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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. David Z. Albert (1992). Quantum Mechanics and Experience. Harvard Up.
    Presents a guide to the basics of quantum mechanics and measurement.
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  5. David Z. Albert & Barry Loewer (1991). The Measurement Problem: Some “Solutions”. Synthese 86 (1):87 - 98.
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  6. 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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  7. 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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  8. 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: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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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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  16. 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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  17. Thomas Bonk (2001). How Reichenbach Solved the Quantum Measurement Problem. Dialectica 55 (4):291–314.
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  18. Carlos Alexandre Brasil, L. A. De Castro & R. D. J. Napolitano (2013). How Much Time Does a Measurement Take? Foundations of Physics 43 (5):642-655.
    We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to (...)
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  19. Harvey R. Brown & David Wallace (2005). Solving the Measurement Problem: De Broglie-Bohm Loses Out to Everett. [REVIEW] Foundations of Physics 35 (4):517-540.
    The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.
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  20. Harvey Brown & David Wallace (2005). Solving the Measurement Problem: De Broglie-Bohm Loses Out to Everett. [REVIEW] Foundations of Physics 35 (4):517-540.
    The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.
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  21. Matthew J. Brown (2009). Relational Quantum Mechanics and the Determinacy Problem. British Journal for the Philosophy of Science 60 (4):679-695.
    Carlo Rovelli's relational interpretation of quantum mechanics holds that a system's states or the values of its physical quantities as normally conceived only exist relative to a cut between a system and an observer or measuring instrument. Furthermore, on Rovelli's account, the appearance of determinate observations from pure quantum superpositions happens only relative to the interaction of the system and observer. Jeffrey Barrett ([1999]) has pointed out that certain relational interpretations suffer from what we might call the ‘determinacy problem', but (...)
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  22. Jeffrey Bub (1988). From Micro to Macro: A Solution to the Measurement Problem of Quantum Mechanics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:134 - 144.
    Philosophical debate on the measurement problem of quantum mechanics has, for the most part, been confined to the non-relativistic version of the theory. Quantizing quantum field theory, or making quantum mechanics relativistic, yields a conceptual framework capable of dealing with the creation and annihilation of an indefinite number of particles in interaction with fields, i.e. quantum systems with an infinite number of degrees of freedom. I show that a solution to the standard measurement problem is available if we exploit the (...)
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  23. Paul Busch & Abner Shimony (1996). Insolubility of the Quantum Measurement Problem for Unsharp Observables. Studies in History and Philosophy of Science Part B 27 (4):397-404.
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  24. Maria Luisa Dalla Chiara (1977). Logical Self Reference, Set Theoretical Paradoxes and the Measurement Problem in Quantum Mechanics. Journal of Philosophical Logic 6 (1):331 - 347.
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  25. John F. Cyranski (1978). Quantum Measurement as a Communication with Nature. Foundations of Physics 8 (11-12):805-822.
    It is assumed that experiments yield results that are not isomorphic with reality, but represent a distorted image of reality. Reality is related to observation via a communication channel of finite capacity. Quantum uncertainties are due to the bound on the amount of information available. Use is made of recent results from information and communication theories.
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  26. B. D'Espagnat (1987). Empirical Reality, Empirical Causality, and the Measurement Problem. Foundations of Physics 17 (5):507-529.
    Does physics describe anything that can meaningfully be called “independent reality,” or is it merely operational? Most physicists implicitly favor an intermediate standpoint, which takes quantum physics into account, but which nevertheless strongly holds fast to quite strictly realistic ideas about apparently “obvious facts” concerning the macro-objects. Part 1 of this article, which is a survey of recent measurement theories, shows that, when made explicit, the standpoint in question cannot be upheld. Part 2 brings forward a proposal for making minimal (...)
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  27. Andrew Elby (1994). The 'Decoherence' Approach to the Measurement Problem in Quantum Mechanics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:355 - 365.
    Decoherence results from the dissipative interaction between a quantum system and its environment. As the system and environment become entangled, the reduced density operator describing the system "decoheres" into a mixture (with the interference terms damped out). This formal result prompts some to exclaim that the measurement problem is solved. I will scrutinize this claim by examining how modal and relative-state interpretations can use decoherence. Although decoherence cannot rescue these interpretations from general metaphysical difficulties, decoherence may help these interpretations to (...)
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  28. Arthur Fine (1993). Measurement and Quantum Silence. In. In S. French & H. Kamminga (eds.), Correspondence, Invariance and Heuristics. Kluwer. 279--294.
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  29. S. French (2002). A Phenomenological Solution to the Measurement Problem? Husserl and the Foundations of Quantum Mechanics. Studies in History and Philosophy of Science Part B 33 (3):467-491.
    The London and Bauer monograph occupies a central place in the debate concerning the quantum measurement problem. Gavroglu has previously noted the influence of Husserlian phenomenology on London's scientific work. However, he has not explored the full extent of this influence in the monograph itself. I begin this paper by outlining the important role played by the monograph in the debate. In effect, it acted as a kind of 'lens' through which the standard, or Copenhagen, 'solution' to the measurement problem (...)
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  30. Yehudah Freundlich (1972). Mind, Matter, and Physicists. Foundations of Physics 2 (2-3):129-148.
    Some aspects of the problem of measurement in quantum theory are treated. We stress that the problem is both physical and conceptual, that the physical problem has been solved and the conceptual one is inherent in quantum theory. We also deal with some remarks made by Wigner concerning physics and the explanation of life, and present alternative positions on the mind-matter relationship within a deterministic framework, as we see them.
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  31. Izuru Fujiwara (1972). Quantum Theory of State Reduction and Measurement. Foundations of Physics 2 (2-3):83-110.
    The central problem in the quantum theory of measurement, how to describe the process of state reduction in terms of the quantum mechanical formalism, is solved on the basis of the relativity of quantal states, which implies that once the apparatus is detected in a well-defined state, the object state must reduce to a corresponding one. This is a process termed by Schrödinger disentanglement. Here, it is essential to observe that Renninger's negative result does constitute an actual measurement process. From (...)
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  32. Barry C. Gilbert & Sue Sulcs (1996). The Measurement Problem Resolved and Local Realism Preserved Via a Collapse-Free Photon Detection Model. Foundations of Physics 26 (11):1401-1439.
    A new realislic local model of light propagation and detection is described. The authors propose a novel stochastic model of low-intensity photon detection in which background noise is added to a part of the photon prior to absorption. In this model, in agreement with Planck, there is no quantization of the propagating field. The model has some similarities to theories advanced by E. Santos and T. Marshall in the last decade, but also has substantial deviations from these. A mechanism, conserving (...)
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  33. Daniel M. Greenberger (2001). The Interpretation of Quantum Mechanics. Studies in History and Philosophy of Science Part B 32 (1):127-129.
    Review of Peter Mittelstaedt, The Interpretation of Quantum Mechanics and the Measurement Process (Cambridge: Cambridge University Press, 1998), 140pp., ISBN 0-521-55445-4, hardback US$44.95, £30.00.
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  34. Daniel M. Greenberger & Alaine YaSin (1989). “Haunted” Measurements in Quantum Theory. Foundations of Physics 19 (6):679-704.
    Sometimes it is possible in quantum theory for a system to interact with another system in such a way that the information contained in the wave function becomes very scrambled and apparently incoherent. We produce an example which is exactly calculable, in which a macroscopic change is induced in the environment, and all phase information for the system is apparently lost, so that a measurement has seemingly been made. But actually, although the wave function has been badly scrambled, all the (...)
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  35. Amit Hagar, Does Protective Measurement Tell Us Anything About Quantum Reality?
    An analysis of the two routes through which one may disentangle a quantum system from a measuring apparatus, hence protect the state vector of a single quantum system from being disturbed by the measurement, reveals that the argument from protected measurement to the reality of the state vector of a single quantum system is circular. From this negative result I draw some lessons on the available "interpretations" of quantum theory and on the debate on the quantum measurement problem.
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  36. Richard Healey (1995). Dissipating the Quantum Measurement Problem. Topoi 14 (1):55-65.
    The integration of recent work on decoherence into a so-called modal interpretation offers a promising new approach to the measurement problem in quantum mechanics. In this paper I explain and develop this approach in the context of the interactive interpretation presented in Healey (1989). I begin by questioning a number of assumptions which are standardly made in setting up the measurement problem, and I conclude that no satisfactory solution can afford to ignore the influence of the environment. Further, I argue (...)
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  37. Roger A. Hegstrom & Fernando Sols (1995). A Model of Quantum Measurement in Josephson Junctions. Foundations of Physics 25 (5):681-700.
    A model for the quantum measurement of the electronic current in a Josephson junction is presented and analyzed. The model is similar to a Stern-Gerlach apparatus, relying on the deflection of a spin-polarized particle beam by the magnetic field created by the Josephson current. The aim is (1) to explore, with the help of a simple model, some general ideas about the nature of the information which can be obtained by measurements upon a quantum system and (2) to find new (...)
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  38. R. I. G. Hughes (1989). The Structure and Interpretation of Quantum Mechanics. Harvard University Press.
    R.I.G Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful.
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  39. Lars-Göran Johansson (2007). Interpreting Quantum Mechanics. A Realist View in Schrödinger's Vein. Ashgate.
    Presenting a realistic interpretation of quantum mechanics and, in particular, a realistic view of quantum waves, this book defends, with one exception, ...
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  40. Alexey Kryukov (2007). On the Measurement Problem for a Two-Level Quantum System. Foundations of Physics 37 (1):3-39.
    A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the (...)
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  41. Douglas Kutach (1998). Review of The Interpretation of Quantum Mechanics and the Measurement Process. [REVIEW] British Journal for the Philosophy of Science 49 (4):649-651.
    Book review of The Interpretation of Quantum Mechanics and the Measurement Process.
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  42. Franck Laloë (2012). Do We Really Understand Quantum Mechanics? Cambridge University Press.
    Machine generated contents note: Introduction; 1. Historical perspective; 2. Present situation, remaining conceptual difficulties; 3. The theorem of Einstein, Podolsky and Rosen; 4. Bell theorem; 5. More theorems; 6. Quantum entanglement; 7. Applications of quantum entanglement; 8. Quantum measurement; 9. Experiments, quantum reduction seen in real time; 10. Various interpretations; Conclusion; Appendices; Index.
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  43. Hans Laue (1978). The Role of Position in Quantum Theory. Foundations of Physics 8 (1-2):1-30.
    The paper puts forward the proposal to do relativistic quantum theory without a position operator and without a position probability amplitude. The proposed scheme employs space and time in a fundamental manner and treats them equitably as in special relativity by defining the state vectors as functions of configuration spacetime. From a discussion of the conceptual structure and of the problem of measurement of quantum theory, there emerges an understanding which shows that the absence of a satisfactory position probability density (...)
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  44. A. J. Leggett (1988). Experimental Approaches to the Quantum Measurement Paradox. Foundations of Physics 18 (9):939-952.
    I examine the question of how far experiments that look for the effects of superposition of macroscopically distinct states are relevant to the classic measurement paradox of quantum mechanics. Existing experiments on superconducting devices confirm the predictions of the quantum formalism extrapolated to the macroscopic level, and to that extent provide strong circumstantial evidence for its validity at this level, but do not directly test the principle of superposition of macrostates. A more ambitious experiment, not obviously infeasible with current technology, (...)
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  45. Peter J. Lewis (2007). How Bohm's Theory Solves the Measurement Problem. Philosophy of Science 74 (5):749-760.
    I examine recent arguments based on functionalism that claim to show that Bohm's theory fails to solve the measurement problem, or if it does so, it is only because it reduces to a form of the many-worlds theory. While these arguments reveal some interesting features of Bohm's theory, I contend that they do not undermine the distinctive Bohmian solution to the measurement problem. ‡I would like to thank Harvey Brown, Martin Thomson-Jones, and David Wallace for helpful discussions. †To contact the (...)
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  46. Tim Maudlin (1995). Why Bohm's Theory Solves the Measurement Problem. Philosophy of Science 62 (3):479-483.
    Abraham Stone recently has published an argument purporting to show that David Bohm's interpretation of quantum mechanics fails to solve the measurement problem. Stone's analysis is not correct, as he has failed to take account of the conditions under which the theorems he cites are proven. An explicit presentation of a Bohmian measurement illustrates the flaw in his reasoning.
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  47. Nicholas Maxwell (1995). A Philosopher Struggles to Understand Quantum Theory: Particle Creation and Wavepacket Reduction. In M. Ferrero & A. van der Merwe (eds.), Fundamental Problems in Quantum Physics.
    Work on the central problems of the philosophy of science has led the author to attempt to create an intelligible version of quantum theory. The basic idea is that probabilistic transitions occur when new stationary or particle states arise as a result of inelastic collisions.
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  48. Nicholas Maxwell (1994). Particle Creation as the Quantum Condition for Probabilistic Events to Occur. Physics Letters A 187 (2 May 1994):351-355.
    A new version of quantum theory is proposed, according to which probabilistic events occur whenever new statioinary or bound states are created as a result of inelastic collisions. The new theory recovers the experimental success of orthodox quantum theory, but differs form the orthodox theory for as yet unperformed experiments.
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  49. Nicholas Maxwell (1993). Beyond Fapp: Three Approaches to Improving Orthodox Quantum Theory and An Experimental Test. In F. Selleri and G. Tarozzi van der Merwe, F. Selleri & G. Tarozzi (eds.), Bell's Theorem and the Foundations of Modern Physics. World Scientific.
    Because it fails to solve the wave-particle problem, orthodox quantum theory is obliged to be about observables and not quantum beables. As a result the theory is imprecise, ambiguous, ad hoc, lacking in explanatory power, restricted in scope and resistant to unification. A new version of quantum theory is needed that is about quantum beables.
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  50. Nicholas Maxwell (1993). Does Orthodox Quantum Theory Undermine, or Support, Scientific Realism? Philosophical Quarterly 44 (171):139-157.
    It is usually taken for granted that orthodox quantum theory poses a serious problem for scientific realism, in that the theory is empirically extraordinarily successful, and yet has instrumentalism built into it. This paper stand this view on its head. I argue that orthodox quantum theory suffers from a number of serious (if not always noticed) defects precisely because of its inbuilt instrumentalism. This defective character of orthdoox quantum theory thus undermines instrumentalism, and supports scientific realism. I go on to (...)
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