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数理解析研究所講究録

Micro-Macro Duality and Emergence of Macroscopic Levels(Micro-Macro Duality in Quantum Analysis)

Izumi Ojima

Published Jul 1, 2007• 1 citation
OpenAlex

Abstract

The mutual relation between quantum Micro and classical Macro is clanified by a unified formulation of instruments describing measurement processes and the associated amplification processes, from which some perspective towards a description of emergence processes of spacetime structure is suggested.

Related papers

MICRO-MACRO DUALITY AND EMERGENCE OF MACROSCOPIC LEVELS

IZUMI OJIMA

The mutual relation between quantum Micro and classical Macro is clarified by a unified formulation of instruments describing measurement processes and the associated amplification processes, from which some perspective towards a description of emergence processes of spacetime structure is suggested.

arXiv:0705.2945•Quantum Bio-Informatics•Mar 1, 2008•10 citations

Micro-Macro Duality and Emergence of

Macroscopic Levels

The mutual relation between quantum Micro and classical Macro is clarified by a unified formulation of instruments describing measurement processes and the associated amplification processes, from which some perspective towards a description of emergence processes of spacetime structure is suggested.

•Jan 1, 2007•0 citations

Micro-Macro Duality in Quantum Physics

Izumi Ojima

Micro-Macro Duality means here the universal mutual relations between the microscopic quantum world and various macroscopic classical levels, which can be formulated mathematically as categorical adjunctions. It underlies a unified scheme for generalized sectors based upon selection criteria proposed by myself in 2003 to control different branches of physics from a unified viewpoint, which has played essential roles in extending the Doplicher-Haag-Roberts superselection theory to various situations with spontaneously as well as explicitly broken symmetries. Along this line of thought, the state correlations between a system and a measuring apparatus necessary for measurements can canonically be formulated within the context of group duality; the obtained measurement scheme is not restricted to the quantum mechanical situations with finite number of particles but can safely be applied to quantum field theory with infinite degrees of freedom whose local subalgebras are given by type III von Neumann algebras.

arXiv:math-ph/0502038•Stochastic Analysis: Classical and Quantum•Oct 1, 2005•38 citations

A Unified Scheme of Measurement and Amplification Processes Based on Micro-Macro Duality — Stern-Gerlach Experiment as a Typical Example

Ryo Harada, Izumi Ojima

A unified scheme for quantum measurement processes is formulated on the basis of micro-macro duality as a mathematical expression of the general idea of quantum-classical correspondence. In this formulation, we can naturally accommodate the amplification processes necessary for magnifying quantum state changes at the microscopic end of the probe system into the macroscopically visible motion of the measuring pointer. Its essence is exemplified and examined in the concrete model of the Stern-Gerlach experiment for spin measurement, where the Helgason duality controlling the Radon transform is seen to play essential roles.

arXiv:0810.3400•Open Systems & Information Dynamics•Mar 1, 2009•10 citations

On Entropies of Quantum Communication Processes(Micro-Macro Duality in Quantum Analysis)

Noboru Watanabe

数理解析研究所講究録•Jul 1, 2007•0 citations

The Interpretation of Quantum Mechanics and the Measurement Process

Enrico G. Beltrametti

Although it is 70 years old, there are still areas of quantum theory which are open to interpretation. This book deals with such interpretational problems, and in particular with the issue of the measurement process. The main theme is whether quantum mechanics can be viewed as a (semantically) complete theory, namely as a theory capable of describing not only the physical object under observation but also the measuring instruments used to detect the properties of that physical object. The problematic aspects arise from the fact that the measuring instruments themselves behave as classical physical systems. Thus, we are faced with the open problem of the transition from the quantum to the classical, or more explicitly, the problem of why the composition of many quantum micro-objects gives rise to classical macro-objects. This book goes carefully, exhaustively, and deeply into the interpretational problems of quantum mechanics induced by the measurement process. The solution of many relevant issues, as well as the problems that remain unsolved, emerge clearly. The discussion itself is self-contained and the technical parts are reader-friendly. This book is of value to graduate students and researchers who have an interest in the physical, mathematical, and philosophical foundations of quantum mechanics.

Measurement Science and Technology•Oct 1, 1998•22 citations
Micro-Macro Duality means here the universal mutual relations between the microscopic quantum world and various macroscopic classical levels, which can be formulated mathematically as categorical adjunctions. It underlies a unified scheme for generalized sectors based upon selection criteria proposed by myself in 2003 to control different branches of physics from a unified viewpoint, which has played essential roles in extending the Doplicher-Haag-Roberts superselection theory to various situations with spontaneously as well as explicitly broken symmetries. Along this line of thought, the state correlations between a system and a measuring apparatus necessary for measurements can canonically be formulated within the context of group duality; the obtained measurement scheme is not restricted to the quantum mechanical situations with finite number of particles but can safely be applied to quantum field theory with infinite degrees of freedom whose local subalgebras are given by type III von Neumann algebras.
A unified scheme for quantum measurement processes is formulated on the basis of micro-macro duality as a mathematical expression of the general idea of quantum-classical correspondence. In this formulation, we can naturally accommodate the amplification processes necessary for magnifying quantum state changes at the microscopic end of the probe system into the macroscopically visible motion of the measuring pointer. Its essence is exemplified and examined in the concrete model of the Stern-Gerlach experiment for spin measurement, where the Helgason duality controlling the Radon transform is seen to play essential roles.
Although it is 70 years old, there are still areas of quantum theory which are open to interpretation. This book deals with such interpretational problems, and in particular with the issue of the measurement process. The main theme is whether quantum mechanics can be viewed as a (semantically) complete theory, namely as a theory capable of describing not only the physical object under observation but also the measuring instruments used to detect the properties of that physical object. The problematic aspects arise from the fact that the measuring instruments themselves behave as classical physical systems. Thus, we are faced with the open problem of the transition from the quantum to the classical, or more explicitly, the problem of why the composition of many quantum micro-objects gives rise to classical macro-objects. This book goes carefully, exhaustively, and deeply into the interpretational problems of quantum mechanics induced by the measurement process. The solution of many relevant issues, as well as the problems that remain unsolved, emerge clearly. The discussion itself is self-contained and the technical parts are reader-friendly. This book is of value to graduate students and researchers who have an interest in the physical, mathematical, and philosophical foundations of quantum mechanics.