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

Physics-Uspekhi

The uncertainty principle and measurement accuracy

Aleksandr V. Belinsky, V. B. Lapshin

Published Mar 3, 2017• 6 citations
Publisher

Abstract

Abstract A gedanken experiment is proposed in which the momentum and position of a photon can be measured simultaneously in such a way that the product of their respective errors is less than the right-hand side of the appropriate Heisenberg uncertainty relation.
DOI
10.3367/ufne.2017.02.038069

Related papers

Remarks on Uncertainty Principles

E. U. Condon

Since the publication of Heisenberg’s paper1 on the “anschaulichen Inhalt” of quantum mechanics, discussions of the fundamental limitations on the accuracy of physical measurements have been much in the foreground. According to Heisenberg, the quantum mechanics implies that it is impossible to measure simultaneous values of a coordinate and its conjugate momentum with unlimited precision. Instead, if Δp be the estimated error or uncertainty in a momentum and Δq that in the associated coordinate one must have the inequality, $$ \Delta p\Delta q>\frac{h}{{2\pi}} $$ (1) This inequality has come to be known quite generally as Heisenberg’s uncertainty relation.

Science•May 31, 1929•15 citations

U

P. W. Atkins

Abstract Heisenberg’s uncertainty principle states that: The product of the uncertainties in the simultaneous specifications of two °complementary observables can never be less than a small quantity of the order of h. The precise form of the principle is given in Box U.1. It implies that as one observable is constrained to have a more precise value, so its partner becomes more ill-defined. An experiment designed to measure the two observables simultaneously will be able to determine one precisely only at the expense of losing information about the other (see °duality). The principle was established by Werner Heisenberg in 1927, as a consequence of his formulation of °matrix mechanics.

•Apr 11, 1991•0 citations

Heisenberg's Uncertainty Principle

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics.Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted.The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity.Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally.Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.

WORLD SCIENTIFIC eBooks•May 1, 2000•0 citations

A thought experiment violating Heisenberg's uncertainty principle

M. C. Robinson

In principle, it is possible to make simultaneous and precise measurements of a particle's velocity using two different methods, which should give identical results. It is shown that these results permit the calculation of the particle's position and momentum with a combined error [Formula: see text] at every instant of time in an arbitrarily large interval. It is also shown that, in the special case considered, the statistical interpretation of the wave function is invalid.

Canadian Journal of Physics•May 1, 1969•13 citations

Harmonic Oscillators, Heisenberg's Uncertainty Principle and Simultaneous Measurement Precision for Position and Momentum

Donald Jack Kouri

At the recent QSCP XIX, the author claimed a procedure of using a scaled Fourier transform (the scaling being determined by the detailed interaction and particle mass for a harmonic oscillator) to achieve simultaneous resolution of position and momentum greater than the standard Heisenberg value of 1/2. The procedure is, in fact, invalid for quantum mechanics. The purpose of this paper is simply to give the correct analysis of the uncertainty product, thereby clarifying the error made.

arXiv:1409.2468•Sep 8, 2014•4 citations

Quantum measurement theory and the uncertainty principle

Masanao Ozawa

Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the constraint that the product of their mean errors should be no less than a limit set by Planck's constant. However, Heisenberg with the subsequent completion by Kennard has long been credited only with a constraint for state preparation represented by the product of the standard deviations. Here, we show that Heisenberg actually proved the constraint for the accuracy of simultaneous measurement but assuming an obsolete postulate for quantum mechanics. This assumption, known as the repeatability hypothesis, formulated explicitly by von Neumann and Schrodinger, was broadly accepted until the 1970s, but abandoned in the 1980s, when completely general quantum measurement theory was established. We also survey the author's recent proposal for a universally valid reformulation of Heisenberg's uncertainty principle under the most general assumption on quantum measurement.

•Jul 8, 2015•0 citations
Since the publication of Heisenberg’s paper1 on the “anschaulichen Inhalt” of quantum mechanics, discussions of the fundamental limitations on the accuracy of physical measurements have been much in the foreground. According to Heisenberg, the quantum mechanics implies that it is impossible to measure simultaneous values of a coordinate and its conjugate momentum with unlimited precision. Instead, if Δp be the estimated error or uncertainty in a momentum and Δq that in the associated coordinate one must have the inequality, ΔpΔq>h2π \Delta p\Delta q>\frac{h}{{2\pi}} ΔpΔq>2πh​ (1) This inequality has come to be known quite generally as Heisenberg’s uncertainty relation.
Abstract Heisenberg’s uncertainty principle states that: The product of the uncertainties in the simultaneous specifications of two °complementary observables can never be less than a small quantity of the order of h. The precise form of the principle is given in Box U.1. It implies that as one observable is constrained to have a more precise value, so its partner becomes more ill-defined. An experiment designed to measure the two observables simultaneously will be able to determine one precisely only at the expense of losing information about the other (see °duality). The principle was established by Werner Heisenberg in 1927, as a consequence of his formulation of °matrix mechanics.
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics.Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted.The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity.Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally.Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the constraint that the product of their mean errors should be no less than a limit set by Planck's constant. However, Heisenberg with the subsequent completion by Kennard has long been credited only with a constraint for state preparation represented by the product of the standard deviations. Here, we show that Heisenberg actually proved the constraint for the accuracy of simultaneous measurement but assuming an obsolete postulate for quantum mechanics. This assumption, known as the repeatability hypothesis, formulated explicitly by von Neumann and Schrodinger, was broadly accepted until the 1970s, but abandoned in the 1980s, when completely general quantum measurement theory was established. We also survey the author's recent proposal for a universally valid reformulation of Heisenberg's uncertainty principle under the most general assumption on quantum measurement.