Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

Theory of Measurement of Quantum Mechanics: Mechanism of Reduction of Wave Packet. I

S. Machida, Mikio Namiki

Published May 1, 1980• 131 citations
Publisher

Abstract

New theory of measurement is presented to show that quantum mechanics can describe the whole processes of quantum-mechanical measurement leading to the so-called reduction of wave packet if applied properly to the total system of object and apparatus. We introduce a simple model, where momenta of particles are measured using a perfect rigid mirror, to yield the reduction of wave packet in a clear-cut way. Microscopic uncertainties of macroscopic quantities and the dynamical scattering theory play the essential roles. Before entering into the main part, we briefly summarize the controversial points in the theory of measurement.

DOI
10.1143/ptp.63.1457

Related papers

Theory of Measurement in Quantum Mechanics: Mechanism of Reduction of Wave Packet. II

S. Machida, Mikio Namiki

General scope and general formulation of the theory of quantum-mechanical measurement are given. Essential points of our theory are that macroscopic apparatus is associated with many Hilbert spaces and the dynamical scattering theory is applied to microscopic interactions between object and apparatus. It is shown that our theory gets over the Furry-Wigner-Fine criticisms.

Progress of Theoretical Physics•Jun 1, 1980•67 citations

Theory of Measurement in Quantum Mechanics

Saburo Amai

The question as to whether quantum mechanics can be applied to a macroscopic system, which has recently been raised through discussions of the problem of how to interpret the so-called “reduction of a wave packet”, is discussed. It is shown by a detailed analysis of the destruction of interference which brings about the reduction, that a supplementary assumption on the preciseness of measurements must at least be introduced in order to interpret the reduction process as an objective process, and it does not, however, necessarily imply inapplicability of quantum mechanics to a macroscopic system.

Progress of Theoretical Physics•Oct 1, 1963•4 citations

Quantum Theory of Measurement

Takasi Endo

Quantum theory of phase relaxation (T. Endo: J. Phys. Soc. Jpn 56 (1987) 1684) is applied to reduction process of a wave packet due to measurement. Reduction of a wave packet is a dynamic process derived from interactions between an object quantum system and a measuring apparatus without ensemble averaging.

Journal of the Physical Society of Japan•Jan 15, 1988•5 citations

"Theory of Measurement" in Differential-Space Quantum Theory

Armand Siegel, Norbert Wiener

The "reduction of the wave packet" is an essential feature of the quantum description of measurement. Since it means an abrupt change in the wave function, it therefore also implies an abrupt change in the statistical description of the system. If the differential-space theory of quantum systems rests on a description of reality more detailed than quantum mechanics, it must contain an account of this change which is consistent with the strictly probabilistic point of view of the theory. It is here shown that the theory does satisfy this necessary condition. The need of a special postulate for the measurement process is eliminated in this formulation, and a new explicitness is introduced into the description.

Physical Review•Jan 1, 1956•29 citations

Elements of Measurement Theory

Bernard d’Espagnat

This chapter examines the reasons why measurement theory is a particularly controversial part of modern theoretical physics. The problem of measurement in quantum mechanics is considered as nonexistent or trivial by an impressive body of theoretical physicists and as presenting almost insurmountable difficulties by a somewhat lesser but steadily growing number of their colleagues. The law of evolution in time constitutes the essential part of the conventional measurement theory. In this theory, the existence of a Hamiltonian describing the instrument-system interaction is postulated, not derived. In other words, this assumption is considered as a legitimate idealization of the experimental facts. A wave packet reduction can be considered as a phenomenological procedure that, in many instances, can be applied in order to calculate the results of successive observations and the correlations between them without introducing into the formulas the complicated wave functions of the various instruments.

CRC Press eBooks•Mar 5, 2018•0 citations

The quantum theory of measurement within dynamical reduction models

Bassi, A, Salvetti, D G M

We analyze in mathematical detail, within the framework of the QMUPL model of spontaneous wave function collapse, the von Neumann measurement scheme for the measurement of a 1/2 spin particle. We prove that, according to the equation of the model: i) throughout the whole measurement process, the pointer of the measuring device is always perfectly well localized in space; ii) the probabilities for the possible outcomes are distributed in agreement with the Born probability rule; iii) at the end of the measurement the state of the microscopic system has collapsed to the eigenstate corresponding to the measured eigenvalue. This analysis shows rigorously how dynamical reduction models provide a consistent solution to the measurement problem of quantum mechanics.

•Feb 1, 2007•19 citations
New theory of measurement is presented to show that quantum mechanics can describe the whole processes of quantum-mechanical measurement leading to the so-called reduction of wave packet if applied properly to the total system of object and apparatus. We introduce a simple model, where momenta of particles are measured using a perfect rigid mirror, to yield the reduction of wave packet in a clear-cut way. Microscopic uncertainties of macroscopic quantities and the dynamical scattering theory play the essential roles. Before entering into the main part, we briefly summarize the controversial points in the theory of measurement.
The question as to whether quantum mechanics can be applied to a macroscopic system, which has recently been raised through discussions of the problem of how to interpret the so-called “reduction of a wave packet”, is discussed. It is shown by a detailed analysis of the destruction of interference which brings about the reduction, that a supplementary assumption on the preciseness of measurements must at least be introduced in order to interpret the reduction process as an objective process, and it does not, however, necessarily imply inapplicability of quantum mechanics to a macroscopic system.
The "reduction of the wave packet" is an essential feature of the quantum description of measurement. Since it means an abrupt change in the wave function, it therefore also implies an abrupt change in the statistical description of the system. If the differential-space theory of quantum systems rests on a description of reality more detailed than quantum mechanics, it must contain an account of this change which is consistent with the strictly probabilistic point of view of the theory. It is here shown that the theory does satisfy this necessary condition. The need of a special postulate for the measurement process is eliminated in this formulation, and a new explicitness is introduced into the description.
This chapter examines the reasons why measurement theory is a particularly controversial part of modern theoretical physics. The problem of measurement in quantum mechanics is considered as nonexistent or trivial by an impressive body of theoretical physicists and as presenting almost insurmountable difficulties by a somewhat lesser but steadily growing number of their colleagues. The law of evolution in time constitutes the essential part of the conventional measurement theory. In this theory, the existence of a Hamiltonian describing the instrument-system interaction is postulated, not derived. In other words, this assumption is considered as a legitimate idealization of the experimental facts. A wave packet reduction can be considered as a phenomenological procedure that, in many instances, can be applied in order to calculate the results of successive observations and the correlations between them without introducing into the formulas the complicated wave functions of the various instruments.
We analyze in mathematical detail, within the framework of the QMUPL model of spontaneous wave function collapse, the von Neumann measurement scheme for the measurement of a 1/2 spin particle. We prove that, according to the equation of the model: i) throughout the whole measurement process, the pointer of the measuring device is always perfectly well localized in space; ii) the probabilities for the possible outcomes are distributed in agreement with the Born probability rule; iii) at the end of the measurement the state of the microscopic system has collapsed to the eigenstate corresponding to the measured eigenvalue. This analysis shows rigorously how dynamical reduction models provide a consistent solution to the measurement problem of quantum mechanics.