The interesting double-prism experiment of Ghose, Home, and Agarwal 5) has been suggested 5, 8, 16, 7, 6) as a challenge to Bohr´s views of complementarity. With the linguistic complementarity 14) as a general notion of complementarity, we analyze Bohr´s views of complementarity. We find that a careful formulation of Bohr´s wave-particle complementarity, with an explicit characterization of measurability as a particular low-level kind of quantum theoretical inferribility, is in fact not confronted by the double-prism experiment. Much less is the outcome a challenge to Bohr´s primary view of complementarity, namely as a tension between definability and observability in a quantum mechanical observation language. This primary view of Bohr, which is visible already in his Como paper 1), is a general formulation of quantum mechanical complementarity. Although it connects well to the subsequent metamathematical development of the wider linguistic complementarity, as a tension between describability and interpretability in a language, it is today surprisingly seldom referred to in quantum mechanical texts. Rather, discussions of the role of complementarity for the interpretability problem for quantum theory tend to focus on Bohr´s view of complementarity in terms of phenomena, which he conceived in his later discussions with Einstein (and which appears less clear than Bohr´s primary view of complementarity). The hierarchical structuring of quantum theory which is suggested in our analysis of the double-prism experiment, and in the analysis of complementarity in terms of phenomena, is of interest also for the general interpretability problem for quantum theory, and for questions about a quantum mechanical reality.
The interesting double-prism experiment of Ghose, Home, and Agarwal 5) has been suggested 5, 8, 16, 7, 6) as a challenge to Bohr´s views of complementarity. With the linguistic complementarity 14) as a general notion of complementarity, we analyze Bohr´s views of complementarity. We find that a careful formulation of Bohr´s wave-particle complementarity, with an explicit characterization of measurability as a particular low-level kind of quantum theoretical inferribility, is in fact not confronted by the double-prism experiment. Much less is the outcome a challenge to Bohr´s primary view of complementarity, namely as a tension between definability and observability in a quantum mechanical observation language. This primary view of Bohr, which is visible already in his Como paper 1), is a general formulation of quantum mechanical complementarity. Although it connects well to the subsequent metamathematical development of the wider linguistic complementarity, as a tension between describability and interpretability in a language, it is today surprisingly seldom referred to in quantum mechanical texts. Rather, discussions of the role of complementarity for the interpretability problem for quantum theory tend to focus on Bohr´s view of complementarity in terms of phenomena, which he conceived in his later discussions with Einstein (and which appears less clear than Bohr´s primary view of complementarity). The hierarchical structuring of quantum theory which is suggested in our analysis of the double-prism experiment, and in the analysis of complementarity in terms of phenomena, is of interest also for the general interpretability problem for quantum theory, and for questions about a quantum mechanical reality.
In a large variety of disciplines, fundamental studies often straddle in self-referential situations, in need of relativization to language and complementaristic resolution. In such attempts, the languages at play are hardly visible themselves. Only shadows of language, somewhat characteristic of the various disciplines, become visible and tractable. We select two domains, quantum mechanics and cybernetics, for a comparative study of their complementarity concepts with consequence for understandings of observability, describability, and objectivity. In particular, we compare Bohr–Pauli's ‘non-detachability of the observer’ and von Foerster's aphorisms for objectivity. In quantum mechanics, with its emphasis on experimentability and measurability, Bohr's primary view of complementarity takes the form of a tension between definability and measurability. In cybernetics, we have a central interest in inferribility above the more constructive measurability, and the linguistic complementarity takes the form of a tension between describability and interpretability. In quests for a complete quantum mechanical measurement language, we face an interesting situation, that of simulating semantic measurability by syntactic inferribility. It calls for a cybernetic tie, whereby the two processes of assertibility, by measurability and by provability, become united under complementarity. Although semantic and syntactic processes are complementary within the measurement language, they may be unfolded in levels of constructivity, allowing identification of the lowest levels. Namely, identification of the constructivity level of a basic measurement sentence, i.e., a sentence which can be affirmed by a direct measurement (without involving further inferences), with the lowest constructivity level of syntactic provability. We exemplify with an explanation of a recent challenge against Bohr's wave–particle compementarity. Namely, by the so called double-prism experiment of Ghose, Home, and Agarwal. We find the experiment quite interesting, not because of the alleged challenge, but by realizing that its interpretation requires a levelled approach to quantum theory.
A detailed analysis of Einstein's version of the double-slit experiment, in which one tries to observe both wave and particle properties of light, is performed. Quantum nonseparability appears in the derivation of the interference pattern, which proves to be surprisingly sharp even when the trajectories of the photons have been determined with fairly high accuracy. An information-theoretic approach to this problem leads to a quantitative formulation of Bohr's complementarity principle for the case of the double-slit experiment. A practically realizable version of this experiment, to which the above analysis applies, is proposed.
This article explores Bohr's argument, advanced under the heading of 'complementarity,' concerning quantum phenomena and quantum mechanics, and its physical and philosophical implications.In Bohr, the term complementarity designates both a particular concept and an overall interpretation of quantum phenomena and quantum mechanics, in part grounded in this concept.While the argument of this article is primarily philosophical, it will also address, historically, the development and transformations of Bohr's thinking, under the impact of the development of quantum theory and Bohr's confrontation with Einstein, especially their exchange concerning the EPR experiment, proposed by Einstein, Podolsky and Rosen in 1935.Bohr's interpretation was progressively characterized by a more radical epistemology, in its ultimate form, which was developed in the 1930s and with which I shall be especially concerned here, defined by his new concepts of phenomenon and atomicity.According to this epistemology, quantum objects are seen as indescribable and possibly even as inconceivable, and as manifesting their existence only in the effects of their interactions with measuring instruments upon those instruments, effects that define phenomena in Bohr's sense.The absence of causality is an automatic consequence of this epistemology.I shall also consider how probability and statistics work under these epistemological conditions.
xi 4.5.24.5.3The double-slit experiment The microscope 4.6 Meaning of the 'complementarity' concept 4.6.1 4.6.24.6.34.6.44.6.5 4.6.6 4.6.7 Two meanings of 'to determine' Heisenberg's disturbance theory of measurement Complementarity according to Bohr Particle-wave duality Parallel and circular complementarity Complementarity and the projection postulate Complementarity and consciousness 4.7 Critique of the complementarity principle Einstein Margenau Ballentine Recent developments Complementarity and empiricist interpretation The Einstein-Podolsky-Rosen problem 6 Individual-particle and ensemble interpretations of quantum mechanics 275 6.
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 applicability in quantum science. Book-length scholarly examinations even provide speculations about the relevance of complementarity in fields as different from physics as biology, psychology and social anthropology, connections which were apparently of interest to Bohr himself (see Jammer [2], Murdoch [3] and Whitaker [4]). Confusion evident in Como following his talk was not eliminated by Bohr's article [1], and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments [5] as well as expert examinations [6-9] show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group [10-13] and others [14-20] to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demonstrate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to complete Bohr's formulation of complementarity, debated for decades because of its incompleteness.
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