Measurement in quantum mechanics and classical statistical mechanics

Erik Deumens

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?

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.

PEKKA J. LAHTI

Shiro Ishikawa

In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.

N. N. Bogolyubov, A. M. Kurbatov, A. S. Shumovskiǐ