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

American Journal of Physics

Remarks on the Theory of Measurement

Mutsuo M. Yanase

Published Mar 1, 1964• 18 citations
Publisher

Abstract

A new classification of quantum mechanical quantities according to their measurability is discussed. We have three different types of quantities: first, exactly measurable quantities which commute with all the conserved quantities; second, approximately measurable quantities which do not commute with all additive conserved quantities; and finally nonmeasurable quantities which are conjugate to the absolute invariants. The epistemological implications of the measurement process are discussed and it is pointed out that the quantum mechanical description of this process does not furnish an adequate explanation of the acquisition of knowledge.

DOI
10.1119/1.1970177

Related papers

Analysis of the Quantum Mechanical Measurement Process

Eugene Paul Wigner, Mutsuo M. Yanase

The quantum mechanical measurement process is analysed in detail, especially from the group theoretical point of view. The first three chapters review the results obtained before briefly. In §1, the classical theory of measurement, originated by von Neumann, is birefly described. The importance of considering more general schemes of measurements than the original one is, however, emphasized. In §2, the role of conservation laws, in imposing limitations on the possibility of measurements, is discussed. Accurately measurable quantities are defined in this context. In §3, the role of conservation laws is further analysed. It is shown that the conserved quantity of the apparatus cannot be used for a “pointer reading.” The following two chapters discuss the nature of the exactly measurable quantities. In §4, exactly measurable quantities are explicitly determined. It is shown that the measurement of projection operators in the Hilbert space of the object which commute with the operators of the restricted Poincaré group give all the information on the states of the object that can be obtained by accurate measurements. In §5, the measurement on objects which are composed of more than one particle is discussed. The last chapter, §6, deals with approximately measurable quantities, but no complete estimate of the unavoidable inaccuracy of the measurement of these is obtained. It also contains some concluding remarks.

Annals of the Japan Association for Philosophy of Science•Jan 1, 1973•2 citations

Measurement of Quantum Mechanical Operators

Huzihiro Araki, Mutsuo M. Yanase

The limitation on the measurement of an operator imposed by the presence of a conservation law is studied. It is shown that an operator which does not commute with a conserved (additive) quantity cannot be measured exactly (in the sense of von Neumann). It is also shown for a simple case that an approximate measurement of such an operator is possible to any desired accuracy.

Physical Review•Oct 15, 1960•353 citations

On the quantum theory of measurement

Paul K. Feyerabend

THE PROBLEM Within classical physics the relation between physical theory and ordinary experience was conceived in the following way: ordinary experience is something that can be described and understood in terms of physics. Such a description involves, apart from physical theory, certain approximations. But the conditons under which those approximations apply (they correspond to the initial conditions of, say, celestial mechanics), taken together with the theory, are supposed to be sufficient for giving a full account of ordinary experience. Consequently, classical theory of measurement (which, like any other theory of measurement, links together terms of ordinary experience and theoretical terms), is a piece of applied physics and all processes which happen during measurement can be analysed on the basis of the equations of motion only. When we enter quantum mechanics (QM), we are apparently presented with a completely different picture. For according to the current interpretation of elementary quantum mechanics, ordinary experience – and this now means classical physics – and physical theory (and this now means QM), belong to two completely different levels and it is impossible to give an account of the first in terms of the second. Any transition from the quantum level to the level of classical physics must be taken, not as a transition within QM from the general to the particular, but as an essentially new element which is incapable of further analysis.

Cambridge University Press eBooks•Oct 29, 1981•19 citations

On the Theory of Measurement in Quantum Mechanical Systems

Loyal Durand

This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description (classical in the limited sense implied by the correspondence principle of Bohr) of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics.

Philosophy of Science•Apr 1, 1960•10 citations

Quantum Measurements in thePresence of Symmetry

Leon Loveridge

This thesis concerns how symmetries impinge on quantum mechanical measurements, and preclude certain self adjoint operators from representing observable quantities. After developing the requisite mathematical machinery and aspects of quantum measurement theory necessary for our analysis, we proceed to critically review the literature surrounding the remarkable theorem of Wigner, Araki and Yanase (WAY) that prohibits accurate and repeatable measurements of any observable not commuting with an additive conserved quantity, as well as discussing the conditions under which approximate measurements with approximate degrees of repeatability can be achieved. We strengthen the original statement of the WAY theorem and generalise it to the case of position measurements obeying momentum conservation, leading to a solution of a long-standing problem of Stein and Shimony. A superselection rule appearing as the existence of an observable which commutes with all others gives rise to a stronger restriction than the WAY theorem, yielding self adjoint operators which do not represent observable quantities. We analyse various perspectives on superselection rules, aiming to clarify different viewpoints appearing in the literature since the inception of the topic in 1952. We exploit an explicit description of relative phase observables which have been lacking in other contributions, delineating conditions under which relative and (prohibited) absolute phases become statistically close. By providing simple models we are able to mimic a number of attempts to overcome superselection rules, in order to highlight the generic features of such attempts. We show that the statistical proximity of absolute and relative quantities arises only when there is a highly localised phase reference, and that the superselection rule compatible relative phase factors between certain superpositions takes on the appearence of a forbidden relative phase factor in this limit. However, we argue that these relative phase factors can be determined fully within the confines of a superselection rule.

•Jul 1, 2012•4 citations

Exact Solutions for Spin Conserving Models and the Wigner-Araki-Yanase Theorem

Michael Steiner, Ronald Rendell

The Wigner-Araki-Yanase (WAY) theorem is a well-known theorem regarding limitations of quantum measurement in the presence of additive conservation laws. Under the assumptions of the von Neumann measurement model, for which the system conserved quantity $L_{S}$ is bounded, given a conserved total additive system plus apparatus quantity $L_{SA}$, the measurement operator $E_{S}$ must commute with $L_{S}$. Prior proofs have exploited the properties of unitary evolution constrained by momentum conserving operations that tend to obscure the physical nature of the WAY theorem and as well lead to bounds on performance. As it is generally agreed that momentum is always exactly conserved in measurement, we instead develop a general angular momentum conserving model of measurement. This model is shown to lead to a simple explanation of the major implications of the WAY theorem and provides exact results of the effects of measurement based on the apparatus model. This is shown by both tracing the apparatus from the density matrix and also via a system-only channel model based on Kraus operators.

quant-pharXiv:2606.02861•Jun 3, 2026•0 citations
A new classification of quantum mechanical quantities according to their measurability is discussed. We have three different types of quantities: first, exactly measurable quantities which commute with all the conserved quantities; second, approximately measurable quantities which do not commute with all additive conserved quantities; and finally nonmeasurable quantities which are conjugate to the absolute invariants. The epistemological implications of the measurement process are discussed and it is pointed out that the quantum mechanical description of this process does not furnish an adequate explanation of the acquisition of knowledge.
The quantum mechanical measurement process is analysed in detail, especially from the group theoretical point of view. The first three chapters review the results obtained before briefly. In §1, the classical theory of measurement, originated by von Neumann, is birefly described. The importance of considering more general schemes of measurements than the original one is, however, emphasized. In §2, the role of conservation laws, in imposing limitations on the possibility of measurements, is discussed. Accurately measurable quantities are defined in this context. In §3, the role of conservation laws is further analysed. It is shown that the conserved quantity of the apparatus cannot be used for a “pointer reading.” The following two chapters discuss the nature of the exactly measurable quantities. In §4, exactly measurable quantities are explicitly determined. It is shown that the measurement of projection operators in the Hilbert space of the object which commute with the operators of the restricted Poincaré group give all the information on the states of the object that can be obtained by accurate measurements. In §5, the measurement on objects which are composed of more than one particle is discussed. The last chapter, §6, deals with approximately measurable quantities, but no complete estimate of the unavoidable inaccuracy of the measurement of these is obtained. It also contains some concluding remarks.
THE PROBLEM Within classical physics the relation between physical theory and ordinary experience was conceived in the following way: ordinary experience is something that can be described and understood in terms of physics. Such a description involves, apart from physical theory, certain approximations. But the conditons under which those approximations apply (they correspond to the initial conditions of, say, celestial mechanics), taken together with the theory, are supposed to be sufficient for giving a full account of ordinary experience. Consequently, classical theory of measurement (which, like any other theory of measurement, links together terms of ordinary experience and theoretical terms), is a piece of applied physics and all processes which happen during measurement can be analysed on the basis of the equations of motion only. When we enter quantum mechanics (QM), we are apparently presented with a completely different picture. For according to the current interpretation of elementary quantum mechanics, ordinary experience – and this now means classical physics – and physical theory (and this now means QM), belong to two completely different levels and it is impossible to give an account of the first in terms of the second. Any transition from the quantum level to the level of classical physics must be taken, not as a transition within QM from the general to the particular, but as an essentially new element which is incapable of further analysis.
This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description (classical in the limited sense implied by the correspondence principle of Bohr) of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics.
This thesis concerns how symmetries impinge on quantum mechanical measurements, and preclude certain self adjoint operators from representing observable quantities. After developing the requisite mathematical machinery and aspects of quantum measurement theory necessary for our analysis, we proceed to critically review the literature surrounding the remarkable theorem of Wigner, Araki and Yanase (WAY) that prohibits accurate and repeatable measurements of any observable not commuting with an additive conserved quantity, as well as discussing the conditions under which approximate measurements with approximate degrees of repeatability can be achieved. We strengthen the original statement of the WAY theorem and generalise it to the case of position measurements obeying momentum conservation, leading to a solution of a long-standing problem of Stein and Shimony. A superselection rule appearing as the existence of an observable which commutes with all others gives rise to a stronger restriction than the WAY theorem, yielding self adjoint operators which do not represent observable quantities. We analyse various perspectives on superselection rules, aiming to clarify different viewpoints appearing in the literature since the inception of the topic in 1952. We exploit an explicit description of relative phase observables which have been lacking in other contributions, delineating conditions under which relative and (prohibited) absolute phases become statistically close. By providing simple models we are able to mimic a number of attempts to overcome superselection rules, in order to highlight the generic features of such attempts. We show that the statistical proximity of absolute and relative quantities arises only when there is a highly localised phase reference, and that the superselection rule compatible relative phase factors between certain superpositions takes on the appearence of a forbidden relative phase factor in this limit. However, we argue that these relative phase factors can be determined fully within the confines of a superselection rule.
The Wigner-Araki-Yanase (WAY) theorem is a well-known theorem regarding limitations of quantum measurement in the presence of additive conservation laws. Under the assumptions of the von Neumann measurement model, for which the system conserved quantity LSL_{S}LS​ is bounded, given a conserved total additive system plus apparatus quantity LSAL_{SA}LSA​, the measurement operator ESE_{S}ES​ must commute with LSL_{S}LS​. Prior proofs have exploited the properties of unitary evolution constrained by momentum conserving operations that tend to obscure the physical nature of the WAY theorem and as well lead to bounds on performance. As it is generally agreed that momentum is always exactly conserved in measurement, we instead develop a general angular momentum conserving model of measurement. This model is shown to lead to a simple explanation of the major implications of the WAY theorem and provides exact results of the effects of measurement based on the apparatus model. This is shown by both tracing the apparatus from the density matrix and also via a system-only channel model based on Kraus operators.