The Quantum Mechanical Arrow of Time

Abstract

The dynamics of probability distributions on classical phase space, discussed under various aspects in Chap. 3, may be formally translated into quantum mechanics by means of the canonical quantization rules. Many authors of standard textbooks therefore maintain that the foundation of irreversibility in quantum mechanics is identical to that in classical physics. There could then only be quantitative differences arising from different spectral properties of the ‘corresponding’ Liouville operators. However, this approach to statistical quantum mechanics completely ignores the fundamental interpretational differences of concepts that formally correspond to one another (such as probability distributions and density operators — see Sect. 4.2). It therefore conceals essential aspects of quantum theory which may be important for irreversibility in general (recall the general discussion in the Introduction):

• 1. The quantum mechanical probability interpretation represents an indeterminism of controversial origin. Most physicists seem to regard it as an objective dynamical indeterminism (see Fig. 3.8), and some even as representing a fundamental arrow of time that would go beyond dynamics. Others have instead suggested that one may explain the unpredictability of quantum mechanical measurement results in terms of conventional statistical arguments, viz., by means of thermal fluctuations that are related to the amplification process which leads to macroscopic outcomes.