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Summary Traditional formulations of quantum mechanics rely on an unanalysed concept of measurement. Quantum systems are treated as evolving via the unitary Schrodinger evolution, except when they are measured or observed; then, all components of the state are discarded except the one corresponding to the actual measurement result. The component which remains is then regarded as the new state of the system and again is evolved forwards according to the unitary evolution. The measurement problem is the problem of explaining why this two-stage procedure employing a primitive concept of measurement works so well.
Key works Bell 2004 contains a number of exceptionally clear discussions of the measurement problem. Bohr 1935 contains the first explicit claim that measurement plays a fundamental role in quantum theory.
Introductions Albert 1992
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  1. Stephen L. Adler (2003). Why Decoherence has Not Solved the Measurement Problem: A Response to P.W. Anderson. Studies in History and Philosophy of Science Part B 34 (1):135-142.
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  2. Y. Aharonov & M. Vardi (1981). An Operational Approach for Testing the Postulate of Measurement in Quantum Theory. Foundations of Physics 11 (1-2):121-125.
    We interpret the (formal) postulates of measurement in quantum theory in terms of measurement procedures that can be done in the laboratory (at least in principle).
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  3. Yakir Aharonov, Jeeva Anandan & Lev Vaidman (1996). The Meaning of Protective Measurements. Foundations of Physics 26 (1):117-126.
    Protective measurement, which we have introduced recently, allows one to observe properties of the state of a single quantum system and even the Schrödinger wave itself. These measurements require a protection, sometimes due to an additional procedure and sometimes due to the potential of the system itself The analysis of the protective measurements is presented and it is argued, contrary to recent claims, that they observe the quantum state and not the protective potential. Some other misunderstandings concerning our proposal are (...)
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  4. D. Albert (1997). On the Phenomenology of Quantum-Mechanical Superpositions. Poznan Studies in the Philosophy of the Sciences and the Humanities 55:196-215.
  5. D. Albert & B. Loewer (1991). Some Alleged Solutions to the Measurement Problem. Synthese 88:87-98.
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  6. David Z. Albert (1992). Quantum Mechanics and Experience. Harvard Up.
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  7. David Z. Albert & Barry Loewer (1991). The Measurement Problem: Some “Solutions”. Synthese 86 (1):87 - 98.
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  8. 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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  9. Valia Allori (2013). Primitive Ontology and the Structure of Fundamental Physical Theories. In Alyssa Ney & David Z. Albert (eds.), The Wave Function: Essays in the Metaphysics of Quantum Mechanics. Oxford University Press.
    For a long time it was believed that it was impossible to be realist about quantum mechanics. It took quite a while for the researchers in the foundations of physics, beginning with John Stuart Bell [Bell 1987], to convince others that such an alleged impossibility had no foundation. Nowadays there are several quantum theories that can be interpreted realistically, among which Bohmian mechanics, the GRW theory, and the many-worlds theory. The debate, though, is far from being over: in what respect (...)
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  10. Valia Allori (2010). Quantum Theory: A Philosopher's Overview. [REVIEW] International Studies in the Philosophy of Science 24 (3):330-333.
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  11. Valia Allori, Sheldon Goldstein, Roderich Tumulka & Nino Zanghi (2013). Predictions and Primitive Ontology in Quantum Foundations: A Study of Examples. British Journal for the Philosophy of Science (2):axs048.
    A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a ‘primitive ontology’ (PO), i.e. variables describing the distribution of matter in four-dimensional space–time. In this article, we illustrate the value of having a PO. We do so by focussing on the role that the PO plays for extracting predictions from a given theory and discuss valid and invalid derivations of predictions. To (...)
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  12. Valia Allori & Nino Zanghi (2004). What is Bohmian Mechanics. International Journal of Theoretical Physics 43:1743-1755.
    Bohmian mechanics is a quantum theory with a clear ontology. To make clear what we mean by this, we shall proceed by recalling first what are the problems of quantum mechanics. We shall then briefly sketch the basics of Bohmian mechanics and indicate how Bohmian mechanics solves these problems and clarifies the status and the role of of the quantum formalism.
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  13. Martin S. Altschul (1978). Coordinate Transformations and the Theory of Measurement. Foundations of Physics 8 (1-2):69-92.
    We discuss the criteria for deriving new information from coordinate transformations, focusing on the property of implementability, or measurability in practice. We contrast the role of coordinate transformations in classical and quantum physics, and demonstrate that many well-known applications fail to meet the criteria for new information. Finally, we discuss some mathematical properties of the coordinate transformations, and then relate these properties to a practical measurement scheme.
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  14. Charis Anastopoulos (2006). Classical Versus Quantum Probability in Sequential Measurements. Foundations of Physics 36 (11):1601-1661.
    We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we (...)
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  15. Aristidis Arageorgis (2001). Barrett, Jeffrey Allan. The Quantum Mechanics of Minds and Worlds. [REVIEW] Review of Metaphysics 54 (4):904-905.
  16. Frank Arntzenius (1993). How to Discover That the Real is Unreal. Erkenntnis 38 (2):191 - 202.
    The measurement problem in quantum mechanics is presented in a completely non-technical way by means of the results of some very simple experiments. These experimental results themselves, rather than the formalism of quantum theory, are shown to be extremely hard to incorporate in a sensible state-space picture of the world. A novel twist is then added which makes the problem even harder than it appears to be in other presentations of the measurement problem.
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  17. Harald Atmanspacher (1989). The Aspect of Information Production in the Process of Observation. Foundations of Physics 19 (5):553-577.
    The physical process of observation is considered from a specific information theoretical viewpoint. Using the modified concept of an information based on infinite alternatives, a formalism is derived describing the elementary transfer of one bit of information. This bit of information is produced on a virtual (nonreal) sub-quantum level of physical description. The interpretation of the formalism yields the following, complementary points: (i) the effect of spatiotemporal delocalization on the sub-quantum level, and (ii) a possible access to the concept of (...)
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  18. Gennaro Auletta (2005). Quantum Information and Inferential Reasoning. Foundations of Physics 35 (1):155-156.
    Information may be extracted from a quantum–mechanical system only by means of inference. For this reason, the observer, although not required as such for obtaining an eigenstate of the measured observable on a given system, is necessary for obtaining information.
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  19. Guido Bacciagaluppi (2013). Insolubility Theorems and EPR Argument. European Journal for Philosophy of Science 3 (1):87-100.
    I present a very general and simple argument—based on the no-signalling theorem—showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility (...)
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  20. Guido Bacciagaluppi, The Role of Decoherence in Quantum Mechanics. Stanford Encyclopedia of Philosophy.
    Interference phenomena are a well-known and crucial feature of quantum mechanics, the two-slit experiment providing a standard example. There are situations, however, in which interference effects are (artificially or spontaneously) suppressed. We shall need to make precise what this means, but the theory of decoherence is the study of (spontaneous) interactions between a system and its environment that lead to such suppression of interference. This study includes detailed modelling of system-environment interactions, derivation of equations (‘master equations’) for the (reduced) state (...)
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  21. Manuel Bächtold (2008). Five Formulations of the Quantum Measurement Problem in the Frame of the Standard Interpretation. Journal for General Philosophy of Science 39 (1):17 - 33.
    The aim of this paper is to give a systematic account of the so-called “measurement problem” in the frame of the standard interpretation of quantum mechanics. It is argued that there is not one but five distinct formulations of this problem. Each of them depends on what is assumed to be a “satisfactory” description of the measurement process in the frame of the standard interpretation. Moreover, the paper points out that each of these formulations refers not to a unique problem, (...)
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  22. J. E. Baggott (2004). Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory. Oxford University Press.
    Quantum theory is one the most important and successful theories of modern physical science. It has been estimated that its principles form the basis for about 30 per cent of the world's manufacturing economy. This is all the more remarkable because quantum theory is a theory that nobody understands. The meaning of Quantum Theory introduces science students to the theory's fundamental conceptual and philosophical problems, and the basis of its non-understandability. It does this with the barest minimum of jargon and (...)
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  23. L. E. Ballentine (1992). Can One Detect the State of an Individual System? Foundations of Physics 22 (3):333-342.
    Some interpretations of quantum mechanics regard a mixed quantum state as a ensemble, each individual member of which has a definite but unknown state vector. Other interpretations ascribe a state vector only to anensemble of similarly prepared systems, but not to anindividual. Previous attempts to detect the hypothetical individual state vectors have failed, essentially because the state operator (density matrix) enters the relevant equations linearly. An example from nonlinear dynamics, in which a density matrix enters nonlinearly, is examined because it (...)
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  24. Jeffrey A. Barrett, Wigner's Friend and Bell's Field Beables.
    A field-theoretic version of Wigner’s friend (1961) illustrates how the quantum measurement problem arises for field theory. Similarly, considering spacelike separate measurements of entangled fields by observers akin to Wigner’s friend shows the sense in which relativistic constraints make the measurement problem particularly difficult to resolve in the context of a relativistic field theory. We will consider proposals by Wigner (1961), Bloch (1967), Helwig and Kraus (1970), and Bell (1984) for resolving the measurement problem for quantum field theory. We will (...)
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  25. J. S. Bell (2004). Against ”Measurement'. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. 213--231.
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  26. J. S. Bell (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press.
    This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current understanding of (...)
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  27. J. S. Bell (1992). Six Possible Worlds of Quantum Mechanics. Foundations of Physics 22 (10):1201-1215.
  28. Js Bell (1992). 6 Possible Worlds of Quantum-Mechanics (Reprinted From Possible Worlds in Humanities Arts and Sciences, Pg 359-373, 1989. [REVIEW] Foundations of Physics 22 (10):1201-1215.
  29. Mara Beller (1996). The Conceptual and the Anecdotal History of Quantum Mechanics. Foundations of Physics 26 (4):545-557.
    The aim of this paper is to combine the intellectual and the psychosocial aspects. blurring the distinction between the conceptual and the anecdotal history of quantum mechanics. The full realization of the importance of such “anecdotal” factors leads to the revision of our understanding of the conceptual development itself. The paper concludes with the suggestion that a major part of numerous inconsistencies in the Copenhagen interpretation of quantum physics are of a psychosocial origin.
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  30. Y. Ben-Menahem (2002). Quantum Theory and the Flight From Realism - Christopher Norris, Routledge, London, New York, IX +266pp., $26.00 Paperback, ISBN 0-415-22322-. [REVIEW] Studies in History and Philosophy of Science Part B 33 (3):587-591.
  31. Yemima Ben-Menahem (1997). Dummett Vs Bell on Quantum Mechanics. Studies in History and Philosophy of Science Part B 28 (2):277-290.
  32. Paul Benioff (1975). On Procedures for the Measurement of Questions in Quantum Mechanics. Foundations of Physics 5 (2):251-255.
    It is shown that there exist observablesA and Borel setsE such that the procedure “measureA and give as output the number 1 (0) if theA measurement outcome is (is not) inE” does not correspond to a measurement of the proposition observable ℰA(E) usually assigned to such procedures. This result is discussed in terms of limitations on choice powers of observers.
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  33. Paul Benioff (1973). On Definitions of Validity Applied to Quantum Theories. Foundations of Physics 3 (3):359-379.
    In this work, quantum theories are considered which consist in essence of a map from state preparation proceduresw to states and a map from decision proceduresQ to probability operator measures. Two definitions of validity, similar to that given elsewhere, are given and compared for these theories. One definition is given in terms of one carrying out of somew followed by someQ, denoted by(Q, w). The other is given in terms of infinite repetitions(Q, w) ofw followed byQ. Both definitions are discussed (...)
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  34. Rodney W. Benoist, Jean-Paul Marchand & Wolfgang Yourgrau (1978). Addendum to Statistical Inference and Quantum Mechanical Measurement. Foundations of Physics 8 (1-2):117-118.
  35. Rodney W. Benoist, Jean-Paul Marchand & Wolfgang Yourgrau (1977). Statistical Inference and Quantum Mechanical Measurement. Foundations of Physics 7 (11-12):827-833.
    We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result is (...)
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  36. Carlton W. Berend (1942). A Note on Quantum Theory and Metaphysics. Journal of Philosophy 39 (22):608-611.
  37. Otto Bergmann (1988). A Quantum Mechanical Version of the Paper by E. Schrödinger “Über Die Umkehrung der Naturgesetze”. Foundations of Physics 18 (3):373-378.
    The principal results of Schrödinger's paper are reviewed and a possible extension of his formalism for diffusion processes to general quantum mechanical processes is given. The formalism is not in accord with the general theory of transformation of quantum mechanics and violates the basic assumption of the unpredictable change of a system due to a measurement. Nevertheless, the formalism leads to a density operator which is constructed according to accepted quantum mechanical rules.
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  38. János A. Bergou (1999). Entangled Fields in Multiple Cavities as a Testing Ground for Quantum Mechanics. Foundations of Physics 29 (4):503-519.
    Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and postselective quantum mechanics, QND measurements, complementarity, and tests of quantum mechanics itself against, e.g., the so-called causal communication constraint. We show how to produce various nonlocal entangled states of multiple cavity fields that are useful for these tests, using cavity QED techniques. First, we discuss the generation of the Bell basis states in two entangled cavities, (...)
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  39. Joseph Berkovitz (2000). The Nature of Causality in Quantum Phenomena. Theoria 15 (1):87-122.
    The correlations between distant systems in typical quantum situations, such as Einstein-Podolosky-Rosen experiments, strongly suggest that the quantum realm involves curious types of non-Iocal influences. In this paper, I study in detail the nature of these non-Iocal influences, as depicted by various quantum theories. I show how different quantum theories realise non-Iocality in different ways, whichreflect different ontological settings.
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  40. M. Berry (2010). Alisa Bokulich * Reexamining the Quantum-Classical Relation: Beyond Reductionism and Pluralism. British Journal for the Philosophy of Science 61 (4):889-895.
  41. Tomasz Bigaj (2001). Three-Valued Logic, Indeterminacy and Quantum Mechanics. Journal of Philosophical Logic 30 (2):97-119.
    The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying Łukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form "X will be the case at time t" is true (resp. false) at time t, then this sentence must be already true (resp. false) (...)
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  42. M. Bitbol (1988). The Concept of Measurement and Time Symmetry in Quantum Mechanics. Philosophy of Science 55 (3):349-375.
    The formal time symmetry of the quantum measurement process is extensively discussed. Then, the origin of the alleged association between a fixed temporal direction and quantum measurements is investigated. It is shown that some features of such an association might arise from epistemological rather than purely physical assumptions. In particular, it is brought out that a sequence of statements bearing on quantum measurements may display intrinsic asymmetric properties, irrespective of the location of corresponding measurements in time t of the Schrodinger (...)
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  43. Michel Bitbol (2011). Traces of Objectivity: Causality and Probabilities in Quantum Physics. Diogenes 58 (4):30-57.
  44. Michel Bitbol, Consciousness, Situations, and the Measurement Problem of Quantum Mechanics.
    There are two versions of the putative connection between consciousness and the measurement problem of quantum mechanics : consciousness as the cause of state vector reduction, and state vector reduction as the physical basis of consciousness. In this article, these controversial ideas are neither accepted uncritically, nor rejected from the outset in the name of some prejudice about objective knowledge. Instead, their origin is sought in our most cherished (but disputable) beliefs about the place of mind and consciousness in the (...)
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  45. Simon Bitbol, Michel, Guy, Perspectival Realism and Quantum Mechanics.
    A complete reappraisal of the philosophical meaning of Everett's interpretation of quantum mechanics is carried out, by analysing carefully the role of the concept of "observer" in physics. It is shown that Everett's interpretation is the limiting case of a series of conceptions of the measurement problem which leave less and less of the observer out of the quantum description of the measuring interaction. This limiting case, however, should not be considered as one wherein nothing is left outside the description. (...)
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  46. Ph Blanchard & A. Jadczyk (1996). Relativistic Quantum Events. Foundations of Physics 26 (12):1669-1681.
    Standard quantum theory is inadequate to explain the mechanisms by which potential becomes actual. It is inadequate and therefore unable to describe generation of events. Niels Bohr emphasized long ago that the classical part of the world is necessary. John Bell stressed the same point: that “measurement≓ cannot even be defined within the standard quantum theory, and he sought a solution within hidden variable theories and his concept of “beables.≓Today it is customary to try to explain emergence of the classical (...)
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  47. D. Bohm & B. J. Hiley (1984). Measurement Understood Through the Quantum Potential Approach. Foundations of Physics 14 (3):255-274.
  48. David Bohm (1952). A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables, I and II. Physical Review (85):166-193.
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  49. Niels Bohr (1987). The Philosophical Writings of Niels Bohr. Ox Bow Press.
    v. 1. Atomic theory and the description of nature -- v. 2. Essays 1932-1957 on atomic physics and human knowledge -- v. 3. Essays 1958-1962 on atomic physics and human knowledge -- v. 4. Causality and complementarity.
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  50. Niels Bohr (1963/1987). Essays 1958-1962 on Atomic Physics and Human Knowledge. Ox Bow Press.
    Quantum physics and philosophy--causality and complementarity -- The unit of human knowledge -- The connection between the sciences -- Light and life revisited -- The Rutherford memorial lecture 1958 -- The genesis of quantum mechanics -- The Solvay meetings and the development of quantum physics.
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