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arXiv:quant-ph/9912058 · Journal of Modern Optics

Subdynamics as a mechanism for objective description

Ludovico Lanz, Olaf Melsheimer, Bassano Vacchini

Published Oct 1, 2000• 3 citations
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Abstract

The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This discussion requires some improvement of non-equilibrium statistical mechanics which is briefly presented.

DOI
10.1080/09500340008235139

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The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This discussion requires some improvement of non-equilibrium statistical mechanics which is briefly presented.
The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This discussion requires some improvement of non-equilibrium statistical mechanics that is briefly presented. 1 Evolution of the atomistic idea: the new relationship micromacrosystems Classical physics was fully compatible with a deeply rooted, venerable philosophy: the wealth of objects called macrosystems, we become aware of in our experience at a certain space-time scale, arises by different structures of very many, very elementary, possibly of very few kinds, unavoidably elusive objects, microsystems at the previous scale; already in ancient times Lucretio called them primordia rerum. For a physicist the fundamental challenge is to learn about microsystems and discover the basic links; what remains is to face complexity: correlations of simple properties of single microsystems provide all describable variety. One expects that this scheme can be reproduced at smaller time-scales, to leave open the adventure of discerning more remote links. Since generally human being feels himself not completely fitting inside the
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence for particles. In this approach particles appear as interaction carriers between preparation and registration apparatuses. We further briefly point out the more modern and versatile formalism of quantum theory, stressing the relevance of probabilistic concepts in its formulation. At last we discuss the role of macrosystems, focusing on quantum field theory for their description and introducing objective state parameters for them.
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail) evolve towards a stationary long-time behavior ("equilibration")? In how far is this steady state in agreement with the microcanonical ensemble as predicted by Statistical Mechanics ("thermalization")? In the first part of the paper, a recently developed quantum mechanical treatment of the problem is briefly summarized, putting particular emphasis on the realistic modeling of experimental measurements and non-equilibrium initial conditions. Within this framework, equilibration can be proven under very weak assumptions about those measurements and initial conditions, while thermalization still requires quite strong additional hypotheses. In the second part, an analogous approach within the framework of classical mechanics is developed and compared with the quantum case. In particular, the assumptions to guarantee classical equilibration are now rather strong, while thermalization then follows under relatively weak additional conditions.