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

Kagaku tetsugaku

On the Quantum Theory of Measurement

Gen-Ichiro Nagasaka

Published Jan 1, 1970• 11 citations
Publisher

Abstract

Since the formulation of measurement process by von Neumann, numerous attempts have been made to remove the various paradoxical aspects involved in the theory. The present exposition reveals that a serious linguistic confusion existed in the original formulation by von Neumann and no author has ever given serious considerations. A new approach to the problem is proposed which is based upon an interpretation of quantum mechanics basically in the spirit of Copenhagen Interpretation.

DOI
10.4216/jpssj.3.131

Related papers

The Measurement Process in the Individual Interpretation of Quantum Mechanics

Hans Primas

Von Neumann’s (1927 , 1932 ) measurement theory is based on an uncritical acceptance of the historical disturbance doctrine of measurements. It is an ineffectual attempt to relate empirical data to the partial Boolean structure of quantum mechanics. In this paper, I will argue that the measurement problem of quantum mechanics is soluble if it is reasonably posed. All difficulties stem from an indiscriminate conceptual approach and inadequate mathematical formulations.

CRC Press eBooks•Oct 19, 2017•4 citations

A New Interpretation of Quantum Mechanics

Shiro Ishikawa

The Copenhagen interpretation is the most authorized interpretation of quantum mechanics, but there are a number of ideas that are associated with the Copenhagen interpretation. It is ceratin that this fact is not necessarily desirable. Thus, we propose a new interpretation of measurement theory, which is the linguistic aspect (or, the mathematical generalization) of quantum mechanics. Although this interpretation is superficially similar to a part of so-called Copenhagen interpretation, we show that it has a merit to be applicable to both quantum and classical systems. For example, we say that Bell’s inequality is broken even in classical systems.

Journal of Quantum Information Science•Jan 1, 2011•63 citations

A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II

David Böhm

In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of "hidden" variables, developed in a previous paper. We find that in principle, these "hidden" variables determine the precise results of each individual measurement process. In practice, however, in measurements that we now know how to carry out, the observing apparatus disturbs the observed system in an unpredictable and uncontrollable way, so that the uncertainty principle is obtained as a practical limitation on the possible precision of measurements. This limitation is not, however, inherent in the conceptual structure of our interpretation. We shall see, for example, that simultaneous measurements of position and momentum having unlimited precision would in principle be possible if, as suggested in the previous paper, the mathematical formulation of the quantum theory needs to be modified at very short distances in certain ways that are consistent with our interpretation but not with the usual interpretation.We give a simple explanation of the origin of quantum-mechanical correlations of distant objects in the hypothetical experiment of Einstein, Podolsky, and Rosen, which was suggested by these authors as a criticism of the usual interpretation.Finally, we show that von Neumann's proof that quantum theory is not consistent with hidden variables does not apply to our interpretation, because the hidden variables contemplated here depend both on the state of the measuring apparatus and the observed system and therefore go beyond certain of von Neumann's assumptions.In two appendixes, we treat the problem of the electromagnetic field in our interpretation and answer certain additional objections which have arisen in the attempt to give a precise description for an individual system at the quantum level.

Physical Review•Jan 15, 1952•2,052 citations

Interpretations of Quantum Mechanics

The problems of modern physics are man made.The Copenhagen version of quantum mechanics is formulated in a vague prosaic way, inconsistencies and paradoxes are the price.New interpretations try to solve the problem, however a reformulation rather than an interpretation is needed.In this manuscript I will point out, where the Copenhagen formulation of quantum mechanics is flawed and how one can make sense out of it.Then I will show, that it is possible to give a precise formulation of quantum mechanics without losing its compelling ability in describing experiments.

IMPERIAL COLLEGE PRESS eBooks•Oct 1, 2011•0 citations

Interpretations of Quantum Mechanics

Peter Pickl

The problems of modern physics are man made. The Copenhagen version of quantum mechanics is formulated in a vague prosaic way, inconsistencies and paradoxes are the price. New interpretations try to solve the problem, however a reformulation rather than an interpretation is needed. In this manuscript I will point out, where the Copenhagen formulation of quantum mechanics is flawed and how one can make sense out of it. Then I will show, that it is possible to give a precise formulation of quantum mechanics without losing its compelling ability in describing experiments.

EPJ Web of Conferences•Jan 1, 2014•0 citations

Measurement in Quantum Mechanics: Decoherence and the Pointer Basis

Anu Venugopalan

Quantum Mechanics represents one of the greatest triumphs of the scientific enterprise of the twentieth century. The stunning success of quantum theory has led to many revolutionary inventions and its extraordinary concepts describe the heart of several important real world applications like transistors and lasers. The theory makes accurate predictions about a wide range of physical phenomena and has historically withstood the tests and scrutiny of every experimental investigation. However, inspite of the fact that quantum theory is widely regarded by the scientific establishment as the fundamental theory of nature and is immensly successful and useful, its conceptual framework makes many predictions which are difficult to comprehend “classically. The theory is, pardoxically, powerful and confusing at the same time. Quantum theory’s unusual predictions originate from its basic formailsm which involves concepts like probability amplitudes and the linear superposition principle(Dirac, 1947). The quantum view appears abstract and counterintuitive and at odds with classical perceptions. Many of the conceptual problems of quantum mechanics are encompassed in what is known as the quantum measurement problem(Peres, 1986; von Neumann, 1932; Wheeler & Zurek, 1983). Conventionally, the measurement paradox is supposedly ’resolved’ by forcing a notion of a sudden collapse of the state vector of the system being measured. However, the nature of this mechanism is at odds with the basic tenets of quantum mechanics and hence may lie outside its realm thus questioning the validity of the theory it self. Closely related with the problem of measurement in quantum mechanics is the question of its connection with the emergence of classicality and the elusive boundary between quantum and classical worlds. What is the connection between the ‘classical’ and the ‘quantum’ worlds? Is there a definite relationship? Are classical mechanics and quantum mechanics two mutually exclusive incompatible theories or are they two aspects of the same underlying philosophy? Classical objects are eventually composed of elements of the microworld which can be described quantum mechanically. So, how and where can there be a boundary between the two worlds? In the following section we begin by introducing the quantum measurement problem. In the next section we will discuss attempts to understand and explain away the underlying paradoxes in quantum theory as highlighted in the quantum measurement problem and the question of the quantum-classical connection. From among the various explanations that seek a resolution to the conceptual problems of quantum mechanics, we focus on the ‘environment induced decoherence theory’ an approach that employs the methods developed by several authors to analyse the quantum mechanics of Measurement in Quantum Mechanics: Decoherence and the Pointer Basis

InTech eBooks•Feb 22, 2012•2 citations
Since the formulation of measurement process by von Neumann, numerous attempts have been made to remove the various paradoxical aspects involved in the theory. The present exposition reveals that a serious linguistic confusion existed in the original formulation by von Neumann and no author has ever given serious considerations. A new approach to the problem is proposed which is based upon an interpretation of quantum mechanics basically in the spirit of Copenhagen Interpretation.
The Copenhagen interpretation is the most authorized interpretation of quantum mechanics, but there are a number of ideas that are associated with the Copenhagen interpretation. It is ceratin that this fact is not necessarily desirable. Thus, we propose a new interpretation of measurement theory, which is the linguistic aspect (or, the mathematical generalization) of quantum mechanics. Although this interpretation is superficially similar to a part of so-called Copenhagen interpretation, we show that it has a merit to be applicable to both quantum and classical systems. For example, we say that Bell’s inequality is broken even in classical systems.
In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of "hidden" variables, developed in a previous paper. We find that in principle, these "hidden" variables determine the precise results of each individual measurement process. In practice, however, in measurements that we now know how to carry out, the observing apparatus disturbs the observed system in an unpredictable and uncontrollable way, so that the uncertainty principle is obtained as a practical limitation on the possible precision of measurements. This limitation is not, however, inherent in the conceptual structure of our interpretation. We shall see, for example, that simultaneous measurements of position and momentum having unlimited precision would in principle be possible if, as suggested in the previous paper, the mathematical formulation of the quantum theory needs to be modified at very short distances in certain ways that are consistent with our interpretation but not with the usual interpretation.We give a simple explanation of the origin of quantum-mechanical correlations of distant objects in the hypothetical experiment of Einstein, Podolsky, and Rosen, which was suggested by these authors as a criticism of the usual interpretation.Finally, we show that von Neumann's proof that quantum theory is not consistent with hidden variables does not apply to our interpretation, because the hidden variables contemplated here depend both on the state of the measuring apparatus and the observed system and therefore go beyond certain of von Neumann's assumptions.In two appendixes, we treat the problem of the electromagnetic field in our interpretation and answer certain additional objections which have arisen in the attempt to give a precise description for an individual system at the quantum level.
The problems of modern physics are man made.The Copenhagen version of quantum mechanics is formulated in a vague prosaic way, inconsistencies and paradoxes are the price.New interpretations try to solve the problem, however a reformulation rather than an interpretation is needed.In this manuscript I will point out, where the Copenhagen formulation of quantum mechanics is flawed and how one can make sense out of it.Then I will show, that it is possible to give a precise formulation of quantum mechanics without losing its compelling ability in describing experiments.
The problems of modern physics are man made. The Copenhagen version of quantum mechanics is formulated in a vague prosaic way, inconsistencies and paradoxes are the price. New interpretations try to solve the problem, however a reformulation rather than an interpretation is needed. In this manuscript I will point out, where the Copenhagen formulation of quantum mechanics is flawed and how one can make sense out of it. Then I will show, that it is possible to give a precise formulation of quantum mechanics without losing its compelling ability in describing experiments.
Quantum Mechanics represents one of the greatest triumphs of the scientific enterprise of the twentieth century. The stunning success of quantum theory has led to many revolutionary inventions and its extraordinary concepts describe the heart of several important real world applications like transistors and lasers. The theory makes accurate predictions about a wide range of physical phenomena and has historically withstood the tests and scrutiny of every experimental investigation. However, inspite of the fact that quantum theory is widely regarded by the scientific establishment as the fundamental theory of nature and is immensly successful and useful, its conceptual framework makes many predictions which are difficult to comprehend “classically. The theory is, pardoxically, powerful and confusing at the same time. Quantum theory’s unusual predictions originate from its basic formailsm which involves concepts like probability amplitudes and the linear superposition principle(Dirac, 1947). The quantum view appears abstract and counterintuitive and at odds with classical perceptions. Many of the conceptual problems of quantum mechanics are encompassed in what is known as the quantum measurement problem(Peres, 1986; von Neumann, 1932; Wheeler & Zurek, 1983). Conventionally, the measurement paradox is supposedly ’resolved’ by forcing a notion of a sudden collapse of the state vector of the system being measured. However, the nature of this mechanism is at odds with the basic tenets of quantum mechanics and hence may lie outside its realm thus questioning the validity of the theory it self. Closely related with the problem of measurement in quantum mechanics is the question of its connection with the emergence of classicality and the elusive boundary between quantum and classical worlds. What is the connection between the ‘classical’ and the ‘quantum’ worlds? Is there a definite relationship? Are classical mechanics and quantum mechanics two mutually exclusive incompatible theories or are they two aspects of the same underlying philosophy? Classical objects are eventually composed of elements of the microworld which can be described quantum mechanically. So, how and where can there be a boundary between the two worlds? In the following section we begin by introducing the quantum measurement problem. In the next section we will discuss attempts to understand and explain away the underlying paradoxes in quantum theory as highlighted in the quantum measurement problem and the question of the quantum-classical connection. From among the various explanations that seek a resolution to the conceptual problems of quantum mechanics, we focus on the ‘environment induced decoherence theory’ an approach that employs the methods developed by several authors to analyse the quantum mechanics of Measurement in Quantum Mechanics: Decoherence and the Pointer Basis