What Niels Bohr called the `epistemological lesson' of `complementarity' was the result of reasoning analogically from the classical conception of a mechanical state to a new quantum mechanical conception of an `object' in a mechanical state. Bohr proposed to redefine the `objectivity' essential for scientific description in terms of the epistemological demand for unambiguously communicable descriptions of observational results, a move which has profound consequences for how we can understand the concept of the quantum mechanical state and the nature of the `system' which is `in' this state. Here it is argued that the old notion of the `object' which is in a classical mechanical state is drawn from a substance/property ontology derived from Aristotle's analysis of categorical propositions. In moving to describing a system in a quantum mechanical state, the system that is `in' such a state can no longer be so regarded as a substance possessing properties. Bohr argues that the concept refers to an interaction which has a feature of wholeness or `individuality' that implies that the distinction between `object system' and `observing system' is relative to the context of the description. This conclusion, in turn, implies the need for a combination of complementary modes of description; however, because of his reticence in making ontological claims, he failed to develop this dimension of his new framework of complementarity.
Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's complementarity thus holds in a much broader sense than anticipated.
I argue that quantum optical experiments that purport to refute Bohr's principle of complementarity (BPC) fail in their aim. Some of these experiments try to refute complementarity by refuting the so called particle-wave duality relations, which evolved from the Wootters-Zureck reformulation of BPC (WZPC). I therefore consider it important for my forgoing arguments to first recall the essential tenets of BPC, and to clearly separate BPC from WZPC, which I will argue is a direct contradiction of BPC. This leads to a need to consider the meaning of particle-wave duality relations and to question…
Bohr's principle of complementarity lies at the central place of quantum mechanics, according to which the light is chosen to behave as a wave or particles, depending on some exclusive detecting devices. Later, intermediate cases are found, but the total information of the wave-like and particle-like behaviors are limited by some inequalities. One of them is Englert-Greenberger (EG) duality relation. This relation has been demonstrated by many experiments with the classical detecting devices. Here by introducing a quantum detecting device into the experiment, we find the limit of the duality r…
In its most orthodox form, Bohr's Complementarity Principle states that a quanton (a quantum system consisting of a Boson or Fermion) can either behave as a particle or as wave, but never simultaneosuly as both. A less orthodox interpretation of this Principle is the ``duality condition'' embodied in a mathematical inequality due to Englert [B-G Englert, Phys. Rev. Lett., Vol. 77, 2154 (1996)] which allows wave and particle attributes to co-exist, but postulates that a stronger manifestation of the particle nature leads to a weaker manifestation of the wave nature and vice versa. In this Lette…
An experimental test of quantum complementarity principle based on single neutral atom trapped in a blue detuned bottle trap was here performed. A Ramsey interferometer was used to assess the wavelike behavior or particle-like behavior with second $π/2$-rotation on or off. The wavelike behavior or particle-like behavior is characterized by the visibility $V$ of the interference or the predictability $P$ of which-path information, respectively. The measured results fulfill the complementarity relation $P^2+V^2\leq1$. Imbalance losses were deliberately introduced to the stem and find the complem…
A model of the Einstein-Bohr double-slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has the double slits in it, as well as the state of a particle incoming to the double slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting the interference pattern and distinguishing the particle path. Comparing the Kennard-Robertson type and the Ozawa-type uncertainty relations, we conclude that the uncertainty relation involved in the double-slit experiment is not the Ozawa…
After introducing sketchily Bohr's wave-particle complementarity principle in his own words, a derivation of an extended form of the principle from standard quantum mechanics is performed. Reality-evaluation of each step is given. The derived theory is applied to simple examples and the extended entities are illustrated in a thought experiment. Assessment of the approach of Bohr and of this article is taken up again with a rather negative conclusion as far as reflecting reality is concerned. The paper ends with selected incisive opinions on Bohr's dogmatic attitude and with some comments by th…
We have implemented a novel double-slit "which-way" experiment which raises interesting questions of interpretation. Coherent laser light is passed through a converging lens and then through a dual pinhole producing two beams crossing over at the focal point of the lens, and fully separating further downstream providing which-way information. A thin wire is then placed at a minimum of the interference pattern formed at the cross-over region. No significant reduction in the total flux or resolution of the separated beams is found, providing evidence for coexistence of perfect interference and w…
Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his approach to quantum mechanics over de Broglie's had no reasonable foundation. But Bohr's interpretation changed little from the time of its first appearance, and stood independent of any philosophical presuppositions. The principle of complementarity is itself best read as a conjecture of unusually wide scope, on the nature and future course of…
The photon box thought experiment can be considered a forerunner of the EPR-experiment: by performing suitable measurements on the box it is possible to ``prepare'' the photon, long after it has escaped, in either of two complementary states. Consistency requires that the corresponding box measurements be complementary as well. At first sight it seems, however, that these measurements can be jointly performed with arbitrary precision: they pertain to different systems (the center of mass of the box and an internal clock, respectively). But this is deceptive. As we show by explicit calculation,…
There is presented a contextual statistical model of the probabilistic description of physical reality. Here contexts (complexes of physical conditions) are considered as basic elements of reality. There is discussed the relation with QM. We propose a realistic analogue of Bohr's principle of complementarity. In the opposite to the Bohr's principle, our principle has no direct relation with mutual exclusivity for observables. To distinguish our principle from the Bohr's principle and to give better characterization, we change the terminology and speak about supplementarity, instead of compleme…
Based on modern quantum measurement theory, we use Zurek's "triple model" to study, from the viewpoint of quantum information theory, the wave and particle nature of a photon in a symmetric Mach-Zehnder interferometer. In the process of quantum measurement, the state of both the system and the detector is not an entangled state but a correlated state. We find that the information gain about the photon is related to the correlations (including classical and quantum correlations) between the photon and the detector. We also derive the relationship between the information gain and the fringe visi…
Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term "complementarity", as a physical concept, was spoken publicly [1], revealing Bohr's own thinking about Louis de Broglie's "duality". Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity's importance and broad applic…
The two-slit experiment with quantum particles provides many insights into the behaviour of quantum mechanics, including Bohr's complementarity principle. Here we analyze Einstein's recoiling slit version of the experiment and show how the inevitable entanglement between the particle and the recoiling slit as a which-way detector is responsible for complementarity. We derive the Englert-Greenberger-Yasin duality from this entanglement, which can also be thought of as a consequence of sum-uncertainty relations between certain complementary observables of the recoiling slit. Thus, entanglement i…
The Einstein-Rupp experiments have been unduly neglected in the history of quantum mechanics. While this is to be explained by the fact that Emil Rupp was later exposed as a fraud and had fabricated the results, it is not justified, due to the importance attached to the experiments at the time. This paper discusses Rupp's fraud, the relation between Albert Einstein and Rupp, and the Einstein-Rupp experiments, and argues that these experiments were an influence on Niels Bohr's development of complementarity and Werner Heisenberg's formulation of the uncertainty relations.
We test Bohr's complementary relation, which captures the most counterintuitive difference of a classical and a quantum world, for single and bipartite neutral kaons. They present a system that is naturally interfering, oscillating and decaying. Moreover, kaons break the CP symmetry (C...charge conjugation, P...parity). In detail we discuss the effect of the CP violation on Bohr's relation, i.e. the effect on the "particle-like" information and the "wave-like" information. Further we show that the quantity that complements the single partite information for bipartite kaons is indeed concurrenc…
In quantum physics, the notion of contextuality has a variety of interpretations which are typically associated with the names of their inventors, say Bohr, Bell, Kochen and Specker, and recently Dzhafarov. In fact, Bohr was the first who pointed to contextuality of quantum measurements as a part of formulation of his principle of complementarity. (Instead of "contextuality", he considered dependence on "experimental conditions.") Unfortunately, the contextuality counterpart of the complementarity principle was overshadowed by the issue of incompatibility of observables. And the interest for c…
A which-way measurement in Young's double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenberg's uncertainty principle: distinguishing two positions a distance s apart transfers a random momentum q \sim \hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohr's stance is always valid. We address this issue using the experimental technique of weak measurement. …
Interference results when a quantum particle is free to choose among a few indistinguishable paths. A canonical example of Bohr's complementarity principle [1] is a two-path interferometer with an external detector coupled to one of the paths. Then, interference between the two paths vanishes (i.e. dephasing) if one is able to detect, even in principle, the path taken by the particle. This type of which path (WP) experiment was already executed with photons, cooled atoms, neutrons, solitons, and more recently with electrons in a mesoscopic system [2]. In the latter experiment path determinatio…
It is argued that Niels Bohr ultimately arrived at positivistic and antirealist-flavored statements because of weaknesses in his initial objective of accounting for measurement in physical terms. Bohr's investigative approach faced a dilemma, the choices being (i) conceptual inconsistency or (ii) taking the classical realm as primitive. In either case, Bohr's `Complementarity' does not adequately explain or account for the emergence of a macroscopic, classical domain from a microscopic domain described by quantum mechanics. A diagnosis of the basic problem is offered, and an alternative way fo…
Bohr placed complementary bases at the mathematical centre point of his view of quantum mechanics. On the technical side then my question translates into that of classifying complex Hadamard matrices. Recent work (with Barros e Sa) shows that the answer depends heavily on the prime number decomposition of the Hilbert space. By implication so does the geometry of quantum state space.
The NAFL (non-Aristotelian finitary logic) interpretation of quantum mechanics requires that no `physical' reality can be ascribed to the wave nature of the photon. The NAFL theory QM, formalizing quantum mechanics, treats the superposed state ($S$) of a single photon taking two or more different paths at the same time as a logical contradiction that is formally unprovable in QM. Nevertheless, in a nonclassical NAFL model for QM in which the law of noncontradiction fails, $S$ has a meaningful metamathematical interpretation that the classical path information for the photon is not available. I…
A growing number of commentators have, in recent years, noted the important affinities in the views of Immanuel Kant and Niels Bohr. While these commentators are correct, the picture they present of the connections between Bohr and Kant is painted in broad strokes; it is open to the criticism that these affinities are merely superficial. In this essay, I provide a closer, structural, analysis of both Bohr's and Kant's views that makes these connections more explicit. In particular, I demonstrate the similarities between Bohr's argument, on the one hand, that neither the wave nor the particle d…
We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenberg's uncertainty relation for position and modular momentum. We apply our theory to atom interferometry, wherein spontaneously emitted photons provide which way information, and unambiguously resolve the challenge posed by the metamaterial `perfect lens' to complementarity and to the Heisenberg-Bohr interpretation of the Heisenberg microscope thought experiment.
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object. The complementary descriptions approach is a framework for the interpretation of quantum mechanics, more specifically, it focuses in the development of the idea of complementarity and the concept of potentiality in the orthodox quantum formulation. In PART I of this article, we analyze the ideas of Bohr and pr…
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object. The complementary descriptions approach is a framework for the interpretation of quantum mechanics, more specifically, it focuses in the development of the idea of complementarity and the concept of potentiality in the orthodox quantum formulation. In PART I of this article, we analyze the ideas of Bohr and pr…
The Copenhagen interpretation of quantum mechanics, which first took shape in Bohr's landmark 1928 paper on complementarity, remains an enigma. Although many physicists are skeptical about the necessity of Bohr's philosophical conclusions, his pragmatic message about the importance of the whole experimental arrangement is widely accepted. It is, however, generally also agreed that the Copenhagen interpretation has no direct consequences for the mathematical structure of quantum mechanics. Here I show that the application of Bohr's main concepts of complementarity to the subsystems of a closed …
Bohr's complementarity and Schrödinger's entanglement are two prominent physical characters of quantum systems. In this letter, we formally connect them. It is known that complementarity relations for wave-particle duality are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate a complementarity relation and can even reach zero for a maximally mixed state. To fully characterize a quanton, it is not enough to consider its wave-particle aspect; we have also to regard its quantum correlations with other systems. Here we prove tha…
A recent experiment performed by S. S. Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information in a two-path interferometer. We have reproduced this experiment, using true single-photon pulses propagating in a two-path wavefront- splitting interferometer realized with a Fresnel's biprism, and followed by a grating with adjustable transmitting slits. The measured values of interference visibility V and which-path information, characterized by the distinguishability parameter D, are found to obey the complem…
Some recent works have introduced a quantum twist to the concept of complementarity, exemplified by a setup in which the which-way detector is in a superposition of being present and absent. It has been argued that such experiments allow measurement of particle-like and wave-like behavior at the same time. Here we derive an inequality which puts a bound on the visibility of interference and the amount of which-way information that one can obtain, in the context of such modified experiments. As the wave-aspect can only be revealed by an ensemble of detections, we argue that in such experiments,…
Bohr's complementarity principle is of fundamental historic and conceptual importance for Quantum Mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like character of a quantum system, but not both. However, it was eventually realized that these dual behaviors can both manifest partially in the same experimental setup, and, using ad hoc proposed measures for the wave and particle aspects of the quanton, complementarity relations were proposed limiting how strong these manifestations can be. Recently, a formal…
It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consi…
Quantum information technology is one of the fastest growing sectors within information technology. By misleading interpretations of Bohr's definition of complementarity, the foundation of nonlocal correlations of entanglement is concealed and therefore, such nonlocal effects can apparently not be utilized directly in information technology. As the first step to identify the utilizable nonlocal property of entanglement, this paper adjusts the notion of complementarity of first-order and second-order interference. Especially, the nonlocal consequence of the "principle of least action" for entan…
We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the CCRs. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero element.
We experimentally verify the link existing between entanglement and the amount of wave-particle duality in a bipartite quantum system, with superconducting qubits in the IBM Q quantum computer. We consider both pure and mixed states, and study the influence of state purity on the observation of the complementarity "triality" relation of Jakob and Bergou. This work confirms the quantitative completion of local Bohr's complementarity principle by the nonlocal quantum entanglement typical of a truly bipartite quantum system.
Bohr's principle of complementarity predicts that in a welcher weg ("which-way") experiment, obtaining fully visible interference pattern should lead to the destruction of the path knowledge. Here I report a failure for this prediction in an optical interferometry experiment. Coherent laser light is passed through a dual pinhole and allowed to go through a converging lens, which forms well-resolved images of the respective pinholes, providing complete path knowledge. A series of thin wires are then placed at previously measured positions corresponding to the dark fringes of the interference pa…
Bohr's complementarity principle has been challenged by quantum delayed-choice experiments wherein quantum systems are claimed to behave neither as wave nor as a particle, but in an intermediary way. However, this conclusion has been supported by retro-inference and with no direct link with the system quantum state. Here, we consider a framework that employs an operational criterion of physical reality to diagnosis the system ontology directly from the quantum state at each instant of time. We show that, in disparity with previous proposals, our setup ensures a formal link between the output v…
We interpret the philosophy of Niels Bohr as related to the so called "linguistic turn" and consider paraconsistency in the light of the Bohrian notion of complementarity. Following [16], Jean-Yves Beziau has discussed the seemingly contradictory perspectives found in the quantum mechanical double slit experiment in terms of paraconsistent view-points [7, 8]. This interpretation goes in line with the well known Bohrian Neo-Kantian epistemological account of quantum mechanics. In the present paper, we put forward the idea that one can also consider, within quantum mechanics and departing from t…
According to Bohr's principle of complementarity, a quanton can behave either as a wave or a particle, depending on the choice of the experimental setup. Some recent two-path interference experiments have devised methods where one can have a quantum superposition of the two choices, thus indicating that a quanton may be in a superposition of wave and particle nature. These experiments have been of interest from the point of view of Wheeler's delayed-choice experiment. However, it has also been claimed that this experiment can violate complementarity. Here we theoretically analyze a multipath i…
The quantitative formulation of Bohr's complementarity proposed by Greenberger and Yasin is applied to some physical situations for which analytical expressions are available. This includes a variety of conventional double-slit experiments, but also particle oscillations, as in the case of the neutral-kaon system, and Mott scattering of identical nuclei. For all these cases, a unified description can be achieved including a new parameter, $ν$, which quantifies the effective number of fringes one can observe in each specific interferometric set-up.
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general dificulty in the formation of human ideas, inherent in the distinction between subject and object. Earlier, we have introduced a development of the concept of complementarity which constitutes a new approach to the interpretation of quantum mechanics. We argue that this development allows a better understanding of some of the paradigmatic interpretational problems of quantum theory. Within the scheme propose…
We compare different approaches to quantum ontology. In particular, we discuss an interpretation of quantum mechanics that we call objective quantum field theory (OQFT), which involves retrocausal fields. Here, objective implies the existence of fields independent of an observer, but not that the results of conjugate measurements are predetermined: the theory is contextual. The ideas and analyses of Einstein and Bohr through to more recent approaches to objective realism are discussed. We briefly describe measurement induced projections, the guided wave interpretation, many-universes, consiste…
One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particle-like \emph{or} a wave-like behaviour, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave a…
We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems. We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability density is displaced by spatial translations. In contrast a wave-like state is represented by a spatially-delocalized wave function and the corresponding broad position probability density is invariant to spatial translations. The wave-particle dichotomy can therefore be seen as a competition between displacement and invariance of the state with respect to spat…
A modified version of Young's experiment by Shahriar Afshar indirectly reveals the presence of a fully articulated interference pattern prior to the post-selection of a particle in a "which-slit" basis. While this experiment does not constitute a violation of Bohr's Complementarity Principle as claimed by Afshar, both he and many of his critics incorrectly assume that a commonly used relationship between visibility parameter V and "which-way" parameter K has crucial relevance to his experiment. It is argued here that this relationship does not apply to this experimental situation and that it i…
I begin by examining the question of the quantum limits of knowledge by briefly presenting the constraints of the theory that derive from its mathematical structure (in particular the no-go theorems formulated by von Neumann and Kochen and Specker). I then argue that these theorems reflect on a formal level those practical and experimental settings that are needed to come to know the properties of physical systems. In particular, I discuss some aspects of this relationist and contextualist conception of reality by comparing, in their apparent diversity, Bohr holistic and Rovelli relationist in…
The spectacular successes of quantum physics have made it a commonplace to assert that we live in a quantum world. This idea seems to imply a kind of "quantum fundamentalism" according to which everything in the universe (if not the universe as a whole) is fundamentally of a quantum nature and ultimately describable in quantum-mechanical terms. Bohr's conception of quantum mechanics has traditionally been seen as opposed to such a view, not least because of his insistence on the necessity of the concepts of classical physics in the account of quantum phenomena. Recently, however, a consensus s…
By filtering out the philosophic component we can be said that the EPR-paper was directed against the straightforward interpretation of the Heisenberg's uncertainty principle or more generally the Bohr's complementarity principle. The latter expresses contextuality of quantum measurements: dependence of measurement's output on the complete experimental arrangement. However, Bell restructured the EPR-argument against complementarity to justify nonlocal theories with hidden variables of the Bohmian mechanics' type. Then this Bell's kind of nonlocality - {\it subquantum nonlocality} - was lifted …
We propose quantum circuits to test interferometric complementarity using symmetric two-way interferometers coupled to a which-path detector. First, we consider the two-qubit setup in which the controlled transfer of path information to the detector subsystem depletes interference on the probed subspace, testing the visibility-distinguishability trade-off via minimum-error state discrimination measurements. Next, we consider the quantum eraser setup, in which reading out path information in the right basis recovers an interference pattern. These experiments are then carried out in an IBM super…
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.
