Roundtable Discussion II: Quantum Mechanics and its Limits

Andrei Yu. Khrennikov

We present the summary of the general discussion on the probabilistic foundations of quantum theory that took place during the round table at the Int. Conf. "Foundations of Probability and Physics", Växjö, Sweden-2000. It is possible to find at http://www.msi.vxu.se/aktuellt/konferens/Roundtable.html continuation of this Round Table. You can send your contribution by Email to A. Khr. (subject: Round Table).

James T. Cushing

The ubiquity of chaos in classical mechanics (CM), as opposed to the situation in standard quantum mechanics (QM), might be taken as speaking against QM being the fundamental theory of physical phenomena. Bohmian mechanics (BM), as a formulation of quantum theory, may clarify both the existence of chaos in the quantum domain and the nature of the classical limit. Two interesting possibilities are (i) that CM and classical chaos are included in and underwritten by quantum mechanics (BM) or (ii) that BM and CM simply possess a common region of (noninclusive) overlap. In the latter case, neither CM nor QM alone would be sufficient, even in principle, to account for all of the physical phenomena we encounter. In this talk I shall summarize and discuss the implications of some recent work on chaos and on the classical limit within the framework of BM.

H. T. Flint

William Band

In this second part of the paper, the quantum-mechanical equation of change with time is applied to an ensemble, and the quantum-mechanical analog of the classical Liouville theorem is derived. The conflict between the quantum-mechanical equation of change of an isolated system, and the second law of thermodynamics is explained. The connection between entropy and the uncertainty principle and the effect of measurement on entropy are discussed in detail. It is pointed out that in quantum mechanics, the uncertainty principle forbids the complete specification of the boundaries of a truly isolated system. The effects of random disturbances at the boundary, within the limits permitted by the uncertainty principle, are shown to cause a rapid spontaneous approach to maximum entropy of any “isolated” system. Applications to quasi-stationary irreversible effects are briefly discussed, and it is indicated how the concept of random fluctuations of the boundary leads to a deduction of the Fokker-Planck equation for irreversible processes.

Y. Nambu