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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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Interpretation of Quantum Mechanics
  1. Constantin Antonopoulos (2005). Making the Quantum of Relevance. Journal for General Philosophy of Science 36 (2):223 - 241.
    The two Heisenberg Uncertainties (UR) entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → -q) & (q → -p) or defineable as [(p → -q) & (q → -p)] ↔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus a matter of logic, the latter fact dependent, and thus (...)
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  2. A. Arensburg & L. P. Horwitz (1992). A First-Order Equation for Spin in a Manifestly Relativistically Covariant Quantum Theory. Foundations of Physics 22 (8):1025-1039.
    Relativistic quantum mechanics has been formulated as a theory of the evolution ofevents in spacetime; the wave functions are square-integrable functions on the four-dimensional spacetime, parametrized by a universal invariant world time τ. The representation of states with spin is induced with a little group that is the subgroup of O(3, 1) leaving invariant a timelike vector nμ; a positive definite invariant scalar product, for which matrix elements of tensor operators are covariant, emerges from this construction. In a previous study (...)
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  3. J. C. Aron (1981). Stochastic Foundation for Microphysics. A Critical Analysis. Foundations of Physics 11 (9-10):699-720.
    The stochastic scheme proposed in a previous paper as subjacent to quantum mechanics is analyzed in the light of the difficulties and criticisms encountered by similar attempts. It is shown that the limitation of the domain where the theory is valid gives a reply to the criticisms, but restricts its practical usefulness to the description of basic features. A stochastic approach of the hadron mass spectrum, allowing the scheme to emerge in the domain of experimental verification (to be worked out (...)
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  4. Richard T. W. Arthur (1981). Book Review:Quantum Mechanics, a Half Century Later J.L. Lopes, M. Paty. [REVIEW] Philosophy of Science 48 (1):156-.
  5. Alain Aspect & Robin Kaiser (1990). Linear Momentum Conservation in Coherent Population Trapping: A Case Study for a Quantum Filtering Process. [REVIEW] Foundations of Physics 20 (12):1413-1428.
    We discuss the question of linear momentum conservation when an atom coupled to a laser field enters into a state which is not an eigenstate of the linear momentum. Such a situation happens in the recently demonstrated laser cooling of atoms by velocity selective coherent population trapping. We show that this process can be understood as a filtering of the atomic state by the laser field taken as a classical measuring apparatus. In a different approach, the laser field can be (...)
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  6. D. Atkinson (1998). The Light of Quantum Mechanics. Dialectica 52 (2):103–126.
    It is argued that while classical probability theory, as it is encapsulated in the axioms of Kolmogorov and in his criterion for the independence of two events, can consistently be employed in quantum mechanics, this can only be accomplished at an exorbitant price. By considering rst the classic two-slit experiment, and then the passage of one photon through three polarizers, the applicability of Kolmogorov's last axiom is called into question, but the standard rebu of the Copenhagen interpretation is shown to (...)
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  7. Michael N. Audi (1973). Book Review:Perspectives in Quantum Theory: Essays in Honor of Alfred Lande Wolfgang Yourgrau, Alwyn Van Der Merwe. [REVIEW] Philosophy of Science 40 (2):323-.
  8. Jürgen Audretsch & Klaus Mainzer (eds.) (1990). Wieviele Leben Hat Schrödingers Katze? Bibliographisches Institut.
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  9. 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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  10. Alexander Bach (1988). The Concept of Indistinguishable Particles in Classical and Quantum Physics. Foundations of Physics 18 (6):639-649.
    The consequences of the following definition of indistinguishability are analyzed. Indistinguishable classical or quantum particles are identical classical or quantum particles in a state characterized by a probability measure, a statistical operator respectively, which is invariant under any permutation of the particles. According to this definition the particles of classical Maxwell-Boltzmann statistics are indistinguishable.
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  11. J. E. Baggott (2011). The Quantum Story: A History in 40 Moments. Oxford University Press.
    Prologue: Stormclouds : London, April 1900 -- Quantum of action: The most strenuous work of my life : Berlin, December 1900 ; Annus Mirabilis : Bern, March 1905 ; A little bit of reality : Manchester, April 1913 ; la Comédie Française : Paris, September 1923 ; A strangely beautiful interior : Helgoland, June 1925 ; The self-rotating electron : Leiden, November 1925 ; A late erotic outburst : Swiss Alps, Christmas 1925 -- Quantum interpretation: Ghost field : Oxford, August (...)
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  12. 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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  13. M. Bahrami & A. Shafiee (2010). Postponing the Past: An Operational Analysis of Delayed-Choice Experiments. [REVIEW] Foundations of Physics 40 (1):55-92.
    The prominent characteristic of a delayed-choice effect is to make the choice between complementary types of phenomena after the relevant interaction between the system and measuring instrument has already come to an end. In this paper, we first represent a detailed comparative analysis of some early delayed-choice propositions and also most of the experimentally performed delayed-choice proposals in a coherent and unified quantum mechanical formulation. Taking into the account the represented quantum mechanical descriptions and also the rules of probability theory, (...)
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  14. 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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  15. Leslie Ballentine (2008). Classicality Without Decoherence: A Reply to Schlosshauer. [REVIEW] Foundations of Physics 38 (10):916-922.
    Schlosshauer has criticized the conclusion of Wiebe and Ballentine (Phys. Rev. A 72:022109, 2005) that decoherence is not essential for the emergence of classicality from quantum mechanics. I reply to the issues raised in his critique, which range from the interpretation of quantum mechanics to the criterion for classicality, and conclude that the role of decoherence in these issues is much more restricted than is often claimed.
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  16. A. Baltag & S. Smets (2008). A Dynamic-Logical Perspective on Quantum Behavior. Studia Logica 89 (2):187 - 211.
    In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously used to model various (...)
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  17. Alexandru Baltag & Sonja Smets, The Logic of Quantum Programs.
    We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound quantum systems. We give a syntax and a relational semantics in which we abstract away from phases and probabilities. We present a sound proof system for this logic, and we show how to characterize by logical means various forms of entanglement (e.g. the Bell states) and various (...)
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  18. W. Balzer (1981). Piron's Foundation of Quantum Mechanics (Comment on His Paper). Erkenntnis 16 (3):403 - 406.
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  19. Gergely Bana & Thomas Durt (1997). Proof of Kolmogorovian Censorship. Foundations of Physics 27 (10):1355-1373.
  20. William Band & James L. Park (1970). The Empirical Determination of Quantum States. Foundations of Physics 1 (2):133-144.
    A common approach to quantum physics is enshrouded in a jargon which treats state vectors as attributes of physical systems and the concept of state preparation as a filtration scheme wherein a process involving measurement selects from a primordial assembly of systems those bearing some prescribed vector of interest. By contrast, the empirical experiences with which quantum theory is actually concerned relate measurement and preparation in quite an opposite manner. Reproducible preparation schemes are logically and temporally anterior to measurement acts. (...)
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  21. R. L. Barnette (1978). Does Quantum Mechanics Disprove the Principle of the Identity of Indiscernibles? Philosophy of Science 45 (3):466-470.
  22. Jeffrey A. Barrett (2001). The Strange World of Quantum Mechanics Daniel F. Styer. [REVIEW] British Journal for the Philosophy of Science 52 (2):393-396.
  23. Jeffrey A. Barrett (2005). Relativistic Quantum Mechanics Through Frame-Dependent Constructions. Philosophy of Science 72 (5):802-813.
    This paper is concerned with the possibility and nature of relativistic hidden-variable formulations of quantum mechanics. Both ad hoc teleological constructions of spacetime maps and frame-dependent constructions of spacetime maps are considered. While frame-dependent constructions are clearly preferable, they provide neither mechanical nor causal explanations for local quantum events. Rather, the hiddenvariable dynamics used in such constructions is just a rule that helps to characterize the set of all possible spacetime maps. But while having neither mechanical nor causal explanations of (...)
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  24. S. Bartalucci, S. Bertolucci, M. Bragadireanu, M. Cargnelli, C. Curceanu, S. Di Matteo, J.-P. Egger, C. Guaraldo, M. Iliescu, T. Ishiwatari, M. Laubenstein, J. Marton, E. Milotti, D. Pietreanu, T. Ponta, A. Romero Vidal, D. L. Sirghi, F. Sirghi, L. Sperandio, O. Vazquez Doce, E. Widmann & J. Zmeskal (2010). The VIP Experimental Limit on the Pauli Exclusion Principle Violation by Electrons. Foundations of Physics 40 (7):765-775.
    In this paper we describe an experimental test of the validity of the Pauli Exclusion Principle (for electrons) which is based on a straightforward idea put forward a few years ago by Ramberg and Snow (Phys. Lett. B 238:438, 1990). We perform a very accurate search of X-rays from the Pauli-forbidden atomic transitions of electrons in the already filled 1S shells of copper atoms. Although the experiment has a very simple structure, it poses deep conceptual and interpretational problems. Here we (...)
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  25. A. O. Barut (1992). How to Avoid “Quantum Paradoxes”. Foundations of Physics 22 (1):137-142.
    The “theorems” showing the impossibility of ascribing to individual quantum systems a definite value of a set of observables, not necessarily commuting,1–4 are based on the tacit assumption that eachindividual spin component has a discrete dichotomic value. We show explicitly that it is possible to introduce continuous hidden variables for individual spins which avoid these quantum paradoxes without changing any of the observed quantum mechanical results.
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  26. A. O. Barut (1988). Combining Relativity and Quantum Mechanics: Schrödinger's Interpretation of Ψ. [REVIEW] Foundations of Physics 18 (1):95-105.
    The incongruence between quantum theory and relativity theory is traced to the probability interpretation of the former. The classical continium interpretation of ψ removes the difficulty. How quantum properties of matter and light, and in particular the radiative problems, like spontaneous emission and Lamb shift, may be accounted in a first quantized Maxwell-Dirac system is discussed.
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  27. A. O. Barut, M. Božić & Z. Marić (1988). Joint Probabilities of Noncommuting Operators and Incompleteness of Quantum Mechanics. Foundations of Physics 18 (10):999-1012.
    We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.(1) The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond (...)
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  28. Angelo Bassi (ed.) (2006). Quantum Mechanics: Are There Quantum Jumps? Trieste, Italy, 5 Spetember -2005 and on the Present Status of Quantum Mechanics Lošinj, Croatia 7-9 September 2005. [REVIEW] American Institute of Physics.
    This conference brought together experts in different fields related to the foundations of quantum mechanics, ranging from mathematical physics to experimental physics, as well as the philosophy of science. The major topics discussed are: collapse models, Bohemian mechanics and their relativistic extensions, other alternative formulation of quantum mechanics, properties of entanglement, statistical physics and probability theory, new experimental results, as well as philosophical and epistemological issues.
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  29. J. Barretto Bastos Filho & F. Selleri (1995). Propensity, Probability, and Quantum Physics. Foundations of Physics 25 (5):701-716.
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  30. J. Batouli & M. El Baz (2014). Classical Interpretation of a Deformed Quantum Oscillator. Foundations of Physics 44 (2):105-113.
    Following the same procedure that allowed Shcrödinger to construct the (canonical) coherent states in the first place, we investigate on a possible classical interpretation of the deformed harmonic oscillator. We find that, these oscillator, also called q-oscillators, can be interpreted as quantum versions of classical forced oscillators with a modified q-dependant frequency.
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  31. Friedrich Beck (2001). Quantum Brain Dynamics and Consciousness. In P. Loockvane (ed.), The Physical Nature of Consciousness. John Benjamins.
  32. Friedrich Beck (1998). Synaptic Transmission, Quantum-State Selection, and Consciousness. In Stuart R. Hameroff, Alfred W. Kaszniak & A. C. Scott (eds.), Toward a Science of Consciousness II. MIT Press.
  33. Friedrich Beck (1994). Quantum Mechanics and Consciousness. Journal of Consciousness Studies 1 (2):253-255.
    The first issue of JCS published an interview with Roger Penrose on his recent book Shadows of the Mind: A Search for the Missing Science of Consciousness . In it Professor Penrose, among other subjects, presented his views on the role of quantum mechanics on our way towards a better understanding of brain functioning and its relation to consciousness. In this note we comment on some aspects of his reasoning.
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  34. Friedrich Beck & John C. Eccles (2003). Quantum Processes in the Brain: A Scientific Basis of Consciousness. In Naoyuki Osaka (ed.), Neural Basis of Consciousness. John Benjamins. 49--141.
  35. L. Becker (2001). The Quantum Mechanics of Minds and Worlds. Philosophical Review 110 (3):482-484.
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  36. Hugo Bedau & Paul Oppenheim (1961). Complementarity in Quantum Mechanics: A Logical Analysis. Synthese 13 (3):201 - 232.
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  37. D. Bedford & D. Wang (1983). Comments on “On the Quantum Mechanical Superposition of Macroscopically Distinguishable States”. Foundations of Physics 13 (10):987-988.
    The substance of the authors' disagreement with the views of D. Gutkowski and M. V. Valdes Franco is presented.
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  38. Donald Bedford & Derek Wang (1976). Environment, Consciousness, and Quantum Measurement. Foundations of Physics 6 (5):599-605.
    It is shown that (a) the conscious observer plays no essential part in the measurement process, and (b) environmental perturbations of whatever kind fail to account for the evolution of systems into “mixtures” or “dynamically decoupled” systems.
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  39. V. P. Belavkin (1994). Nondemolition Principle of Quantum Measurement Theory. Foundations of Physics 24 (5):685-714.
    We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The “collapsed state-vector” after the “objectification” is simply treated as a random vector of the a posterioristate given by the quantum filtering, i.e., the conditioning of the a prioriinduced state on the corresponding reduced algebra. The nonlinear phenomenological equation of “continuous spontaneous localization” has been derived (...)
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  40. J. S. Bell (1992). Six Possible Worlds of Quantum Mechanics. Foundations of Physics 22 (10):1201-1215.
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  41. J. S. Bell (1982). On the Impossible Pilot Wave. Foundations of Physics 12 (10):989-999.
    The strange story of the von Neumann impossibility proof is recalled, and the even stranger story of later impossibility proofs, and how the impossible was done by de Broglie and Bohm. Morals are drawn.
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  42. 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.
  43. 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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  44. Gordon Belot (2012). Quantum States for Primitive Ontologists. European Journal for Philosophy of Science 2 (1):67-83.
    Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as (...)
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  45. Darrin W. Belousek (2003). Non‐Seperability, Non‐Supervenience, and Quantum Ontology. Philosophy of Science 70 (4):791-811.
    An argument to the effect that quantum mechanics commits us to the existence of non-supervenient relations, and therefore that we should admit such relations into our quantum ontology as fundamental entities, has been given by Teller and reformulated by French. This paper aims, first, to explicate and evaluate that argument; second, to extend its premises in order to assess its relevance for other interpretations of quantum mechanics; and, third, to clarify its implications for holism and individuation in quantum ontology.
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  46. Darrin W. Belousek (2000). Statistics, Symmetry, and (In)Distinguishability in Bohmian Mechanics. Foundations of Physics 30 (1):153-164.
    This paper continues an earlier work by considering in what sense and to what extent identical Bohmian-mechanical particles in many-particle systems can be considered indistinguishable. We conclude that while whether identical Bohmian-mechanical particles ace considered to be “statistically (in)distinguishable” is a matter of theory choice underdetermined by logic and experiment, such particles are in any case “physically distinguishable.”.
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  47. Darrin W. Belousek (2000). Statistics, Symmetry, and the Conventionality of Indistinguishability in Quantum Mechanics. Foundations of Physics 30 (1):1-34.
    The question to be addressed is, In what sense and to what extent do quantum statistics for, and the standard formal quantum-mechanical description of, systems of many identical particles entail that identical quantum particles are indistinguishable? This paper argues that whether or not we consider identical quantum particles as indistinguishable is a matter of theory choice underdetermined by logic and experiment.
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  48. Darrin W. Belousek (1997). Perspectives on Quantum Reality: A Critical Survey. Studies in History and Philosophy of Science Part B 28 (3):415-420.
  49. E. G. Beltrametti & S. Bugajski (2002). Quantum Mechanics and Operational Probability Theory. Foundations of Science 7 (1-2):197-212.
    We discuss a generalization of the standard notion of probability space and show that the emerging framework, to be called operational probability theory, can be considered as underlying quantal theories. The proposed framework makes special reference to the convex structure of states and to a family of observables which is wider than the familiar set of random variables: it appears as an alternative to the known algebraic approach to quantum probability.
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