Statistical Mechanics and Quantum Mechanics

Paolo Grigolini A

Ivo Sachs, Siddhartha Sen, James Sexton

Qian Shang-Wu

By comparison between equations of motion of geometrical optics(GO)and that of classical statistical mechanics(CSM),we find that there should be an analogy between GO and CSM instead of GO and classical mechanics (CM).Furthermore,by comparison between the classical limit(CL)of quantum mechanics(QM)and CSM,we find that CL of QM is CSM not CM,hence we demonstrate that QM is a natural generalization of CSM instead of CM.

Qian Shang-Wu, Xu Lai-Zi

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.

Carl S. Helrich

Theory

Quantum mechanics is a statistical theory (see, e.g., Margenau [239, 240], Ballentine [25, 26], Klyshko [216], Holevo [115, 116], Khrennikov [192]). It cannot tell us anything about an individual quantum system, e.g., an electron or a photon. It predicts only probabilities for results of measurements for large ensembles of quantum systems. Classical statistical mechanics (CSM) does the same.Why are QM and CSM based on different probabilistic models?