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Quantum Mechanics

Edited by Michael Cuffaro (Ludwig Maximilians Universität, München)
Assistant editors: Radin Dardashti, Brian Padden
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Summary Issues in the philosophy of quantum mechanics include first and foremost, its interpretation. Probably the most well-known of these is the 'orthodox' Copenhagen interpretation associated with Neils Bohr, Werner Heisenberg, Wolfgang Pauli, John von Neumann, and others. Beginning roughly at the midway point of the previous century, philosophers' attention began to be drawn towards alternative interpretations of the theory, including Bohmian mechanics, the relative state formulation of quantum mechanics and its variants (i.e., DeWit's "many worlds" variant, Albert and Loewer's "many minds" variant, etc.), and the dynamical collapse family of theories. One particular interpretational issue that has attracted very much attention since the seminal work of John Bell, is the issue of the extent to which quantum mechanical systems do or do not admit of a local realistic description. Bell's investigation of the properties of entangled quantum systems, inspired by the famous thought experiment of Einstein, Podolsky, and Rosen, seems to lead one to the conclusion that the only realistic "hidden variables" interpretation compatible with the quantum mechanical formalism is a nonlocal one. In recent years, some of the attention has focused on applications of quantum mechanics and their potential for illuminating quantum foundations. These include the sciences of quantum information and quantum computation. Additional areas of research include philosophical investigation into the extensions of nonrelativistic quantum mechanics (such as quantum electrodynamics and quantum field theory more generally), as well as more formal logico-mathematical investigations into the structure of quantum states, state spaces, and their dynamics.
Key works Bohr 1928 and Heisenberg 1930 expound upon what has since become known as the 'Copenhagen interpretation' of quantum mechanics. The famous 'EPR' thought experiment of Einstein et al 1935 aims to show that quantum mechanics is an incomplete theory which should be supplemented by additional ('hidden') parameters. Bohr 1935 replies. More on Bohr's views can be found in Faye 1991, Folse 1985. Inspired by the EPR thought experiment, Bell 2004 [1964] proves what has since become known as "Bell's theorem." This, and a related result due to Kochen & Specker 1967 serve to revive the discussion of hidden variables and alternative interpretations of quantum mechanics. Jarrett 1984 analyses the key "factorisability" assumption Bell uses to derive his theorem into two distinct sub-assumptions, which Jarrett refers to as "locality" and "completeness". Two important volumes dedicated to the topics of entanglement and nonlocality are Cushing & McMullin 1989 and Maudlin 2002. Among the more discussed alternative interpretations of quantum mechanics are: Bohmian mechanics (Bohm 1952, and see also Cushing et al 1996), and Everett's relative state formulation (Everett Iii 1973). The latter gives rise to many variants, including the many worlds, many minds, and decoherence-based approaches (see Saunders et al 2010). Other notable interpretations and alternative theories include dynamical collapse theories (Ghirardi et al 1986), as well as the Copenhagen-inspired Quantum Bayesianism view (Fuchs 2003). An attempt to axiomatize quantum mechanics in terms of information theoretic constraints, and a discussion of the relevance of this for the interpretation of quantum mechanics is given in Clifton et al 2003. Discussion of this and other issues in quantum information theory can be found in: Timpson 2013. Key works in the philosophy of quantum field theory include: Redhead 1995, Redhead 1994, Ruetsche 2013, Teller 1995.
Introductions Hughes 1989 is an excellent introduction to the formalism and interpretation of quantum mechanics. Albert 1992 is another, which focuses particularly on the problem of measurement in quantum mechanics.
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  1. D. Aerts, J. Broekaert & L. Gabora (forthcoming). The Quantum Nature of Common Processes. Foundations of Science.
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  2. Ernst Cassirer (1923/2003). Substance and Function. Dover Publications.
    In this double-volume work, a great modern philosopher propounds a system of thought in which Einstein's theory of relativity represents only the latest (albeit the most radical) fulfillment of the motives inherent to mathematics and the physical sciences. In the course of its exposition, it touches upon such topics as the concept of number, space and time, geometry, and energy; Euclidean and non-Euclidean geometry; traditional logic and scientific method; mechanism and motion; Mayer's methodology of natural science; Richter's definite proportions; relational (...)
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  3. Eva Cassirer (1958). Methodology and Quantum Physics. [REVIEW] British Journal for the Philosophy of Science 8 (32):334-341.
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  4. M. J. Rave (2008). Interpreting Quantum Interference Using a Berry's Phase-Like Quantity. Foundations of Physics 38 (12):1073-1081.
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  5. Abner Shimony (1978). Metaphysical Problems in the Foundations of Quantum Mechanics. International Philosophical Quarterly 18 (1):3-17.
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  6. Andrzej Staruszkiewicz (2002). Quantum Mechanics of the Supplementary Series. Foundations of Physics 32 (12):1863-1876.
    Unitary, irreducible representations of the proper, orthochronous Lorentz group comprise the main series and the supplementary series. The main series is spanned by the complete set of eigenstates of the self-adjoint Casimir operator C 1=−(1/2)M μν M μν , where M μν are generators of Lorentz transformations. The supplementary series has no such interpretation; moreover it is spurious from the point of view of functional analysis as it does not enter into the integral representation of an arbitrary test function. The (...)
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  7. F. Stary & M. Sorg (2006). Ortho- and Para-Helium in Relativistic Schrödinger Theory. Foundations of Physics 36 (9):1325-1403.
    The characteristic features of ortho- and para-helium are investigated within the framework of Relativistic Schrödinger Theory (RST). The emphasis lies on the conceptual level, where the geometric and physical properties of both RST field configurations are inspected in detail. From the geometric point of view, the striking feature consists in the splitting of the $\mathfrak{u}(2)$ -valued bundle connection $\mathcal{A}_{\mu}$ into an abelian electromagnetic part (organizing the electromagnetic interactions between the two electrons) and an exchange part, which is responsible for their (...)
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  8. A. M. Steane (2003). A Quantum Computer Only Needs One Universe. Studies in History and Philosophy of Science Part B 34 (3):469-478.
    The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum computers to ''perform many computations simultaneously'' except in a highly qualified and to some extent misleading sense. Quantum computation is therefore not well described by interpretations of quantum mechanics which invoke the concept of vast numbers of parallel universes. Rather, entanglement makes available types of (...)
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  9. A. M. Steane (2003). A Quantum Computer Only Needs One Universe. Studies in History and Philosophy of Science Part B 34 (3):469-478.
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  10. W. -H. Steeb (1980). A Comment on the Generalized Liouville Equation. Foundations of Physics 10 (5-6):485-493.
    The generalized Liouville equation is studied in a new light using the Lie derivative of a differential form with respect to a vector field.
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  11. W. -H. Steeb, J. A. Louw & A. Kunick (1987). Quantum Chaos of an Exciton-Phonon System. Foundations of Physics 17 (2):173-181.
    A simple model of an exciton-phonon system is studied in connection with quantum chaos.
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  12. Eugene V. Stefanovich, A Superluminal Effect with Oscillating Neutrinos.
    A simple quantum relativistic model of ν µ − ντ neutrino oscillations in the OPERA experiment is presented. This model suggests that the two components in the neutrino beam are separated in space. After being created in a meson decay, the µ-neutrino moves 18 meters ahead of the beam’s center of energy, while the τ -neutrino is behind. Both neutrinos have subluminal speeds, however the advanced start of the ν µ explains why it arrives in the detector 60 ns earlier (...)
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  13. Eugene V. Stefanovich (2002). Is Minkowski Space-Time Compatible with Quantum Mechanics? Foundations of Physics 32 (5):673-703.
    In quantum relativistic Hamiltonian dynamics, the time evolution of interacting particles is described by the Hamiltonian with an interaction-dependent term (potential energy). Boost operators are responsible for (Lorentz) transformations of observables between different moving inertial frames of reference. Relativistic invariance requires that interaction-dependent terms (potential boosts) are present also in the boost operators and therefore Lorentz transformations depend on the interaction acting in the system. This fact is ignored in special relativity, which postulates the universality of Lorentz transformations and their (...)
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  14. Victor J. Stenger (1995). The Unconscious Quantum: Metaphysics in Modern Physics and Cosmology. Prometheus Books.
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  15. Stig Stenholm (2012). The Construction of Quantum Reality. Foundations of Physics 42 (1):86-97.
    This paper recognizes that quantum theory is not satisfactorily formulated; in spite of its empirical success, we may wish to consider the possibility to find more intuitively acceptable foundations. It is emphasized that the difference between classical physics and quantum theory lies in the fact that the latter depends in an essential way on classical descriptions of the observations from preparation to recording. In addition, only statistical predictions are possible. We discuss the case of entangled quantum systems. Performing an experiment (...)
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  16. Stig Stenholm (2011). The Quest for Reality: Bohr and Wittgenstein, Two Complementary Views. Oxford University Press, Usa.
    Machine generated contents note: -- 1. Prelude: The modern stance -- 2. Twilight of the gods -- 3. The view from Copenhagen -- 4. Epistemological interlude -- 5. Wittgenstein enters the scene -- 6. Shaky foundations -- 7. Physics interface -- 8. Philosophical consequences -- 9. Metaphysics and reality -- 10. Concluding epilogue.
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  17. August Stern (2000). Quantum Theoretic Machines: What is Thought From the Point of View of Physics. Elsevier.
    Making Sense of Inner Sense 'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's greatest (...)
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  18. August Stern (1994). The Quantum Brain: Theory and Implications. North-Holland/Elsevier.
    While for the majority of physicists the problem of the deciphering of the brain code, the intelligence code, is a matter for future generations, the author boldly and forcefully disagrees. Breaking with the dogma of classical logic he develops in the form of the conversion postulate a concrete working hypothesis for the actual thought mechanism. The reader is invited on a fascinating mathematical journey to the very edges of modern scientific knowledge. From lepton and quark to mind, from cognition to (...)
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  19. Ole Steuernagel (2007). Afshar's Experiment Does Not Show a Violation of Complementarity. Foundations of Physics 37 (9):1370-1385.
    A recent experiment performed by S. Afshar [first reported by M. Chown, New Sci. 183:30, 2004] is analyzed. It was claimed that this experiment could be interpreted as a demonstration of a violation of the principle of complementarity in quantum mechanics. Instead, it is shown here that it can be understood in terms of classical wave optics and the standard interpretation of quantum mechanics. Its performance is quantified and it is concluded that the experiment is suboptimal in the sense that (...)
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  20. Michael Stöltzner (2002). Bell, Bohm, and von Neumann: Some Philosophical Inequalities Concerning No-Go Theorems and the Axiomatic Method. In T. Placek & J. Butterfield (eds.), Non-Locality and Modality. Kluwer. 37--58.
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  21. Y. Strauss & L. P. Horwitz (2000). Representation of the Resonance of a Relativistic Quantum Field Theoretical Lee–Friedrichs Model in Lax–Phillips Scattering Theory. Foundations of Physics 30 (5):653-694.
    The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay, law. The Wigner–Weisskopf survival amplitude, describing reversible quantum transitions, may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the evolution does riot correspond to a semigroup (...)
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  22. Witold Strawiński (2008). O kwantowej nielokalności i światach możliwych: uwagi polemiczne. Filozofia Nauki 1.
    In 2006 Tomasz F. Bigaj published in English a book "Non-locality and the Possible Worlds. A Counterfactual Perspective on Quantum Entanglement". He considered the question whether a satisfactory interpretation of quantum mechanics in the standard form should include the assumption of a non-local, immediate influence of one part of a specific quantum system (like two electrons in the singlet state) on the other, spatially separated part of that system. Bigaj - following H. Stapp - chooses as conceptual instruments of his (...)
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  23. M. Strevens (1996). Quantum Mechanics and Frequentism: A Reply to Ismael. British Journal for the Philosophy of Science 47 (4):575-577.
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  24. Michael Strevens (1996). Quantum Mechanics and Frequentism: A Reply to Ismael. British Journal for the Philosophy of Science 47 (4):575-577.
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  25. F. Strocchi (2004). Relativistic Quantum Mechanics and Field Theory. Foundations of Physics 34 (3):501-527.
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  26. Ward Struyve (2010). On Epstein's Trajectory Model of Non-Relativistic Quantum Mechanics. Foundations of Physics 40 (11):1700-1711.
    In 1952 Bohm presented a theory about non-relativistic point-particles that move deterministically along trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm’s particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general very different (...)
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  27. W. M. Stuckey, Michael Silberstein & Michael Cifone, The Relational Blockworld Interpretation of Non-Relativistic Quantum Mechanics.
    We introduce a new interpretation of non-relativistic quantum mechanics (QM) called Relational Blockworld (RBW). We motivate the interpretation by outlining two results due to Kaiser, Bohr, Ulfeck, Mottelson, and Anandan, independently. First, the canonical commutation relations for position and momentum can be obtained from boost and translation operators,respectively, in a spacetime where the relativity of simultaneity holds. Second, the QM density operator can be obtained from the spacetime symmetry group of the experimental configuration exclusively. We show how QM, obtained from (...)
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  28. William Mark Stuckey, Michael Silbserstein & Michael Cifone (2008). Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox. [REVIEW] Foundations of Physics 38 (4):348-383.
    The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the (...)
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  29. A. I. Studenikin (ed.) (1997). Problems of Fundamental Physics: Proceedings, 7th Lomonosov Conference on Elementary Particle Physics (24-30 August 1995, Moscow, Russia). [REVIEW] Urss.
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  30. Werner Stulpe (1994). Some Remarks on Classical Representations of Quantum Mechanics. Foundations of Physics 24 (7):1089-1094.
    It is shown that, to a certain extent, the statistical framework of Hilbert-space quantum mechanics can be reformulated in classical terms.
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  31. M. Suarez (2004). Quantum Selections, Propensities and the Problem of Measurement. British Journal for the Philosophy of Science 55 (2):219-255.
    This paper expands on, and provides a qualified defence of, Arthur Fine's selective interactions solution to the measurement problem. Fine's approach must be understood against the background of the insolubility proof of the quantum measurement. I first defend the proof as an appropriate formal representation of the quantum measurement problem. The nature of selective interactions, and more generally selections, is then clarified, and three arguments in their favour are offered. First, selections provide the only known solution to the measurement problem (...)
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  32. Mauricio Suarez (ed.) (forthcoming). Probabilities, Causes and Propensities in Physics. Springer.
  33. Mauricio Suárez (2007). Quantum Propensities. Studies in History and Philosophy of Science Part B 38 (2):418-438.
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  34. K. Svozil (1998). Analogues of Quantum Complementarity in the Theory of Automata. Studies in History and Philosophy of Science Part B 29 (1):61-80.
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  35. Karl Svozil (2002). Conventions in Relativity Theory and Quantum Mechanics. Foundations of Physics 32 (4):479-502.
    The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.
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  36. Pulmannova Sylvia (2002). Hidden Variables and Bell Inequalities on Quantum Logics. Foundations of Physics 32 (2).
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  37. J. L. Synge (1972). A Special Class of Solutions of the Schrödinger Equation for a Free Particle. Foundations of Physics 2 (1):35-40.
    The fundamental solution of the Schrödinger equation for a free particle is modified by the inclusion of an arbitrary scalar and an arbitrary vector, both imaginary. This gives a field free from singularities. By choosing the scalar small and the vector large, one obtains a model of a wavepacket which moves fast and remains concentrated over a long range.
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  38. Gyorgyi Szabo (2012). A Review of “Demystifying the Akasha: Consciousness and the Quantum Vacuum”. [REVIEW] World Futures 68 (1):75 - 76.
    World Futures, Volume 68, Issue 1, Page 75-76, January 2012.
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  39. Marek Szydłowski (1982). Wieloświatowa interpretacja mechaniki kwantowej [recenzja] The Many - Worlds Interpretation of Quantum Mechanics, ed.: Bryce S. De Vitt, Neill Graham, 1973. [REVIEW] Zagadnienia Filozoficzne W Nauce 4.
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  40. P. T. (2002). Quantum State Diffusion - Ian Percival, Quantum State Diffusion, Cambridge University Press, Cambridge, 1998. Studies in History and Philosophy of Science Part B 33 (4):707-716.
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  41. Kin'ya Takahashi & Kensuke S. Ikeda (2001). Complex-Domain Semiclassical Theory: Application to Time-Dependent Barrier Tunneling Problems. [REVIEW] Foundations of Physics 31 (1):177-201.
    Semiclassical theory based upon complexified classical mechanics is developed for periodically time-dependent scattering systems, which are minimal models of multi-dimensional systems. Semiclassical expression of the wave-matrix is derived, which is represented as the sum of the contributions from classical trajectories, where all the dynamical variables as well as the time are extended to the complex-domain. The semiclassical expression is examined by a periodically perturbed 1D barrier system and an excellent agreement with the fully quantum result is confirmed. In a stronger (...)
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  42. Michael Talbot (1986/1988). Beyond the Quantum. Bantam Books.
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  43. V. Tamma, C. O. Alley, W. P. Schleich & Y. H. Shih (2012). Prime Number Decomposition, the Hyperbolic Function and Multi-Path Michelson Interferometers. Foundations of Physics 42 (1):111-121.
    The phase φ of any wave is determined by the ratio x/λ consisting of the distance x propagated by the wave and its wavelength λ. Hence, the dependence of φ on λ constitutes an analogue system for the mathematical operation of division, that is to obtain the hyperbolic function f(ξ)≡1/ξ. We take advantage of this observation to decompose integers into primes and implement this approach towards factorization of numbers in a multi-path Michelson interferometer. This work is part of a larger (...)
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  44. Elliott Tammaro (2012). Mechanics: Non-Classical, Non-Quantum. [REVIEW] Foundations of Physics 42 (2):284-290.
    A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of interest for two primary reasons. Firstly, NCQs arise prominently in semi-classical approximation schemes. Their formal study may yield improved approximation techniques in the near-classical regime. More importantly for the purposes of this note, it may be possible for NCQs to reproduce quantum results over experimentally tested regimes while (...)
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  45. Charles Tandy (ed.) (2006). Death and Anti-Death, Volume 4: Twenty Years After De Beauvoir, Thirty Years After Heidegger. Palo Alto: Ria University Press.
  46. Scott Tanona (2004). Idealization and Formalism in Bohr's Approach to Quantum Theory. Philosophy of Science 71 (5):683-695.
    I reinterpret Bohr's attitude towards quantum mechanical formalism and its empirical content, based on his understanding of the correspondence principle and its approximate applicability. I suggest that Bohr understood complementarity as a limitation imposed by the commutation relations upon the applicability of the idealizations which had grounded the use of the correspondence principle. By discussing this interpretation against the contemporary background of discussions regarding “naïve realism” about operators (as observables), I suggest that a Bohrian view on the empirical content of (...)
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  47. Scott Tanona (2004). Idealization and Formalism in Bohr's Approach to Quantum Theory. Philosophy of Science 71 (5):683-695.
    Bohr held that quantum mechanical symbols find meaning only in the context of an experimental setting. Making a measurement requires establishing a correspondence between a property of the quantum object and a property of the measuring system via the introduction of a classical quantity with which the measuring instrument, classically understood, interacts. However, this correspondence is only approximate and involves the use of certain idealizations, and it is the commutation rules that tell us the limitations to this process. In this (...)
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  48. Paul Tappenden, Varieties of Divergence: A Response to Saunders and Wallace.
    I continue to maintain that David Lewis’s concept of overlapping persons cannot yield pre-measurement uncertainty in the Everett interpretation of quantum mechanics in the way that Simon Saunders and David Wallace originally seemed to suggest. However, I argue that in their reply to me they make it clear that they do not wish to invoke overlap of persons after all. That makes it mysterious why they defended their interpretation of personal overlap in the first place and questionable what role overlap (...)
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  49. G. Tarozzi (1996). Quantum Measurements and Macrophysical Reality: Epistemological Implications of a Proposed Paradox. [REVIEW] Foundations of Physics 26 (7):907-917.
    After an outline of the macrorealistic solutions to the difficulties of the measurement theory, a new paradox is proposed and then discussed in the light of three different interpretations of quantum mechanics.
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  50. Hal Tasaki, Sheldon Goldstein & Takashi Hara, On the Time Scales in the Approach to Equilibrium of Macroscopic Quantum Systems.
    The recent renewed interest in the foundation of quantum statistical mechanics and in the dynamics of isolated quantum systems has led to a revival of the old approach by von Neumann to investigate the problem of thermalization only in terms of quantum dynamics in an isolated system [1, 2]. It has been demonstrated in some general or concrete settings that a pure initial state evolving under quantum dynamics indeed approaches an equilibrium state [3–9]. The underlying idea that a single pure (...)
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