Classical Wave Equation: A Gross Error in Mathematics and Physics

Abstract

A detailed proof of the incorrectness of the classical wave equation is proposed. The correctmethodological basis for the proof is the unity of formal logic and rational dialectics. The proofleads to the following irrefutable statement: the classical wave equation and the derivation of theclassical wave equation are a gross error in mathematics and physics. The proof of this statementis based on the following irrefutable main results: (1) The first gross error is the followingapproximate relationship: “sine of angle is approximately equal to tangent of angle; cosine ofangle is approximately equal to 1”. This relationship means (implies) that the quantity of theangle and the right-angled triangle do not exist. Consequently, the relationship between thetangent of the angle and the derivative of the displacement with respect to coordinate does notexist; (2) The second gross error is that the second-order derivative of the displacement withrespect 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 isdimensionless quantity (i.e. the first-order derivative of the displacement respect to coordinatehas no the dimension “meter”); (3) The third gross error is that the first-order derivative of thedisplacement with respect to coordinate cannot be expanded into the Taylor series, because thesecond-order derivative of the displacement with respect to coordinate does not exist; (4) Thefourth gross error is as follows: (a) the left side of the wave equation contains the condition thattime is a variable quantity, and the coordinate is a constant quantity; (b) the right side of thewave 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) ofcontradiction; (5) The fifth gross error is that the standard derivation of the equation relies on thefollowing false theories: negative number theory, complex numbers theory, trigonometry, vectorcalculus, differential calculus, and Newton's second law. Thus, the classical wave equation doesnot satisfy the criterion of truth and is not a scientific achievement