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

BOHR'S COMPLEMENTARITY AND AFSHAR'S EXPERIMENT: NON-DUALISTIC STUDY AT THE SINGLE-QUANTUM LEVEL

C Ravi Kumar, Nakka Gurappa

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Using a newly proposed `wave-particle non-dualistic interpretation' of the quantum formalism, Bohr's principle of complementarity is analyzed in the context of the single-slit diffraction and the Afshar's experiments - at the single-quantum level. The fundamental flaw in the Afshar's argument is explicitly pointed out.

DOI
10.13140/rg.2.2.22664.98568

Related papers

Wave Particle Duality and the Afshar Experiment

Aurélien Drezet

In an interesting series of articles published few years ago Afshar and coworkers [1,2] reported an optical experiment in which they claimed to refute the well known N. Bohr principle of complementarity [3, 4]. Obviously this result, if justified, would constitute a serious attack against the orthodox interpretation of quantum mechanics (known as the Copenhagen interpretation). This work stirred much debate in different journals (see for examples references [5–12]). We think however that there are still some important misunderstandings concerning the interpretation of this experiment. In a preprint written originally in 2004 [5] (and following some early discussions with Afshar) we claimed already that the interpretation by Afshar et al. can be easily stated if we stay as close as possible from the texts written by Bohr. The aim of the present article (which was initially written in 2005 to precise a bit the thought developed in [5]) is to comment the interpretation discussed in [1]. We will in the following analyze the meaning of Bohr principle and show that far from disproving its content the experiment [1] is actually a complete confirmation of its general validity. The difficulties associated with the understanding of this principle are not new and actually complementarity created troubles even in Einstein mind [3] so that we are here in good company. To summarize a bit emphatically Bohr’s complementarity we here remind that this principle states that if one of a pair of non commuting observables of a quantum object is known for sure, then information about the second (complementary) is lost [3, 4, 15, 16]. This can be equivalently expressed as a kind of duality between different descriptions of the quantum system associated with different experimental arrangements which mutually exclude each other (read in particular [3,4]). Later in the discussion we will try to precise this definition but for the moment it is enough to illustrate the concepts by examples Consider for instance the well known Young double-pinholes interference experiment made with photons. The discrete nature of light precludes the simultaneous observation of a same photon in the aperture plane and in the interference pattern: the photon cannot be absorbed twice. This is already a trivial manifestation of the principle of Bohr. Here it implies that the two statistical patterns associated with the wave in the aperture plane and its Fourier (i. e., momentum) transform require necessarily different photons for their recording. It is in that sense that each experiment excludes and completes reciprocally the other. In the case considered before the photon is absorbed during the first detection (this clearly precludes any other detection). However even a non-destructive solution for detection implying entanglement with other quantum systems has a radical effect of the same nature: the complementarity principle is still valid. For example, during their debate Bohr and Einstein [3] discussed an ideal which-way experiment in which the recoil of the slits is correlated to the motion of the photon. Momentum conservation added to arguments based on the uncertainty relations are sufficient to explain how such entanglement photon-slits can erase fringes [15–19]. It is also important for the present discussion to remind that the principle of complementarity has a perfidious consequence on the experimental meaning of trajectory and path followed by a particle. Indeed the unavoidable interactions existing between photons and detectors imply that a trajectory existing independently of any measurement process cannot be unambiguously defined. This sounds even like a tragedy when we consider once again the two-holes experiment. Indeed for Bohr this kind of experiments shows definitely the essential element of ambiguity which is involved in ascribing conventional physical attributes to quantum systems. Intuitively (i. e., from the point of view of classical particle dynamic) one would expect that a photon detected in the focal plane of the lens must have crossed only one of the hole 1 or 2 before to reach its final destination. However, if this is true, one can not intuitively understand how the presence of the second hole (through which the photon evidently did not go) forces the photon to participate to an interference pattern (which obviously needs an influence coming from both holes). Explanations to solve this paradox have been proposed by de Broglie, Bohm, and others using concepts such as empty waves or quantum potentials [20, 21]. However all these explanations are in agreement with Bohr principle (since they fully reproduce quantum predictions) and can not be experimentally distinguished. Bohr and Heisenberg proposed for all needed purposes a much more pragmatic and simpler answer: don’t bother, the complementarity principle precludes the simultaneous observation of a photon trajectory and of an interference pattern. For Bohr [3]: This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path

•Jan 1, 2011•5 citations

Complementarity and the Afshar Experiment

Tabish Qureshi

A modified two-slit interference experiment, proposed and carried out by Shahriar Afshar [first reported by M. Chown, New Scientist {\\bf 183}, 30 (2004)], claims to demonstrate a violation of Bohr's complementarity principle. We point out the flaw in Afshar's analysis and show why complementarity is robust and cannot be violated in any experiment which is a variant of the conventional two-slit experiment.

•Jan 16, 2007•6 citations

Afshar's experiment revisited: a demonstration of Bohr's complementary principle

Ngoc Diep Lai, V. Jacques, A. Dréau +5 more

A recent experiment performed by Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information a two-path interferometer. The authors have reproduced the same experiment, using true single-photon pulses emitted by a single nitrogen-vacancy (NV) color center in a diamond crystal and propagating in a two-path wavefront-splitting interferometer realized with a Fresnels' biprism, followed by a grating with transmitting slits of adjustable width. The experimental setup is illustrated. The results go far beyond the reported results in the previous works of Afshar et al. and the subtle flaws in their analysis are then pointed out. The measured values of the interference visibility V and the which-path information, characterized by the distinguishability parameter D, are found, with values close to the ideal-case upper bound. This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics, without any violation of Bohr's complementarity principle.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2009•0 citations

Paradox or non-paradox in wave-particle duality

Aurélien Drezet

We analyze the experiment recently realized by S. Afshar et al. [1] in order to refute the principle of complementarity. We discuss the general meaning of this principle and show that contrarily to the claim of the authors Bohr's complementarity is not in danger in this experiment.

arXiv:1008.4261•Aug 25, 2010•0 citations

No Paradox in Wave–Particle Duality

Andrew Knight

The assertion that an experiment by Afshar et al. demonstrates violation of Bohr’s Principle of Complementarity is based on the faulty assumption that which-way information in a double-slit interference experiment can be retroactively determined from a future measurement.

•Jan 1, 2020•3 citations

Complementarity and Afshar's experiment

Aurélien Drezet

In this article we criticize the experiment realized by S. Afshar [Proc. SPIE 5866, 229-244 (July 2005)]. We analyze Bohr's complementarity and show that the interpretation proposed by Afshar is misleading.

arXiv:quant-ph/0508091•Aug 11, 2005•10 citations
Using a newly proposed `wave-particle non-dualistic interpretation' of the quantum formalism, Bohr's principle of complementarity is analyzed in the context of the single-slit diffraction and the Afshar's experiments - at the single-quantum level. The fundamental flaw in the Afshar's argument is explicitly pointed out.
In an interesting series of articles published few years ago Afshar and coworkers [1,2] reported an optical experiment in which they claimed to refute the well known N. Bohr principle of complementarity [3, 4]. Obviously this result, if justified, would constitute a serious attack against the orthodox interpretation of quantum mechanics (known as the Copenhagen interpretation). This work stirred much debate in different journals (see for examples references [5–12]). We think however that there are still some important misunderstandings concerning the interpretation of this experiment. In a preprint written originally in 2004 [5] (and following some early discussions with Afshar) we claimed already that the interpretation by Afshar et al. can be easily stated if we stay as close as possible from the texts written by Bohr. The aim of the present article (which was initially written in 2005 to precise a bit the thought developed in [5]) is to comment the interpretation discussed in [1]. We will in the following analyze the meaning of Bohr principle and show that far from disproving its content the experiment [1] is actually a complete confirmation of its general validity. The difficulties associated with the understanding of this principle are not new and actually complementarity created troubles even in Einstein mind [3] so that we are here in good company. To summarize a bit emphatically Bohr’s complementarity we here remind that this principle states that if one of a pair of non commuting observables of a quantum object is known for sure, then information about the second (complementary) is lost [3, 4, 15, 16]. This can be equivalently expressed as a kind of duality between different descriptions of the quantum system associated with different experimental arrangements which mutually exclude each other (read in particular [3,4]). Later in the discussion we will try to precise this definition but for the moment it is enough to illustrate the concepts by examples Consider for instance the well known Young double-pinholes interference experiment made with photons. The discrete nature of light precludes the simultaneous observation of a same photon in the aperture plane and in the interference pattern: the photon cannot be absorbed twice. This is already a trivial manifestation of the principle of Bohr. Here it implies that the two statistical patterns associated with the wave in the aperture plane and its Fourier (i. e., momentum) transform require necessarily different photons for their recording. It is in that sense that each experiment excludes and completes reciprocally the other. In the case considered before the photon is absorbed during the first detection (this clearly precludes any other detection). However even a non-destructive solution for detection implying entanglement with other quantum systems has a radical effect of the same nature: the complementarity principle is still valid. For example, during their debate Bohr and Einstein [3] discussed an ideal which-way experiment in which the recoil of the slits is correlated to the motion of the photon. Momentum conservation added to arguments based on the uncertainty relations are sufficient to explain how such entanglement photon-slits can erase fringes [15–19]. It is also important for the present discussion to remind that the principle of complementarity has a perfidious consequence on the experimental meaning of trajectory and path followed by a particle. Indeed the unavoidable interactions existing between photons and detectors imply that a trajectory existing independently of any measurement process cannot be unambiguously defined. This sounds even like a tragedy when we consider once again the two-holes experiment. Indeed for Bohr this kind of experiments shows definitely the essential element of ambiguity which is involved in ascribing conventional physical attributes to quantum systems. Intuitively (i. e., from the point of view of classical particle dynamic) one would expect that a photon detected in the focal plane of the lens must have crossed only one of the hole 1 or 2 before to reach its final destination. However, if this is true, one can not intuitively understand how the presence of the second hole (through which the photon evidently did not go) forces the photon to participate to an interference pattern (which obviously needs an influence coming from both holes). Explanations to solve this paradox have been proposed by de Broglie, Bohm, and others using concepts such as empty waves or quantum potentials [20, 21]. However all these explanations are in agreement with Bohr principle (since they fully reproduce quantum predictions) and can not be experimentally distinguished. Bohr and Heisenberg proposed for all needed purposes a much more pragmatic and simpler answer: don’t bother, the complementarity principle precludes the simultaneous observation of a photon trajectory and of an interference pattern. For Bohr [3]: This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path
A recent experiment performed by Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information a two-path interferometer. The authors have reproduced the same experiment, using true single-photon pulses emitted by a single nitrogen-vacancy (NV) color center in a diamond crystal and propagating in a two-path wavefront-splitting interferometer realized with a Fresnels' biprism, followed by a grating with transmitting slits of adjustable width. The experimental setup is illustrated. The results go far beyond the reported results in the previous works of Afshar et al. and the subtle flaws in their analysis are then pointed out. The measured values of the interference visibility V and the which-path information, characterized by the distinguishability parameter D, are found, with values close to the ideal-case upper bound. This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics, without any violation of Bohr's complementarity principle.