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

Princeton University Press eBooks

Are the Quantum Rules Exact? The Case of the Imperfect Measurements

Bernard d’Espagnat

Published Jul 5, 2017• 0 citations
Publisher

Abstract

Should we doubt the exactness of the predictive quantum rules of calculation? Although this question is sometimes raised in connection with the one on how to physically understand quantum mechanics, these two questions should not be mixed up. It is recalled here that even the first one is stil an object of controversy, and it is shown (a) that in one specific case the arguments put forward in support of such doubts are hardly cogent but (b) that, nevertheless, at least in one specific other context, the question is worth attention. This is the problem of repeated imperfect measurements. Relative to it, a theoretical possibility is shown of discriminating between the thesis that the quantum rules are exact and a powerful theory of which it is proved that it cannot be reconciled with the assumption.

DOI
10.1515/9781400886975-030

Related papers

Quantum (Statistical) Mechanics, Measurement and Information

Roger Balian

Ever since the beginning of quantum mechanics, the measurement problem has been a subject of sometimes discontinued but nevertheless recurrent concern. As students, most physicists have raised questions about it, but the spectacular and renewed successes of quantum theory were a strong incentive for them to work out applications without further worrying about foundations. In each generation, however, some dissatisfaction reemerges, which leads to slow progress, and we may expect that the measurement problem will some day be cleared up rather than forgotten. The situation recalls statistical mechanics, the foundations of which still give rise to scientific discussions, in spite of more than one century’s achievements. Actually, the paradoxes of irreversibility and of Maxwell’s demon share some common features with quantum measurements, to wit, they involve probabilities in a crucial fashion and their explanation requires elucidating the role of the observer.

CRC Press eBooks•Oct 19, 2017•0 citations

Einstein et la complémentarité au sens de Bohr : du retrait dans le tumulte aux arguments d'incomplétude

Michel Paty

SUMMARY. — In this article, I examine Einstein's objections to quantum mechanics, with the formalism's interpretation in terms of complementarity as the historical setting. From 1924 to 1927, the period of development of a formalised quantum theory, Einstein raised certain questions that kept him from joining the throng of ardent supporters. Against the theory and its interpretation of 1927, he at first advanced arguments with the idea of eventually finding a flaw in quantum mechanics, and casting doubts upon its pretensions of completeness. Finally acknowledging, in 1931, the theory's coherence and accuracy at describing phenomena, he then tried to put forth objections to the theory's interpretation, which aimed at demonstrating the theory's incompleteness. These arguments culminated in the « Einstein-Podolsky-Rosen » article of 1935, and Einstein repeated them continually until his death. The analysis here calls, of course, for assessments of both the import of Einstein's arguments in relation to physics today, as well as to Einstein's own conceptions where theoretical physics is concerned, but these go beyond the aims of the present article.

Revue d histoire des sciences•Jan 1, 1985•4 citations

Are the quantum rules exact? The case of the imperfect measurements

Bernard d’Espagnat

Foundations of Physics•Apr 1, 1986•9 citations

Quantum Theory: Exact or Approximate?

Stephen L. Adler, Angelo Bassi

Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and philosophy. There are two distinct approaches. One is to assume that quantum theory is exact, but that the interpretive postulates need modification, to eliminate apparent contradictions. The second approach is to assume that quantum mechanics is not exact, but instead is a very accurate approximation to a deeper level theory, which reconciles the deterministic and probabilistic aspects. We will focus on this second approach.

arXiv:0912.2211•Dec 11, 2009•5 citations

Is Indeterminism Supported by Quantum Theory?

Rollin W. Workman

Two initially different arguments for indeterminism are often based either upon the Uncertainty Relations or the statistical interpretation of the wave equation of quantum mechanics. Both arguments ultimately involve three factors: (1) the assumption that elementary entities are enough like classical particles for it to make sense to say they are either determined or indetermined, (2) the fact that no exact measurements are possible of quantities supposed to characterize elementary entities, (3) the pragmatic supposition that determinism is false unless exact predictions are theoretically possible. If it is legitimate to use (3) to prove indeterminism, then an equally legitimate argument can be based upon (2) which denies (1). Thus, it is doubtful that quantum mechanics supports indeterminism, though it may show that the concepts of ‘determined’ and ‘indetermined’ are inapplicable to the world.

Philosophy of Science•Jul 1, 1959•28 citations

Note on the Quantum-Mechanical Theory of Measurement

W. H. Furry

In recent notes by Einstein, Podolsky and Rosen and by Bohr, attention has been called to the fact that certain results of quantum mechanics are not to be reconciled with the assumption that a system has independently real properties as soon as it is free from mechanical interference. We here investigate in general, and in abstract terms, the extent of this disagreement. When suitably formulated, such an assumption gives to certain types of questions the same answers as does quantum mechanics; this is true of the formulas usually given in discussions of the theory of measurement. There exists, however, a general class of cases in which contradictions occur. That such contradictions are not restricted to the abstract mathematical theory, but can be realized in the commonest physical terms, is shown by the working out of an example..

Physical Review•Mar 1, 1936•244 citations
Should we doubt the exactness of the predictive quantum rules of calculation? Although this question is sometimes raised in connection with the one on how to physically understand quantum mechanics, these two questions should not be mixed up. It is recalled here that even the first one is stil an object of controversy, and it is shown (a) that in one specific case the arguments put forward in support of such doubts are hardly cogent but (b) that, nevertheless, at least in one specific other context, the question is worth attention. This is the problem of repeated imperfect measurements. Relative to it, a theoretical possibility is shown of discriminating between the thesis that the quantum rules are exact and a powerful theory of which it is proved that it cannot be reconciled with the assumption.
Ever since the beginning of quantum mechanics, the measurement problem has been a subject of sometimes discontinued but nevertheless recurrent concern. As students, most physicists have raised questions about it, but the spectacular and renewed successes of quantum theory were a strong incentive for them to work out applications without further worrying about foundations. In each generation, however, some dissatisfaction reemerges, which leads to slow progress, and we may expect that the measurement problem will some day be cleared up rather than forgotten. The situation recalls statistical mechanics, the foundations of which still give rise to scientific discussions, in spite of more than one century’s achievements. Actually, the paradoxes of irreversibility and of Maxwell’s demon share some common features with quantum measurements, to wit, they involve probabilities in a crucial fashion and their explanation requires elucidating the role of the observer.
SUMMARY. — In this article, I examine Einstein's objections to quantum mechanics, with the formalism's interpretation in terms of complementarity as the historical setting. From 1924 to 1927, the period of development of a formalised quantum theory, Einstein raised certain questions that kept him from joining the throng of ardent supporters. Against the theory and its interpretation of 1927, he at first advanced arguments with the idea of eventually finding a flaw in quantum mechanics, and casting doubts upon its pretensions of completeness. Finally acknowledging, in 1931, the theory's coherence and accuracy at describing phenomena, he then tried to put forth objections to the theory's interpretation, which aimed at demonstrating the theory's incompleteness. These arguments culminated in the « Einstein-Podolsky-Rosen » article of 1935, and Einstein repeated them continually until his death. The analysis here calls, of course, for assessments of both the import of Einstein's arguments in relation to physics today, as well as to Einstein's own conceptions where theoretical physics is concerned, but these go beyond the aims of the present article.
Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and philosophy. There are two distinct approaches. One is to assume that quantum theory is exact, but that the interpretive postulates need modification, to eliminate apparent contradictions. The second approach is to assume that quantum mechanics is not exact, but instead is a very accurate approximation to a deeper level theory, which reconciles the deterministic and probabilistic aspects. We will focus on this second approach.
Two initially different arguments for indeterminism are often based either upon the Uncertainty Relations or the statistical interpretation of the wave equation of quantum mechanics. Both arguments ultimately involve three factors: (1) the assumption that elementary entities are enough like classical particles for it to make sense to say they are either determined or indetermined, (2) the fact that no exact measurements are possible of quantities supposed to characterize elementary entities, (3) the pragmatic supposition that determinism is false unless exact predictions are theoretically possible. If it is legitimate to use (3) to prove indeterminism, then an equally legitimate argument can be based upon (2) which denies (1). Thus, it is doubtful that quantum mechanics supports indeterminism, though it may show that the concepts of ‘determined’ and ‘indetermined’ are inapplicable to the world.
In recent notes by Einstein, Podolsky and Rosen and by Bohr, attention has been called to the fact that certain results of quantum mechanics are not to be reconciled with the assumption that a system has independently real properties as soon as it is free from mechanical interference. We here investigate in general, and in abstract terms, the extent of this disagreement. When suitably formulated, such an assumption gives to certain types of questions the same answers as does quantum mechanics; this is true of the formulas usually given in discussions of the theory of measurement. There exists, however, a general class of cases in which contradictions occur. That such contradictions are not restricted to the abstract mathematical theory, but can be realized in the commonest physical terms, is shown by the working out of an example..