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Summary 'Interpretations' of quantum mechanics are traditionally characterized by their responses to the measurement problem: how can the deterministic unitary quantum dynamics, expressed in the Schrodinger equation, give rise to particular sequences of measurement outcomes with probabilities given by the Born rule? But the main competing responses to the measurement problem are not interpretations of some agreed core theory; rather, they are logically incompatible theories which generally posit some additional dynamical structure over and above the unitary dynamics. For example, Bohmian mechanics adds 'hidden variables', such as particles with precise locations, which are guided by a field with the same structure as the unitary quantum state; and dynamical collapse theories posit a new stochastic dynamical process of state collapse. An important exception is Everettian quantum mechanics, or the 'many worlds interpretation', which adds no new structure and instead attempts to recover determinate measurement outcomes perspectivally.
Key works Bell 2004 set the scene for almost all contemporary discussions, and was an eloquent advocate of Bohmian mechanics. Saunders et al 2010 contains in-depth discussion of the pros and cons of the Everett interpretation.
Introductions Albert 1992 is a vivid and entertaining introduction to the measurement problem. Goldstein 2008 gives a thorough account of Bohmian mechanics. Vaidman 2008 does the same for Everettian quantum mechanics.
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  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. Jonas Rafael Becker Arenhart (2011). A Discussion on Finite Quasi-Cardinals in Quasi-Set Theory. Foundations of Physics 41 (8):1338-1354.
    Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardinal definition fail for collections of indistinguishable objects. In (...)
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  3. 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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  4. 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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  5. 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-.
  6. 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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  7. 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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  8. 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-.
  9. Jürgen Audretsch & Klaus Mainzer (eds.) (1990). Wieviele Leben Hat Schrödingers Katze? Bibliographisches Institut.
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  10. Gennaro Auletta (2005). Quantum Information as a General Paradigm. Foundations of Physics 35 (5):787-815.
    Quantum–mechanical systems may be understood in terms of information. When they interact, they modify the information they carry or represent in two, and only two, ways: by selecting a part of the initial amount of (potential) information and by sharing information with other systems. As a consequence, quantum systems are informationally shielded. These features are shown to be general features of nature. In particular, it is shown that matter arises from quantum–mechanical processes through the constitution of larger ensembles that share (...)
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  11. 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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  12. Guido Bacciagaluppi & Michael Dickson (1999). Dynamics for Modal Interpretations. Foundations of Physics 29 (8):1165-1201.
    An outstanding problem in so-called modal interpretations of quantum mechanics has been the specification of a dynamics for the properties introduced in such interpretations. We develop a general framework (in the context of the theory of stochastic processes) for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks. This framework admits many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them. This approach is applicable (...)
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  13. 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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  14. John C. Baez (1989). Is Life Improbable? Foundations of Physics 19 (1):91-95.
    E. P. Wigner's argument that the probability of the existence of self-reproducing units, e.g., organisms, is zero according to standard quantum theory is stated and analyzed. Theorems are presented which indicate that Wigner's mathematical result in fact should not be interpreted as asserting the improbability of self-reproducing units.
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  15. 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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  16. 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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  17. 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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  18. 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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  19. 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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  20. 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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  21. 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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  22. W. Balzer (1981). Piron's Foundation of Quantum Mechanics (Comment on His Paper). Erkenntnis 16 (3):403 - 406.
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  23. Gergely Bana & Thomas Durt (1997). Proof of Kolmogorovian Censorship. Foundations of Physics 27 (10):1355-1373.
  24. William Band & James L. Park (1976). New Information-Theoretic Foundations for Quantum Statistics. Foundations of Physics 6 (3):249-262.
    When the state of a physical system is not fully determined by available data, it should be possible nevertheless to make a systematic guess concerning the unknown state by applying the principles of information theory. The resulting theoretical blend of informational and mechanical constructs should then constitute a modern structure for statistical physics. Such a program has been attempted by a number of authors, most notably Jaynes, with seeming success. However, we demonstrated in a recent publication that the standard list (...)
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  25. 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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  26. R. L. Barnette (1978). Does Quantum Mechanics Disprove the Principle of the Identity of Indiscernibles? Philosophy of Science 45 (3):466-470.
  27. Jeffrey A. Barrett (2006). A Quantum-Mechanical Argument for Mind–Body Dualism. Erkenntnis 65 (1):97 - 115.
    I argue that a strong mind–body dualism is required of any formulation of quantum mechanics that satisfies a relatively weak set of explanatory constraints. Dropping one or more of these constraints may allow one to avoid the commitment to a mind–body dualism but may also require a commitment to a physical–physical dualism that is at least as objectionable. Ultimately, it is the preferred basis problem that pushes both collapse and no-collapse theories in the direction of a strong dualism in resolving (...)
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  28. 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.
  29. Jeffrey A. Barrett (1997). On Everett's Formulation of Quantum Mechanics. The Monist 80 (1):70 - 96.
    Everett wanted a formulation of quantum mechanics that (i) took the linear dynamics to be a complete and accurate description of the time-evolution of all physical systems and (ii) logically entailed the same subjective appearances predicted by the standard formulation of quantum mechanics. While most everyone would agree with this description of Everett's project, there is little agreement on exactly how his relative-state formulation was supposed to work. In this paper, I consider two very different readings of Everett: the bare (...)
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  30. 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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  31. 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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  32. 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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  33. 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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  34. 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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  35. 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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  36. J. Barretto Bastos Filho & F. Selleri (1995). Propensity, Probability, and Quantum Physics. Foundations of Physics 25 (5):701-716.
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  37. 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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  38. Friedrich Beck (2001). Quantum Brain Dynamics and Consciousness. In P. Loockvane (ed.), The Physical Nature of Consciousness. John Benjamins.
  39. 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.
  40. Friedrich Beck (1994). Quantum Mechanics and Consciousness. Journal of Consciousness Studies 1 (2):253-255.
  41. 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.
  42. L. Becker (2001). The Quantum Mechanics of Minds and Worlds. Philosophical Review 110 (3):482-484.
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  43. Hugo Bedau & Paul Oppenheim (1961). Complementarity in Quantum Mechanics: A Logical Analysis. Synthese 13 (3):201 - 232.
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  44. 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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  45. 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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  46. Daniel J. Bedingham (2011). Relativistic State Reduction Dynamics. Foundations of Physics 41 (4):686-704.
    A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a relativistic field in which a quantized degree of freedom is associated to each point in spacetime. The purpose of this field is to mediate in the interaction between classical stochastic influences and conventional quantum fields. The equations of motion are Lorentz covariant, frame independent, and do not result in (...)
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  47. 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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  48. J. S. Bell (2004). Against ”Measurement'. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. 213--231.
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  49. 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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  50. J. S. Bell (1992). Six Possible Worlds of Quantum Mechanics. Foundations of Physics 22 (10):1201-1215.
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