodological basis for this proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable statement: standard field theory (vector analysis) is a gross error. Gross errors are as follows: (1) field theory is based on differential and integral calculus, which is an incorrect theory; (2) field theory is based on vector calculus, which is an incorrect theory; (3) field theory is formulated within the framework of a geometric coordinate system. But mathematical and physical quantities have no dimension “meter” and cannot be presented (be defined, exist) within the framework of a geometric coordinate system; (4) in the point of view of formal logic and dialectics, the concepts “field in abstracto” and “mathematical field” are identical and meaningless concepts. “Field in abstracto” and “mathematical field” have neither physical properties nor geometric properties; (5) the standard definition of a field is: “A field is a part of space, each point of which corresponds (conforms) to a certain value of some physical quantity”. In the point of view of formal logic, the term “correspondence” is meaningless. The subject-predicate conjunction in a definition must be either “is” or “is not”. Replacement of a dimensionless quantity in mathematical definitions and expressions by a dimensional quantity is an inadmissible operation; 6) a physical field has no points (i.e., values of a physical quantity) in a geometric coordinate system. A material point has coordinates, but a material point is not a point of a physical field. The error is in the assertion that the coordinates of a material point determine (define, identify) the value of a physical quantity; that the value of a physical quantity determines (defines, identifies) the coordinates of a material point; (7) the absurdity is that a dimensionless (i.e., mathematical) quantity is identical to a dimensional (i.e., physical) quantity.
References
[1] V. I. Smirnov. ‘Course in Higher Mathematics’, Volume II. Nauka, Moscow, 1964.
[2] A. F. Bermant. ‘A Short Course in Mathematical Analysis’. Nauka Publishing House, Moscow, 1986.
[3] The Feynman Lectures on Physics Vol. II Ch. 2: Differential Calculus of Vector Fields. Addison-Wesley, (1963). (Library of Congress. Control Number: 2010938208).
[4] "Vector analysis", Encyclopedia of Mathematics, EMS Press, 2001 [1994].
[5] “Vector analysis; a text-book for the use of students of mathematics and physics : Gibbs, J. Willard (Josiah Willard), 1839-1903 : Free Download, Borrow, and Streaming : Internet Archive,” Internet Archive, 1901. https://archive.org/details/vectoranalysiste00gibbiala/page/n7/mode/2up
[6] H.F. Davis, A.D. Snider. “Introduction to Vector Analysis”. Wm. C. Brown Publishers, Dubuque, IA. (1995).
[7] M. Rahman and I. Mulolani, Applied Vector Analysis. CRC Press, 2001.
[8] M. Schwartz, S. Green, W.A. Rutledge. “Vector Analysis with Applications to Geometry and Physics”. Harper & Brothers, New York, NY. (1960).
[9] E.C. Young. “Vector and Tensor Analysis”. Marcel Dekker, New York, NY. (1993).
[10] T. A. A. Broadbent, “A History of Vector Analysis. By M. J. Crowe. Pp. xvii, 270. 123s. 1967 (University of Notre Dame Press).,” The Mathematical Gazette, vol. 53, no. 384, pp. 181–184, May 1969, doi: https://doi.org/10.2307/3614559.
[11] E.B. Wilson. “Vector Analysis”. Yale University Press, New Haven, CT, (1958).
[12] M. R. Spiegel, S.Lipschutz, and D. Spellman, Schaum’s outline of theory and problems of vector analysis and an introduction to tensor analysis. New York: Mcgraw-Hill, 2009.
[13] H. Davis, A. Snider. “Introduction to Vector Analysis”, McGraw-Hill, New York, (1995).
[14] T.Z. Kalanov, “Theoretical analysis of Einstein’s relationship of detailed balance. I”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 11 (1990), pp. 22-24.
[15] T.Z. Kalanov, “Theoretical analysis of Einstein’s relationship of detailed balance. II”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 1 (1991), pp. 21-23.
[16] T.Z. Kalanov, “On the statistics of the photon gas”. Reports of the Academy of Sciences of the USSR, Vol. 316, No. 1 (1991), p. 100.
[17] T.Z. Kalanov, “On the statistics of the electron gas”. Reports of the Academy of Sciences of the USSR, Vol. 316, No. 6 (1991), p. 1386.
[18] T.Z. Kalanov, “On the quantum-statistical theory of ideal monatomic gas. I”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 4 (1991), pp. 20-22.
[19] T.Z. Kalanov, “On statistics of the systems with variable number of particles. I”. Reports of the Academy of Sciences of the Republic of Uzbekistan,No. 7 (1991), pp. 26-28.
[20] T.Z. Kalanov, “On statistics of the systems with variable number of particles. II”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 8 (1991), pp. 23-25.
[21] T.Z. Kalanov, “On the quantum-statistical theory of ideal monatomic gas. II”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 8 (1991), pp. 23-25.
[22] T.Z. Kalanov, “On the quantum-statistical theory of thermal radiation.”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 2 (1992), pp. 20-22.
[23] T.Z. Kalanov, “Physics without Boltzmann’s “statistical entropy””. Reports of the Academy of Sciences of the Republic of Uzbekistan,No. 4-5 (1992), pp. 43-45.
[24] T.Z. Kalanov, “On the problem of substantiation and formulation of unitary basic principles of statistical physics and physical kinetics”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 10-11 (1992), pp. 44-46.
[25] T.Z. Kalanov, “On a approach to the problem of substantiation and formulation of unitary basic principles of statistical physics and physical kinetics”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 1 (1993), pp. 24-26.
[26] T.Z. Kalanov, “The correct theoretical analysis of the Michelson-Morley experiments”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 11-12 (1995), p. 22.
[27] T.Z. Kalanov, “Proof of non-correctness of the Lorentz transformation”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 1-2 (1996), p. 32.
[28] T.Z. Kalanov, “On the theory of relative motion”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 12 (1997), p. 15.
[29] T.Z. Kalanov, “On the theory of time”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 5 (1998), p. 24.
[30] T.Z. Kalanov, “Kinematics of material point: Modern analysis”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 7 (1999), p. 9.
[31] T.Z. Kalanov, “ : The most urgent problem of our time”. Reports of the Academy of Sciences of the Republic of Uzbekistan, No. 5 (1999), p. 9.
[32] T.Z. Kalanov, “Correct quantum-statistical description of ideal systems within the framework of master equation”. Proc. XXVth ICPIG, Nagoya, Japan. Ed. By Toshio Goto / Japan: Nagoya Univ., Vol. 3 (2001), p. 235.
[33] Zikirillayevich Kalanov, Temur, “On logical errors lying in the base of special theory of relativity,” APS April Meeting Abstracts, vol. 46, no. 2, p. K20.016, Apr. 2001, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2001APS..APRK20016Z/abstract
[34] Kalanov, Temur Z, “On a Solution of the Problem of Unitarization of the Elementary Principles of Statistical Physics and Physical Kinetics,” APS April Meeting Abstracts, p. O12.009, Apr. 2002, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2002APS..APRO12009K/abstract
[35] Kalanov, Temur Z, “On the main Errors underlying Statistical Physics,” APS April Meeting Abstracts, p. O12.010, Apr. 2002, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2002APS..APRO12010K/abstract
[36] T.Z. Kalanov, “On the essence of time”. Bulletin of the Amer. Phys. Soc. (April Meeting), Vol. 47, No. 2 (2002), p. 164.
[37] T.Z. Kalanov, “On a new basis of quantum theory”. Bulletin of the Amer. Phys. Soc. (April Meeting), Vol. 47, No. 2 (2002), p. 164.
[38] T.Z. Kalanov, “On the problem of the correspondence principle”. Bulletin of the Amer. Phys. Soc. (April Meeting), Vol. 48, No. 2 (2003), p. 153.
[39] T.Z. Kalanov, “On a new theory of the system of reference”. Bulletin of the Amer. Phys. Soc. (April Meeting), Vol. 48, No. 2 (2003), pp. 153-154.
[40] T.Z. Kalanov, “On the essence of space”. Bulletin of the Amer. Phys. Soc. (April Meeting), Vol. 48, No. 2 (2003), p. 154.
[41] Kalanov, Temur Z, “For the Problem of Knowledge of the Universe,” APS April Meeting Abstracts, vol. 2003, p. Q1.016, Apr. 2003,. [Online]. Available: https://ui.adsabs.harvard.edu/abs/2003APS..APR.Q1016K/abstract
[42] Kalanov, Temur Z, “The Theory of Relativity: An Error of the Transformation of Coordinates,” APS April Meeting Abstracts, vol. 2003, p. Q1.018, Apr. 2003, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2003APS..APR.Q1018K/abstract
[43] T.Z. Kalanov, “On logical errors underlying the special theory of relativity”. Journal of Theoretics (USA). Vol. 6-1 (2004).
[44] T.Z. Kalanov, “The correct theoretical analysis of the foundations of quantum mechanics”. Journal of Ultra Scientists of Physical Sciences (International Journal of Physical Sciences, India), Vol. 16, No. 2 (2004), pp. 191-198.
[45] Kalanov, Temur Z, “On the Correct Theoretical Analysis of the Foundations of Quantum Mechanics,” APS April Meeting Abstracts, p. L1.019, Apr. 2005,
[46] [Online]. Available: https://ui.adsabs.harvard.edu/abs/2005APS..APR.L1019K/abstract
[47] Kalanov, Temur Z, “On a New Theory of Physical Vacuum,” APS April Meeting Abstracts, p. L1.017, Apr. 2005,. [Online]. Available: https://ui.adsabs.harvard.edu/abs/2005APS..APR.L1017K/abstract
[48] Kalanov, Temur Z, “On a New Approach to the Solution of the Problem of Quantization of Energy,” APS April Meeting Abstracts, p. D1.066, Apr. 2006, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2006APS..APR.D1066K/abstract
[49] Kalanov, Temur Z, “On a New Theory of the Black Hole,” APS April Meeting Abstracts, p. D1.064, Apr. 2006, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2006APS..APR.D1064K/abstract
[50] Kalanov, Temur Z, “The Problem of the SETI: A Methodological Error in Cosmology and Astrophysics,” APS April Meeting Abstracts, p. D1.057, Apr. 2006, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2006APS..APR.D1057K/abstract
[51] Kalanov, Temur Z, “On the Hypothesis of Universe’s ``System Block’’,” Bulletin of the American Physical Society, 2006. https://meetings.aps.org/Meeting/APR06/Session/D1.58
[52] Kalanov, Temur Z, “On the Correct Formulation of the First Law of Thermodynamics,” APS April Meeting Abstracts, p. D1.055, Apr. 2006, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2006APS..APR.D1055K/abstract
[53] T.Z. Kalanov, “The second law of thermodynamics: Mathematical error”. Bulletin of the Amer. Phys. Soc. (April Meeting), Vol. 51, No. 2 (2006), p. 60.
[54] Kalanov, Temur Z, “Bose’s Method: A Logical Error,” Bulletin of the American Physical Society, 2006. https://meetings.aps.org/Meeting/APR06/Session/D1.59
[55] Kalanov, Temuz Z, “Dirac’s Theory of Physical Vacuum: Continuation of Bose’s Logical Errors,” APS April Meeting Abstracts, p. D1.060, Apr. 2006, [Online]. Available: http://ui.adsabs.harvard.edu/abs/2006APS..APR.D1060K/abstract
[56] Kalanov, Temur Z, “Bose-Einstein Statistics and Fermi-Dirac Statistics: A Logical Error,” APS April Meeting Abstracts, p. D1.061, Apr. 2006, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2006APS..APR.D1061K/abstract
[57] Kalanov, Temur Z, “On the Correct Analysis of the Maxwell Distribution,” APS April Meeting Abstracts, p. D1.062, Apr. 2006, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2006APS..APR.D1062K/abstract
[58] Kalanov, Temur Z, “On the Correct Analysis of the Foundations of the Special Theory of Relativity,” APS April Meeting Abstracts, p. L1.049, Apr. 2007, Accessed:. [Online]. Available: https://ui.adsabs.harvard.edu/abs/2007APS..APR.L1049K/abstract
[59] Kalanov, Temur Z, “On the Correct Analysis of the Foundations of Theoretical Physics,” APS April Meeting Abstracts, p. L1.048, Apr. 2007, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2007APS..APR.L1048K/abstract
[60] Kalanov, Temur Z, “On the Hypothesis of Control of the Universe,” APS April Meeting Abstracts, p. L1.050, Apr. 2007, [Online]. Available:
[61] Kalanov, Temur Z, “Theoretical Model of God: The Key to Correct Exploration of the Universe,” APS April Meeting Abstracts, p. L1.051, Apr. 2007,
[62] [Online]. Available: https://ui.adsabs.harvard.edu/abs/2007APS..APR.L1051K/abstract
[63] T.Z. Kalanov, “Critical analysis of the special theory of relativity”. Bulletin of Pure and Applied Sciences, Vol. 26D, No. 1 (2007), pp. 1-15.
[64] T.Z. Kalanov, “The correct theoretical analysis of the foundations of classical thermodynamics”. Bulletin of Pure and Applied Sciences, Vol. 26D, No. 2 (2007), pp. 109-118.
[65] T.Z. Kalanov, “The correct theoretical analysis of the foundations of classical thermodynamics”. Indian Journal of Science and Technology, Vol. 2, No. 1 (2009), pp. 12-17.
[66] T.Z. Kalanov, “On the Boltzmann distribution”. Galilean Electrodynamics, Vol. 21, Special Issues 1 (2010), p. 2.
[67] T. Kalanov, “The correct theory of photon gas,” Indian Journal of Science and Technology, vol. 2, no. 2, 2009, [Online]. Available: https://sciresol.s3.us-east-2.amazonaws.com/IJST/Articles/2009/Issue-2/Article1.pdf
[68] T. Kalanov, “On a New Analysis of the Problem of the Planck Constant,” APS April Meeting Abstracts, p. E1.077, May 2009, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2009APS..APR.E1077K/abstract
[69] Z. Kalanov, “Theoretical model of God: proof of existence,” Indian Journal of Science and Technology, vol. 2, no. 3, pp. 1–9, Mar. 2009, doi: https://doi.org/10.17485/ijst/2009/v2i3.19.
[70] Kalanov, Temur Z, “On a New Analysis of the Foundations of Classical Mechanics. I. Dynamics,” APS April Meeting Abstracts, vol. 2010, p. W1.001, Feb. 2010, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2010APS..APR.W1001K/abstract
[71] T.Z. Kalanov, “The theoretical model of God: Proof of the existence and the uniqueness of God”. Scientific GOD Journal, Vol. 1, No. 2 (2010), pp. 85-97.
[72] Temur Kalanov, “The Modern Analysis of the Problem of Multisecting an Angle,” Prespacetime Journal, vol. 1, no. 3, 2010, Available: https://prespacetime.com/index.php/pst/article/view/34
[73] Temur Kalanov, “The Crisis in Theoretical Physics: The Problem of Scientific Truth,” Prespacetime Journal, vol. 1, no. 5, 2010[Online]. Available: https://prespacetime.com/index.php/pst/article/view/68
[74] Temur Kalanov, The Critical Analysis of the Foundations of Theoretical Physics. LAP Lambert Academic Publishing, 2010.
[75] Temur Kalanov, “Analysis of the Problem of Relation between Geometry and Natural Sciences,” Prespacetime Journal, vol. 2, no. 1, 2011, [Online]. Available: https://mail.prespacetime.com/index.php/pst/article/view/143
[76] Kalanov, Temur Z, “On the Critical Analysis of Classical Electrodynamics,” APS April Meeting Abstracts, vol. 2011, p. D1.024, Apr. 2011, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2011APS..APR.D1024K/abstract
[77] T.Z. Kalanov, “Critical analysis of the foundations of differential and integral calculus”. MCMS (Ada Lovelace Publications), (2011), pp. 34-40.
[78] T. Z. Kalanov, “Logical analysis of the foundations of differential and integral calculus,” Indian Journal of Science and Technology, vol. 4, no. 12, pp. 1786–1789, Dec. 2011, doi: https://doi.org/10.17485/ijst/2011/v4i12.35.
[79] T. Z. Kalanov, “Logical analysis of the foundations of differential and integral calculus,” Bulletin of Pure & Applied Sciences- Mathematics and Statistics, vol. 30e, no. 2, pp. 325–332, 2011, [Online]. Available: https://indianjournals.com/article/bpasms-30e-2-018
[80] 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.
[81] T.Z. Kalanov, “Critical analysis of Bose–Einstein and Fermi–Dirac statistics”. Elixir (Statistics), No. 45 (2012), pp. 7657-7659.
[82] 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.
[83] T.Z. Kalanov, “The Boltzmann distribution: a logical error”. Elixir (Adv. Pow.), No. 49 (2012), pp. 9935-9936.
[84] T.Z. Kalanov, “The correct analysis of theory of photon gas”. Elixir (Nuclear & Radiation Physics), No. 50 (2012), pp. 10197-10205.
[85] Kalanov, Temur Z, “On Logical Error Underlying Classical Mechanics,” APS April Meeting Abstracts, vol. 2012, p. E1.050, Mar. 2012, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2012APS..APR.E1050K/abstract
[86] Kalanov, Temur Z, “Critical Analysis of the Mathematical Formalism of Theoretical Physics. I. Foundations of Differential and Integral Calculus,” APS April Meeting Abstracts, vol. 2013, p. K2.004, Apr. 2013, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2013APS..APR.K2004K/abstract
[87] 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.
[88] T. Kalanov, “The Critical Analysis of the Pythagorean Theorem and of the Problem of Irrational Numbers.” [Online]. Available: https://vixra.org/pdf/1305.0013v1.pdf
[89] 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.
[90] 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.
[91] T.Z. Kalanov, “On the logical analysis of the foundations of vector calculus”. International Journal of Multidisciplinary Academic Research, Vol. 1, No. 3 (2013).
[92] 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.
[93] 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.
[94] T. 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, vol. 2, no. 2, pp. 59–68, Available: https://geometry-math-journal.ro/pdf/Volume2-Issue2/Kalanov.pdf
[95] 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.
[96] 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.
[97] 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.
[98] T.Z. Kalanov, “Critical analysis of the mathematical formalism of theoretical physics. II. Foundations of vector calculus”. Unique Journal of Engineering and Advanced Sciences (UJEAS, www.ujconline.net), , Vol. 01, No. 01 (2013).
[99] T. Z. Kalanov, “Critical analysis of the mathematical formalism of theoretical physics. II. foundations of vector calculus,” Bulletin of Pure & Applied Sciences- Mathematics and Statistics, vol. 32e, no. 2, pp. 121–130, 2011, [Online]. Available: https://indianjournals.com/article/bpasms-32e-2-001
[100] T.Z. Kalanov, “Critical analysis of the mathematical formalism of theoretical physics. II. Foundations of vector calculus”. Bulletin of the Amer. Phys. Soc., (April Meeting), Vol. 59, No. 5 (2014).
[101] T.Z. Kalanov, “Critical analysis of the mathematical formalism of theoretical physics. III. Pythagorean theorem”. Bulletin of the Amer. Phys. Soc., (April Meeting), Vol. 59, No. 5 (2014).
[102] T.Z. Kalanov, “On the system analysis of the foundations of trigonometry”. Journal of Physics & Astronomy, (www.mehtapress.com), Vol. 3, No. 1 (2014).
[103] 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.
[104] 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.
[105] 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.
[106] T. Z. Kalanov, “On the system analysis of the foundations of trigonometry,” Bulletin of Pure & Applied Sciences- Mathematics and Statistics, vol. 33e, no. 1, pp. 1–27, 2014, Available: https://indianjournals.com/article/bpasms-33e-1-001
[107] 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.
[108] Kalanov, Temur Z, “Critical Analysis of the Mathematical Formalism of Theoretical Physics. IV. Foundations of Trigonometry,” APS April Meeting Abstracts, vol. 2015, p. T1.041, Apr. 2015, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2015APS..APR.T1041K/abstract
[109] Kalanov, Temur Z, “Critical Analysis of the Mathematical Formalism of Theoretical Physics. V. Foundations of the Theory of Negative Numbers,” APS April Meeting Abstracts, vol. 2015, p. T1.042, Apr. 2015, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2015APS.APR.T1042K/abstract
[110] Kalanov, Temur Z, “Where Are the Logical Errors in the Theory of Big Bang?,” APS April Meeting Abstracts, vol. 2015, p. T1.043, Apr. 2015, Accessed:. [Online]. Available: https://ui.adsabs.harvard.edu/abs/2015APS..APR.T1043K/abstract
[111] T.Z. Kalanov. “Where are the logical errors in the theory of Big Bang?” Scientific GOD Journal, Vol. 5, No. 5 (2014), p. 432-433.
[112] 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. 1-12.
[113] 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.
[114] 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.
[115] T.Z. Kalanov. “On the formal-logical analysis of the foundations of mathematics applied to problems in physics”. Bulletin of the Amer. Phys. Soc., (April Meeting), (2016).
[116] 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.
[117] 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.
[118] 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).
[119] T.Z. Kalanov. “Critical Analysis of the Foundations of Pure Mathematics”.
[120] Philosophy of Mathematics Education Journal, ISSN 1465-2978 (Online). Editor: Paul Ernest), No. 30 (October 2016).
[121] T.Z. Kalanov. “On the correct formulation of the law of the external photoelectric effect”. Journal of Review in Sciences (Scientific Research Gate), Vol. 1, No. 1 (2016), pp. 1–9.
[122] T.Z. Kalanov. “On the correct formulation of the law of the external photoelectric effect”. International Journal of Informative & Futuristic Research (IJIFR), Vol. 4, No. 1 (2016), pp. 4801-4811.
[123] T.Z. Kalanov. “Man vs. computer: Difference of the essences. The problem of the scientific creation”. Journal of Review in Sciences (Scientific Research Gate), Vol. 1, No. 1 (2016), pp. 10-34.
[124] T.Z. Kalanov. “Man vs. computer: Difference of the essences, The problem of the scientific creation”. International Journal of Scientific Research in Computer Science, Engineering and Information Technology (IJSRCSEIT, ISSN: 2456-3307), Vol. 1, No. 2 (2016), pp. 120-14.
[125] T.Z. Kalanov. “Man vs. computer: Difference of the essences. The problem of the scientific creation”. International Journal of Contemporary Research and Review (http://ijcrr.in/index.php/ijcrr), Vol. 7, No. 12 (2016).
[126] T.Z. Kalanov. “Man vs. computer: Difference of the essences. The problem of the scientific creation”. International Journal of Multidisciplinary Education and Research (ISSN: 2455-4588), Vol. 1, No. 9, (2016), pp. 15-31.
[127] T.Z. Kalanov. “Man versus computer: Difference of the essences, The problem of the scientific creation”. BRAIN: Broad Research in Artificial Intelligence and Neuroscience, (ISSN: 2067-3957), Vol. 8, No. 2 (2017), pp. 151-178.
[128] Kalanov, Temur Z, “On the Correct Formulation of the Law of the External Photoelectric Effect,” APS April Meeting Abstracts, vol. 2017, p. F1.035, 2017, [Online]. Available: https://ui.adsabs.harvard.edu/abs/2017APS..APR.F1035K/abstract
[129] 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, Apr. 2017, doi: https://doi.org/10.24203/ajfam.v5i2.2530.
[130] 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.
[131] 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.
[132] 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.
[133] 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.
[134] T.Z. Kalanov. “The formal-logical analysis of the foundation of set theory”.
[135] Bulletin of Pure and Applied Sciences, Vol. 36E, No. 2 (2017), pp. 329 -343.
[136] [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.
[137] 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.
[138] T.Z. Kalanov. “On new foundations of theory of atom”. International Journal of Advanced Research in Physical Science (IJARPS), Vol. 5, No. 1 (2018), pp. 1-9.
[139] T.Z. Kalanov. “The formal-logical analysis of the foundation of set theory”. Scientific Review, Vol. 4, No. 6 (2018), pp. 53-63.
[140] T.Z. Kalanov, “The Doctrine of Reality: A New Paradigm of Science” Journal of Metaphysics and Connected Consciousness. November 18, 2018.
[141] T.Z. Kalanov, “The Doctrine of Reality: A New Paradigm of Science”. Global Scientific Journal, Vol. 6, No. 12 (2018), pp. 59-71.
[142] T.Z. Kalanov, “The Doctrine of Reality: A New Paradigm of Science”. Scientific Review, Vol. 5, No. 1 (2019), pp. 24-32.
[143] T.Z. Kalanov, “The Doctrine of Reality: A New Paradigm of Science”. Scientific GOD Journal, Vol. 10, No. 1 (2019), pp. 1-15.
[144] T.Z. Kalanov, “Hubble Law, Doppler Effect and the Model of "Hot" Universe: Errors in Cosmology”. Open Access Journal of Physics (USA), Vol. 3, No. 2 (2019), pp. 1-16.
[145] T.Z. Kalanov, “Hubble Law, Doppler Effect and the Model of "Hot" Universe: Errors in Cosmology”. Indian Journal of Physics and Application, Vol. 4 No. 1 (2019).
[146] T. Z. Kalanov, “Definition of Derivative Function: Logical Error in Mathematics,” Arya Bhatta Journal of Mathematics and Informatics, vol. 11, no. 2, pp. 173–180, 2019, [Online]. Available: https://indianjournals.com/article/abjmmi-11-2-001
[147] [143] 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.
[148] [144] T.Z. Kalanov, “Definition of Derivative Function: Logical Error in Mathematics”. Aryabhatta Journal of Mathematics & Informatics, Vol. 11, No. 2 (2019), pp. 173-180.
[149] 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.
[150] .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).
[151] T.Z. Kalanov, “Definition of work: Unsolved Problem in Classical Mechanics”. Bulletin of Pure and Applied Sciences (Section D –Physics), Vol. 39D (Physics), No. 1, (2020), pp. 137-148.
[152] T.Z. Kalanov, “Definition of work: Unsolved Problem in Classical Mechanics”. Open Access Journal of Physics, Vol. 4, No. 1, (2020), pp. 29-39. (ISSN 2637-5826).
[153] T.Z. Kalanov, “The doctrine of reality: A new paradigm of science”. Global Scientific Journal (GSJ, www.globalscientificjournal.com), Vol. 6, No. 12, (2018). (Online: ISSN 2320-186).
[154] 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.
[155] T.Z. Kalanov, “On the problem of axiomatization of geometry”. Aryabatta Journal of Mathematics & Informatics, Vol.13, No.2, (2021), pp. 151-166.
[156] T.Z. Kalanov, “On the problem of axiomatization of geometry”. Chemistry Biology and Physical Sciences Academic, 3(1), (2021), pp. 8–25.
[157] T. Z. Kalanov, “On fundamental errors in trigonometry,” Bulletin of Pure & Applied Sciences- Mathematics and Statistics, vol. 41e, no. 1, pp. 16–33, 2022, doi: https://doi.org/10.5958/2320-3226.2022.00004.2.
[158] T. Z. Kalanov, “Theory of complex numbers: Gross error in mathematics and physics,” Bulletin of Pure & Applied Sciences- Mathematics and Statistics, vol. 41e, no. 1, Jun. 2022, doi: https://doi.org/10.5958/2320-3226.2022.00009.1.
[159] T.Z. Kalanov, “Differential Calculus: a gross error in mathematics”.
[160] Bull. Pure Appl. Sci. Sect. E Math. Stat. 42E(2), pp. 109–121 (2023). (e-ISSN:2320-3226, Print ISSN:0970-6577. DOI 10.48165/bpas.2023.42E.2.2).
[161] T. Z. Kalanov, “Classical Wave Equation: A Gross Error in Mathematics and Physics,” Bulletin of Pure and Applied Sciences – Physics, vol. 42, no. 2, pp. 98–107, Dec. 2023, doi: https://doi.org/10.48165/bpas.2023.42d.2.7.
[162] T. Z. Kalanov, “Differential Calculus: a Gross Error in Mathematics,” Space Science Journal, vol. 1, no. 1, pp. 1–12, Mar. 2024, [Online]. Available: https://www.opastpublishers.com/peer-review/differential-calculus-a-gross-error-in-mathematics-7147.html
[163] T. Z. Kalanov, “Differential Calculus : A Gross Error in Mathematics,” Arya Bhatta Journal of Mathematics and Informatics, vol. 16, no. 1, pp. 1–18, 2024, [Online]. Available: https://indianjournals.com/article/abjmmi-16-1-001
[164] T. Z. Kalanov, “Mathematical Logic: Gross Formal--Logical Error in Mathematics (Call to Debate),” Space Science Journal, vol. 1, no. 1, pp. 1–11, Apr. 2024, [Online]. Available: https://www.opastpublishers.com/citation/mathematical-logic-gross-formallogical-error-in-mathematics-call-to-debate-7399.html
[165] T.Z. Kalanov, “Differential Calculus: a gross error in mathematics”. Journal of Pure and Applied Mathematics (ISSN-2752-8081. (Pulsus Group), Vol. 8, No. 2, (March 2024), pp. 01-09.
[166] T. Z. Kalanov, “Classical wave equation: A gross error in mathematics and physics,” Journal of Pure and Applied Mathematics, vol. 8, no. 4, Jul. 2024, doi: https://doi.org/10.37532/2752-%208081.24.8(4).01-06.
[167] [T.Z. Kalanov, “Foundations of Differential Calculus: Does the Theory Satisfy the Criterion of Truth?”. J. Math. Techniques & Comput. Math., Vol.3, No.10, (2024); pp. 01-14.
[168] T. Z. Kalanov, “The korteweg-de vries equation: Gross error in physics,” Arya Bhatta Journal of Mathematics and Informatics, vol. 16, no. 2, pp. 205–210, 2024, doi: https://doi.org/10.5958/2394-9309.2024.00030.3.
[169] T. Z. Kalanov, “Differential Calculus: a Gross Error in Mathematics,” Space Science Journal, vol. 1, no. 1, pp. 1–12, Mar. 2024, [Online]. Available: https://www.opastpublishers.com/citation/differential-calculus-a-gross-error-in-mathematics-7147.html
[170] T. Z. Kalanov.”On the Formal–Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics”. American Journal of Mathematical and Computer Applications, Vol. 1, No. 1, (2025), pp. 01-02.
[171] T.Z. Kalanov. “The Formal-Logical Analysis of the Foundation of Set Theory”. American Journal of Mathematical and Computer Applications, Vol.1, No.1, (2025), pp. 01-13.
[172] T. Z. Kalanov. “The Korteweg - De Vries Equation: Where Is the Error?”. American Journal of Mathematical and Computer Applications, Vol. 1, No. 1, (2025), pp. 01-06.
[173] T. Z. Kalanov. “Classical Wave Equation: A Gross Error in Mathematics and Physics”. American Journal of Mathematical and Computer Applications, Vol. 1, No. 1, (2025), pp. 01-06.
[174] T. Z. Kalanov. “Formal-Logical Analysis of the Starting Point of Mathematical Logic”. American Journal of Mathematical and Computer Applications, Vol. 1, No. 1, (2025), pp. 01- 11.
[175] T. Z. Kalanov. “THE KORTEWEG–DE VRIES EQUATION: THE STARTING-POINT OF GROSS ERRORS IN PHYSICS”. Global Scientific Journal (Online: ISSN 2320-9186, www.globalscientificjournal.com), Vol. 13, No. 2, (2025), pp. 1720-1726.
[176] T. Z. Kalanov, “Mathematical Logic: Gross Formal--Logical Error in Mathematics (Call to Debate),” Space Science Journal, vol. 1, no. 1, pp. 1–11, Apr. 2024, [Online]. Available: https://www.opastpublishers.com/peer-review/mathematical-logic-gross-formallogical-error-in-mathematics-call-to-debate-7399.html
[177] T. Z. Kalanov. (2025). “De Broglie Hypothesis and the Schrödinger Equation: Gross Errors in Mathematics, Physics, Formal Logic and Dialectics”. J. Theor. Phys. & Math., Vol. 3, No. 1, (2025), pp. 1-8.
[178] T. Z. Kalanov. (2025). “De Broglie Hypothesis and the Schrödinger Equation: Gross Errors in Mathematics, Physics, Formal Logic, and Dialectics”. Int. J. Quantum Technol.. Vol. 1, No. 1, pp. 01-10.
[179] T. Z. Kalanov. “Special Theory of Relativity: A Gross Error in Physics (A Lesson for Physicists)”. Aryabhatta Journal of Mathematicss & Informatics, Vol. 17, No. 2, (2025), pp. 223-232.
[180] T. Z. Kalanov. ” Special Theory of Relativity: A Gross Error in Physics (A Lesson for Physicists)”. Novel Journal of Applied Sciences Research, Vol. 2, No. 5, (2025), pp. 01-06.
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