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arXiv:quant-ph/0211128 · Conference on the Foundations of Quantum Mechanics: Historical Analysis and Open Questions

TIME SCALE AND COMPLETELY POSITIVE DYNAMICAL EVOLUTIONS

Bassano Vacchini

Published May 1, 2000• 0 citations
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Abstract

It is argued that in the description of macroscopic systems inside quantum mechanics the study of the dynamics of selected degrees of freedom slowly varying on a suitable time scale, corresponding to relevant observables for the given reduced description, is particularly meaningful. A formalism developing these ideas in the more simple case of a microsystem interacting with a macroscopic system is briefly outlined, together with an application to the field of neutron optics. The obtained reduced description relies on a T-matrix formalism and has the property of complete positivity.

DOI
10.1142/9789812793560_0031

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It is argued that in the description of macroscopic systems inside quantum mechanics the study of the dynamics of selected degrees of freedom slowly varying on a suitable time scale, corresponding to relevant observables for the given reduced description, is particularly meaningful. A formalism developing these ideas in the more simple case of a microsystem interacting with a macroscopic system is briefly outlined, together with an application to the field of neutron optics. The obtained reduced description relies on a T-matrix formalism and has the property of complete positivity.
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
Current interpretations of quantum mechanics suggest that the classical concepts of space and time are not applicable to microscopic systems. Salecker and Wigner have recently proved that these concepts have no operational meaning for microsystems. Therefore, space-time descriptions may be valid only for macroscopic systems. It is here suggested that space and time themselves arise from, but do not have analogs in, the properties of microscopic particles, in the same way that thermodynamic properties arise as a result of interactions among the many actually existing particles of the universe. Neither the particles nor the interactions need to be described in spatial-temporal terms. This macroscopic interpretation of space-time seems compatible with the known properties of the physical world, suggests a more direct interpretation of the statistical nature of microscopic events, and offers a new approach to some physical problems.
Circumstances are described wherein no state at a given time (nor any definite evolution from one time to another) can be ascribed to a given physical system, but wherein the system can nonetheless be associated with definite dispersion-free values of a new sort of observable, which we call a "multiple-time" observable. The description of physical systems in terms of these new observables is discussed. It emerges as a by-product of our work that no experiment whatever (albeit that its result is certain) can be carried out on a system without disturbing the values of other measurable quantities.
Thermodynamics of irreversible processes is taken as the phenomenological starting point for the description of macroscopic systems in quantum mechanics and state parameters, which are amenable to be attributed an objective meaning, are introduced inside non relativistic quantum field theory when the macroscopic system is locally at equilibrium. Conditions for these state parameters to obey a deterministic time evolution are indicated and discussed. The formalism is developed also considering the case of more component systems and bound states. The situation in which the deterministic dynamics of the state parameters breaks down is also envisaged and it is argued that in this case a stochastic generalisation of the theory is called for. First attempts in this direction are outlined, naturally leading to a rooting of the concept of microsystem inside both quantum theory and an objective phenomenological context.