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
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
Updating the wave-particle duality Maria C. Bosca e-mail: bosca@ugr.es Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incorporate the simultaneous use of the two classical descriptions in the interpretation of experiments, loosing their original mutual exclusivity , which is incorporated as an extreme case in the new interferometric duality, a continuous quantum concept . The wave-particle duality, therefore, must be formulated as an interpretative addition to quantum mechanics, to which is possible to renounce if any pretension of visualize quantum phenomena in terms of classical concepts and intuitions is abandoned.
Young’s double-slit experiment played a crucial role in establishing the wave nature of light. In this chapter, the shocking result that incident electrons yield a similar interference pattern as that formed by light waves is described. It is shown that the only way the experimental results could be explained is via a wave function description of electrons. It is also shown that, in the same experiment, the interference fringes disappear if the which-path information becomes available. This is the essence of wave–particle duality. The first of the Einstein–Bohr debates on wave-particle duality and Bohr’s principle of complementarity in the double-slit experiment is also discussed. Also presented are the counterintuitive notions of delayed choice and quantum eraser effects showing how the availability or erasure of information generated in the future can affect how the data in the present can be interpreted.
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.
Abstract Young’s double-slit experiment played a crucial role in establishing the wave nature of light. In this chapter, the shocking result that incident electrons yield a similar interference pattern as that formed by light waves is described. It is shown that the only way the experimental results could be explained is via a wavefunction description of electrons. It is also shown that the interference fringes disappear if the which-path information becomes available. This is the essence of wave–particle duality. The first of the Einstein–Bohr debates on wave–particle duality and Bohr’s principle of complementarity in the double-slit experiment are also discussed. The counterintuitive notions of delayed choice and quantum eraser effects showing how the availability or erasure of information generated in the future can affect how the data in the present can be interpreted are presented. Quantum interference is responsible for novel phenomena like interaction-free measurement and counterfactual communication.
This work is about Bohmian mechanics, a non-relativistic quantum theory about the motion of particles and their trajectories, named after its inventor David Bohm (Bohm,1952). This mechanics resolves all paradoxes associated with the measurement problem in nonrelativistic quantum mechanics. It accounts for quantum randomness, absolute uncertainty, the meaning of the wave function of a system, collapse of the wave function, and familiar (macroscopic) reality. We review the purpose for which Bohmian trajectories were invented: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. To achieve this we analyse an optical interferometry experiment devised and carried out 2005 by Shahriar Afshar (Afshar,2005). The radical claim of Afshar implies in his own words the 'observation of physical reality in the classical sense' for both 'which path (particle-like)' and 'interference (wave-like)' properties of photons in the same experimental setup through the violation of the Englert-Greenberger duality relation (Englert,1996) that according to Englert can be regarded as quantifying of the 'principle of complementarity'.
In the history of quantum mechanics, much has been written about the double-slit experiment, and much debate as to its interpretation has ensued. Indeed, to explain the interference patterns for sub-atomic particles, explanations have been given not only in terms of the principle of complementarity and wave-particle duality but also in terms of quantum consciousness and parallel universes. In this paper, the topic will be discussed from the perspective of spin-coupling in the hope of further clarification. We will also suggest that this explanation allows for a realist interpretation of the Afshar Experiment.