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Summary The 'Copenhagen interpretation' is a label for a loose collection of ideas originating in the work of Werner Heisenberg and Niels Bohr. What exactly amounts to is disputed; but it characteristically denies that quantum mechanics describes an objective microscopic reality, emphasizing instead the essential role of observation and the measurement context.
Key works Heisenberg 1958 and Bohr 1958 are central to the Copenhagen interpretation. Beller 1999 gives a critical history of the interpretation.
Introductions Howard 2004
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  1. T. Acton, S. Caffrey, S. Dunn, P. Vinson & K. Svozil (1998). Analogues of Quantum Complementarity in the Theory of Automata - a Prolegomenon to the Philosophy of Quantum Mechanics. Studies in History and Philosophy of Science Part B 29 (1):61-80.
    Complementarity is not only a feature of quantum mechanical systems but occurs also in the context of finite automata.
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  2. Guillaume Adenier (ed.) (2007). Quantum Theory, Reconsideration of Foundations 4: Växjö (Sweden), 11-16 June, 2007. American Institute of Physics.
    This conference was devoted to the 80 years of the Copenhagen Interpretation, and to the question of the relevance of the Copenhagen interpretation for the present understanding of quantum mechanics. It is in this framework that fundamental questions raised by quantum mechanics, especially in information theory, were discussed throughout the conference. As has become customary in our series of conference in Växjö, we were glad to welcome a fruitful assembly of theoretical physicists, experimentalists, mathematicians and even philosophers interested in the (...)
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  3. Valia Allori (2013). On the Metaphysics of Quantum Mechanics. In Soazig Lebihan (ed.), Precis de la Philosophie de la Physique. Vuibert.
    What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wave function ontology: the view according to which the wave function mathematically represents in a complete way fundamentally all there is in the world. Erwin Schroedinger was one of the first proponents of such a view, but he dismissed it after he realized it led to macroscopic superpositions (if the wave function evolves in (...)
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  4. Harald Atmanspacher (2002). Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond. [REVIEW] Foundations of Physics 32 (3):379-406.
    The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.
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  5. Gennaro Auletta & Gino Tarozzi (2004). On the Physical Reality of Quantum Waves. Foundations of Physics 34 (11):1675-1694.
    The main interpretations of the quantum-mechanical wave function are presented emphasizing how they can be divided into two ensembles: The ones that deny and the other ones that attribute a form of reality to quantum waves. It is also shown why these waves cannot be classical and must be submitted to the restriction of the complementarity principle. Applying the concept of smooth complementarity, it is shown that there can be no reason to attribute reality only to the events and not (...)
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  6. Guido Bacciagaluppi (2009). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press.
    This book will be of interest to graduate students and researchers in physics and in the history and philosophy of quantum theory.
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  7. Manuel Bächtold (2008). Interpreting Quantum Mechanics According to a Pragmatist Approach. Foundations of Physics 38 (9):843-868.
    The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions.
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  8. Robert W. Batterman (1991). Chaos, Quantization, and the Correspondence Principle. Synthese 89 (2):189 - 227.
  9. Mara Beller (1992). The Birth of Bohr's Complementarity: The Context and the Dialogues. Studies in History and Philosophy of Science Part A 23 (1):147-180.
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  10. David Bohm (1962). Classical and Non-Classical Concepts in the Quantum Theory. An Answer to Heisenberg's Physics and Philosophy. British Journal for the Philosophy of Science 12 (48):265-280.
  11. David Bohm (1962). Classical and Non-Classical Concepts in the Quantum Theory. British Journal for the Philosophy of Science 12 (48):265-280.
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  12. Niels Bohr (1937). Causality and Complementarity. Philosophy of Science 4 (3):289-298.
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  13. Matthew J. Brown (2014). Quantum Frames. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 45:1-10.
  14. Jeffrey Bub (1968). Hidden Variables and the Copenhagen Interpretation--A Reconciliation. British Journal for the Philosophy of Science 19 (3):185-210.
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  15. Mario Bunge (1955). Strife About Complementarity (II). British Journal for the Philosophy of Science 6 (22):141-154.
  16. Mario Bunge (1955). Strife About Complementarity (I). British Journal for the Philosophy of Science 6 (21):1-12.
  17. Paul Busch & Pekka J. Lahti (1985). A Note on Quantum Theory, Complementarity, and Uncertainty. Philosophy of Science 52 (1):64-77.
    Uncertainty relations and complementarity of canonically conjugate position and momentum observables in quantum theory are discussed with respect to some general coupling properties of a function and its Fourier transform. The question of joint localization of a particle on bounded position and momentum value sets and the relevance of this question to the interpretation of position-momentum uncertainty relations is surveyed. In particular, it is argued that the Heisenberg interpretation of the uncertainty relations can consistently be carried through in a natural (...)
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  18. Kristian Camilleri (2009). Constructing the Myth of the Copenhagen Interpretation. Perspectives on Science 17 (1):pp. 26-57.
    According to the standard view, the so-called ‘Copenhagen interpretation’ of quantum mechanics originated in discussions between Bohr and Heisenberg in 1927, and was defended by Bohr in his classic debate with Einstein. Yet recent scholarship has shown Bohr’s views were never widely accepted, let alone properly understood, by his contemporaries, many of whom held divergent views of the ‘Copenhagen orthodoxy’. This paper examines how the ‘myth of the Copenhagen interpretation’ was constructed by situating it in the context of Soviet Marxist (...)
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  19. John Cramer, A Farewell to Copenhagen?
    This column is about experimental tests of the various interpretations of quantum mechanics. The question at issue is whether we can perform experiments that can show whether there is an "observer-created reality" as suggested by the Copenhagen Interpretation, or a peacock’s tail of rapidly branching alternate universes, as suggested by the Many-Worlds Interpretation, or forward-backward in time handshakes, as suggested by the Transactional Interpretation? Until recently, I would have said that this was an impossible task, but a new experiment has (...)
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  20. John Cramer, The Quantum Handshake.
    Alternate View Column AV-16 Keywords: quantum, paradoxes,transactional, Copenhagen, interpretation Published in the November-1986 issue of Analog Science Fiction & Fact Magazine; This column was written and submitted 4/4/86 and is copyrighted © 1986, John G. Cramer. All rights reserved. No part may be reproduced in any form without the explicit permission of the author.
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  21. John G. Cramer (1986). The Transactional Interpretation of Quantum Mechanics. Reviews of Modern Physics 58 (3):647-687.
    Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. (...)
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  22. Michael Cuffaro (2010). The Kantian Framework of Complementarity. Studies in History and Philosophy of Science Part B 41 (4):309-317.
    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 (...)
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  23. Dennis Dieks (2003). Book Review: Foundations of Quantum Mechanics, an Empiricist Approach. By Willem M. De Muynck. Kluwer Academic Publishers, Dordrecht/Boston/London, 2002, Xxiv+680 Pp., $219.00 (Hardcover). ISBN 1-4020-0932-1. [REVIEW] Foundations of Physics 33 (6):1003-1006.
  24. Allen C. Dotson (2008). Refocusing Bohr's Quantum Postulate. Studies in History and Philosophy of Science Part B 39 (3):610-619.
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  25. Allen C. Dotson (1995). On Creating Values of Physical Properties Nonlocally. Foundations of Physics 25 (9):1359-1370.
    Can a value of a physical property be created instantaneously by a distant act of measurement? This paper develops an answer to that question by reconciling ideas expressed by Bohr in 1958 with the “standard” Copenhagen interpretation. The point of view thereby obtained is then applied to recently described correlation experiments of various sorts.
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  26. Jan Faye, Copenhagen Interpretation of Quantum Mechanics. Stanford Encyclopedia of Philosophy.
    As the theory of the atom, quantum mechanics is perhaps the most successful theory in the history of science. It enables physicists, chemists, and technicians to calculate and predict the outcome of a vast number of experiments and to create new and advanced technology based on the insight into the behavior of atomic objects. But it is also a theory that challenges our imagination. It seems to violate some fundamental principles of classical physics, principles that eventually have become a part (...)
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  27. E. E. Fitchard (1979). Proposed Experimental Test of Wave Packet Reduction and the Uncertainty Principle. Foundations of Physics 9 (7-8):525-535.
    A practical experiment using coincidence techniques is suggested to test the validity of the following concepts:(1) wave packet reduction and(2) the measurement-uncertainty principle for position and momentum. The suggested experiment uses the time-of-flight method to determine an electron's momentum and a coincident photon, emitted from a system excited by the electron, to determine its initial position. It is shown that this method does constitute a simultaneous measurement of position and momentum for a single system. Also, it is pointed out that (...)
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  28. Gordon N. Fleming, Uses of a Quantum Master Inequality.
    An inequality in quantum mechanics, which does not appear to be well known, is derived by elementary means and shown to be quite useful. The inequality applies to 'all' operators and 'all' pairs of quantum states, including mixed states. It generalizes the rule of the orthogonality of eigenvectors for distinct eigenvalues and is shown to imply all the Robertson generalized uncertainty relations. It severely constrains the difference between probabilities obtained from 'close' quantum states and the different responses they can have (...)
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  29. Henry J. Folse Jr (1974). The Copenhagen Interpretation of Quantum Theory and Whitehead's Philosophy of Organism. Tulane Studies in Philosophy 23:32-47.
  30. Henry J. Folse (1995). Niels Bohr and the Construction of a New Philosophy. Studies in History and Philosophy of Science Part B 26 (1):107-116.
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  31. Yehudah Freundlich (1977). Two Views of an Objective Quantum Theory. Foundations of Physics 7 (3-4):279-300.
    Is the Copenhagen interpretation really a subjective one? What is the special role that observations play in quantum theory? Is there really something peculiar about the projection postulate? Why does the Copenhagenist treat probabilities as properties of individual systems? Is there a measurement problem, and if so, can itin principle be solved within the framework of quantum theory? We offer aconceptual treatment of the Copenhagen interpretation of quantum mechanics in which these questions are answered and contrast it with another interpretation (...)
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  32. Maria Carla Galavotti (1995). Operationism, Probability and Quantum Mechanics. Foundations of Science 1 (1):99-118.
    This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the classical (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to physical theories, despite the (...)
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  33. Ravi Gomatam, Niels Bohr's Interpretation and the Copenhagen Interpretation.
    The Copenhagen interpretation, which informs the textbook presentation of quantum mechanics, depends fundamentally on the notion of ontological wave-particle duality and a viewpoint called “complementarity”. In this paper, Bohr’s own interpretation is traced in detail and is shown to be fundamentally different from and even opposed to the Copenhagen interpretation in virtually all its particulars. In particular, Bohr’s interpretation avoids the ad hoc postulate of wave function ‘collapse’ that is central to the Copenhagen interpretation. The strengths and weakness of both (...)
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  34. Ravi Gomatam, Complementarity — Did Bohr Miss the Boat?
    In part-1, I shall outline the principle details of Bohr’s interpretation. Bohr’s basic interpretive insight is ‘ quantum inseparability’ . Complementarity of phenomena and a “revision to our attitude towards physical explanation” then follow. Together , these can be said to constitute Bohr’s general viewpoint of ‘complementarity’. Bohr does not quite clearly spell out the content of these three ideas; I do.
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  35. Hans Halvorson (2004). Complementarity of Representations in Quantum Mechanics. Studies in History and Philosophy of Science Part B 35 (1):45-56.
    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.
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  36. Chris Heunen (2012). Complementarity in Categorical Quantum Mechanics. Foundations of Physics 42 (7):856-873.
    We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a ‘point-free’ definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.
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  37. Chris Heunen, Klaas Landsman & Bas Spitters, The Principle of General Tovariance.
    We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining (...)
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  38. C. A. Hooker (1971). Energy and the Interpretation of Quantum Mechanics. Australasian Journal of Philosophy 49 (3):262 – 270.
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  39. Don Howard (2004). Who Invented the “Copenhagen Interpretation”? A Study in Mythology. Philosophy of Science 71 (5):669-682.
    What is commonly known as the Copenhagen interpretation of quantum mechanics, regarded as representing a unitary Copenhagen point of view, differs significantly from Bohr's complementarity interpretation, which does not employ wave packet collapse in its account of measurement and does not accord the subjective observer any privileged role in measurement. It is argued that the Copenhagen interpretation is an invention of the mid‐1950s, for which Heisenberg is chiefly responsible, various other physicists and philosophers, including Bohm, Feyerabend, Hanson, and Popper, having (...)
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  40. Michael Huemer, Quantum Mechanics for Philosophers.
    You pass an electron through an inhomogeneous magnetic field (this is produced by a type of magnet, but don’t worry about the details). The field causes the electron to swerve. It is found that all electrons swerve by the same amount, and half of them swerve up, while the other half swerve down. See a video illustration of this.
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  41. L. Kannenberg (1989). Quantum Formalism Via Signal Analysis. Foundations of Physics 19 (4):367-383.
    The general properties of signals permit a nonaxiomatic reconstruction of the quantum “probability” formalism independent of the standard Copenhagen interpretation of quantum mechanics. Performance standards are specified for candidate clock, signaller, and reflector devices, and it is shown that the resulting formalism forces identification of a “probability”- or “intensity”-like structure as the absolute square of an amplitude, the relative phases of amplitudes appearing explicitly in the “probability” composition law. Inequalities are produced which on one interpretation reduce to the Heisenberg relations, (...)
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  42. Patricia Kauark-Leite (2010). Transcendental Philosophy and Quantum Theory. Manuscrito – Rev. Int. Fil 33 (1):243-267.
    In the Critique of Pure Reason Kant argues that the empirical knowledge of the world depends on a priori conditions of human sensibility and understanding, i. e., our capacities of sense experience and concept formation. The objective knowledge presupposes, on one hand, space and time as a priori conditions of sensibility and, on another hand, a priori judgments, like the principle of causality, as constitutive conditions of understanding. The problem is that in the XX century the physical science completely changed (...)
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  43. Patricia Kauark-Leite (2009). The Transcendental Role of the Principle of Anticipations of Perception in Quantum Mechanics. In Michel Bitbol, Jean Petitot & Pierre Kerszberg (eds.), CONSTITUTING OBJECTIVITY The Western Ontario Series in Philosophy of Science.
    The aim of this work is to analyse the diffrerences between the formal structure of anticipation of perception in classical and in quantum context. I argue that a transcendental point of view can be supported in quantum context if objectivity is defined by an invariant anticipative structure, which has only a predictive character. The classical objectivity, which defined a set of properties having a descriptive meaning must be abandoned in quantum context. I will focus my analysis on Kant's Principle of (...)
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  44. Andrew Lugg (1976). Book Review:The Interpretation of Quantum Mechanics Michael Audi. [REVIEW] Philosophy of Science 43 (3):449-.
  45. Edward MacKinnon (2011). Interpreting Physics: Language and the Classical/Quantim Divide. Springer.
    This book is the first to offer a systematic account of the role of language in the development and interpretation of physics. An historical-conceptual analysis of the co-evolution of physics and mathematics leads to the classical/quantum interface. Bohr's interpretation is analyzed and extended to the interpretation of the standard model of particle physics.
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  46. Edward MacKinnon (1986). Book Review:The Philosophy of Niels Bohr: The Framework of Complementarity Henry J. Folse. [REVIEW] Philosophy of Science 53 (3):458-.
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  47. P. N. & Robin Reuvers (2013). A Flea on Schrödinger's Cat. Foundations of Physics 43 (3):373-407.
    We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...)
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  48. Stefano Osnaghi (2008). Van Frasssen, Everett, and the Critique of the Copenhagem View of Measurement. Principia 12 (2):155-176.
    http://dx.doi.org/10.5007/1808-1711.2008v12n2p155 Bas van Fraassen advocates a “Copenhagen variant” of the modal interpretation of quantum mechanics. However, he believes that the Copenhagen approach to measurement is not fully satisfactory, since it seems to rule out the possibility of providing a physical account of the observation process. This was also what John Wheeler had in mind when, in the mid-1950’s, he sponsored the “relative state” formulation proposed by his student Hugh Everett. Wheeler, who considered himself an orthodox Bohrian, tried to convince Bohr (...)
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  49. A. Peres (2002). Karl Popper and the Copenhagen Interpretation. Studies in History and Philosophy of Science Part B 33 (1):23-34.
    Popper conceived an experiment whose analysis led to a result that he deemed absurd. Popper wrote that his reasoning was based on the Copenhagen interpretation and therefore invalidated it. Many authors who have examined Popper's analysis have found in it various technical flaws which are briefly summarized here. However, the aim of the present article is not technical. My concern is to redress logical flaws in Popper's argument: the terminology he uses is ambiguous, his analysis involves counterfactual hypotheses, and it (...)
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  50. Slobodan Perovic (2013). Emergence of Complementarity and the Baconian Roots of Niels Bohr's Method. Studies in History and Philosophy of Science B 44 (3):162-173.
    I argue that instead of a rather narrow focus on N. Bohr's account of complementarity as a particular and perhaps obscure metaphysical or epistemological concept (or as being motivated by such a concept), we should consider it to result from pursuing a particular method of studying physical phenomena. More precisely, I identify a strong undercurrent of Baconian method of induction in Bohr's work that likely emerged during his experimental training and practice. When its development is analyzed in light of Baconian (...)
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