Introduction of a classical level in quantum theory. Continuous monitoring
type: Item
instance of: scholarly article
title: Introduction of a classical level in quantum theory. Continuous monitoring
zbMATH Open document ID: 1390.81055
author: G. M. Prosperi
published in: Foundations of Physics
publication date: 2018-01-25T00:00:00Z
review text: This paper is written in the framework of a peculiar form of \textit{Generalized Quantum Mechanics} (GQM) proposed years ago by the author's group with the aim of describing a quantum measurement process encompassing also the ``intrinsic classical level for some basic macroscopic quantities'' needed to interpret ``the setup and output of an experiment'' according to Bohr and von Neumann. As recalled in a final annex, within the Heisenberg picture, to a set \(A\) of \(p\) compatible observables, and to \(T\subseteq\mathbb R^p\), are associated a positive operator valued measure \(\hat F_A(T)\) (an operator on the Hilbert space \(\mathbb H\)), and an operation valued measure \(\mathcal F_{S_A}(T)\) (a mapping among trace class operators) where \(S_A\) represents the observation apparatus. If then \(\hat\rho\) is the statistical operator (the state of the system), while the probability of observing \(A \in T\) at the time \(t\) is \[ P(A \in T, t) = \mathrm {Tr} [\hat F_A(T,t)\hat\rho] \] the reduction of the state as a consequence of having observed \(A \in T\) at the time \(t_0\) produces the new statistical operator \(\mathcal F_{S_A}(T,t_0)\hat\rho\) after suitable normalization. It can be shown moreover that ``in GQM the observation of a sequence of results at certain successive times can be put on the same foot as the observation of \(A\) at a single time'' In the original papers ``The idea was that certain basic quantities should be chosen once for ever by an additional postulate and they should be thought as having at any time well defined values, considered as \textit{beables} in the sense of Bell, by treating them formally as continuously observed. Then any observation on a microscopic system should be expressed in terms of the modifications that its interaction with the remaining part of the world produces in the value of such basic macroscopic quantities. Obviously the theory remains statistic and to any possible evolution of the basic quantities a precise …
reviewed by: Nicola Cufaro Petroni
Mathematics Subject Classification ID: 81P15
Mathematics Subject Classification ID: 81P05
Mathematics Subject Classification ID: 81T99
Mathematics Subject Classification ID: 76F30
zbMATH DE Number: 6829724
zbMATH Keywords: continuous monitoring
zbMATH Keywords: quantum mechanics
zbMATH Keywords: classical variables
zbMATH Keywords: spinor electrodynamics
MaRDI profile type: Publication
full work available at URL: s10701-016-0023-x
OpenAlex ID: W2500561079
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DOI: 10.1007/S10701-016-0023-X
description: scientific article; zbMATH DE number 6829724