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Journal of Mathematical Techniques and Computational Mathematics

The Wave Function Must Represent a Physical Wave

Published Jul 2, 2024• 0 citations
Publisher

Abstract

The Einstein relationship, the de Broglie relationship, and the Born rule are considered fundamental in quantum mechanics, yet in mathematical logic, as usually written, they are not self-consistent [1]. On the other hand, each has had great success individually at predicting the outcome of experiments. It is shown here that the lack of self-consistency can be remedied if it is assumed the wave is physical, and the equation for the wave, and not the particle, is actually the Schrödinger equation.

DOI
10.33140/jmtcm.03.07.03

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The Einstein relationship, the de Broglie relationship, and the Born rule are considered fundamental in quantum mechanics, yet in mathematical logic, as usually written, they are not self-consistent [1]. On the other hand, each has had great success individually at predicting the outcome of experiments. It is shown here that the lack of self-consistency can be remedied if it is assumed the wave is physical, and the equation for the wave, and not the particle, is actually the Schrödinger equation.
The irrefutable proof of the incorrectness of the de Broglie hypothesis (postulate) and the Schrödinger equation (postulate) is proposed. The correct methodological basis for the 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 conclusion: the de Broglie hypothesis (idea, postulate) and the Schrödinger equation (idea, postulate) are gross errors in mathematics, physics, formal logic and dialectics. This conclusion is based on the following statements: (1) from the point of view of Euler’s formula and the Maclaurin series, the definition of the wave function has neither physical nor mathematical meaning; (2) the substitution of the quantities of energy and momentum, which characterize a quantum (microscopic) particle, into the relationship that describes a macroscopic radiation wave is a gross formal-logical error, because a quantum particle and macroscopic radiation are not identical material objects; (3) in the dialectical and formal-logical points of view, a free classical particle is not identical to a free quantum particle: these particles are non-identical material objects. Therefore, the substitution of the quantities of energy and momentum, characterizing a quantum (microscopic) particle, into the classical relationship that describes the energy and momentum of a classical particle is a gross formal-logical error; (4) in the point of view of formal logic, the concepts of "corpuscular aspect" and "wave aspect" are contradictory (mutually exclusive) concepts. (The concepts of "particle" and "wave" are defined by different essential features of material objects). Therefore, the de Broglie wave function and the Schrödinger wave equation represent a violation of the formal-logical law of lack (absence) of contradiction. This means that the concept of corpuscular-wave dualism is erroneous; (5) The de Broglie wave function and the Schrödinger equation represent a gross dialectical error, because the dimensionless wave function contradicts to the dialectical concept of the measure of a material object (i.e. the dimensionless wave function does not have the qualitative determinacy of a material object, does not characterize the properties of a material object). Therefore, the de Broglie wave function and the Schrödinger equation are meaningless relationships.
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