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arXiv:quant-ph/9807001 · Annals of Physics

Quantum Mechanics without Waves: A Generalization of Classical Statistical Mechanics

Marcello Cini

Published Apr 1, 1999• 11 citations
arXivHTMLPDF
DOI
10.1006/aphy.1998.5892

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By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.
Density distribution function of classical statistical mechanics is generally generalized as a product of a general complex function and its complex Hermitian conjugate function, and the average of classical statistical mechanics is generalized as the average of the quantum mechanics. Furthermore, this paper derives three ones of the five axiom presumptions of quantum mechanics, e.g., deduces Schrȍdinger equation by two general ways, makes the three axiom presumptions into three theorems of quantum mechanics, not only solves the crisis to hard understand, but also gets new theories and new discoveries, e.g., this paper solves the crisis of the origin of the wave-particle duality, derives operators, eigenvalues and eigenstates, deduces commutation relations for coordinate and momentum as well as the time and energy, and discovers quantum mechanics is just a generalization ( mechanics ) theory of the complex square root of ( real density function of ) classical statistical mechanics. Quantum mechanics being just a generalization theory of the complex square root of classical statistical mechanics is both new physics and revolutionary discovery, which are affecting people’s deep philosophical thinking for modern physics development, solve all the crisises of quantum mechanics, quantum information and so on, and make quantum mechanics have scientific solid bases being checked and both no basic axiom presumption and no all the quantum strange incomprehensible properties, because classical statistical mechanics and the complex square root of classical statistical mechanics have the scientific solid bases being checked. In addition, this paper discovers the reason no taking the time derivative of space coordinates in Schrȍdinger equation. Therefore, this paper gives solution to the crisis of the first quantization origin, and mainly deduces quantum physics no all the quantum current strange incomprehensible properties.