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Quantum Mechanics

Edited by Michael Cuffaro (Ludwig Maximilians Universität, München)
Assistant editors: Radin Dardashti, Brian Padden
About this topic
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 2012). 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. 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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  2. Eva Cassirer (1958). Methodology and Quantum Physics. [REVIEW] British Journal for the Philosophy of Science 8 (32):334-341.
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  3. Andor Frenkel (2002). A Tentative Expression of the Károlyházy Uncertainty of the Space-Time Structure Through Vacuum Spreads in Quantum Gravity. Foundations of Physics 32 (5):751-771.
    In the existing expositions of the Károlyházy model, quantum mechanical uncertainties are mimicked by classical spreads. It is shown how to express those uncertainties through entities of the future unified theory of general relativity and quantum theory.
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  4. Andor Frenkel (1990). Spontaneous Localizations of the Wave Function and Classical Behavior. Foundations of Physics 20 (2):159-188.
    We investigate and develop further two models, the GRW model and the K model, in which the Schrödinger evolution of the wave function is spontaneously and repeatedly interrupted by random, approximate localizations, also called “self-reductions” below. In these models the center of mass of a macroscopic solid body is well localized even if one disregards the interactions with the environment. The motion of the body shows a small departure from the classical motion. We discuss the prospects and the difficulties of (...)
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  5. Thomas Frentz (2011). Creative Metaphors, Synchronicity, and Quantum Physics. Philosophy and Rhetoric 44 (2):101-128.
    The very notion of transposition, the constant theme of a theory of tropes, brings operations into play that legitimate a mixed approach involving psychology and linguistics.The recognition that science cannot do without metaphor—that all theories are elaborations of basic metaphors or systems of metaphors—is only one part of a larger emerging awareness of the pervasiveness of metaphor in all language.Metaphor always has about it precisely this revealing of hitherto unexpected connectives which we may note in the progressions of a dream.In (...)
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  6. Alice Fulton (2007). Appendix A. Cascade Experiment. In Karen Michelle Barad (ed.), Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. Duke University Press.
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  7. N. G. (2000). Operation Quantum Physics. Studies in History and Philosophy of Science Part B 31 (1):117-125.
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  8. Fabián H. Gaioli & Edgardo T. Garcia Alvarez (1998). Classical and Quantum Theories of Spin. Foundations of Physics 28 (10):1539-1550.
    A great effort has been devoted to formulating a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in connecting classical and quantum theories rests in finding a parameter that plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneering works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and (...)
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  9. Maria Carla Galavotti (1995). Operationism, Probability and Quantum Mechanics. Foundations of Science 1 (1):99-118.
    This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the classical (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to physical theories, despite the (...)
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  10. Matjaz Gams (ed.) (1997). Mind Versus Computer: Were Dreyfus and Winograd Right? Amsterdam: IOS Press.
    M. Gams et al. (Eds.) IOS Press, "Strong AI": an Adolescent Disorder Donald Michie Professor Emeritus, University of Edinburgh, UK Associate ...
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  11. Kostas Gavroglu & Yorgos Goudaroulis (1989). Quantum Mechanics and Macroscopic Quantum Phenomena: The Case of Superconductivity and Superfluidity. Journal for General Philosophy of Science 20 (2):249-275.
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  12. Julio Gea-Banacloche (1998). Emergence of Classical Radiation Fields Through Decoherence in the Scully-Lamb Laser Model. Foundations of Physics 28 (4):531-548.
    The quantum theory of the laser of Scully and Lamb is used to determine the longest-lived states of the quantized field in an idealized, single-mode laser cavity. It is shown that quasiclassical states (states with well-defined phase and amplitude) are naturally selected. A quantum trajectory analysis provides some insight as to why this is so.
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  13. Danko Georgiev (2013). Quantum No-Go Theorems and Consciousness. Axiomathes 23 (4):683-695.
    Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the standard Hilbert (...)
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  14. G. Gerlich (1981). Some Remarks on Classical Probability Theory in Quantum Mechanics. Erkenntnis 16 (3):335 - 338.
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  15. Dieter Gernert (2011). Distance and Similarity Measures in Generalised Quantum Theory. Axiomathes 21 (2):303-313.
    A summary of recent experimental results shows that entanglement can be generated more easily than before, and that there are improved chances for its persistence. An eminent finding of Generalised Quantum Theory is the insight that the notion of entanglement can be extended, such that, e.g., psychological or psychophysical problem areas can be included, too. First, a general condition for entanglement to occur is given by the term ‘common prearranged context’. A formalised treatment requires a quantitative definition of the similarity (...)
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  16. Robert Geroch & James B. Hartle (1986). Computability and Physical Theories. Foundations of Physics 16 (6):533-550.
    The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature—one based on the issue of whether or not the physically measurable numbers predicted by the theory are computable in the mathematical sense. Applying this formulation to one approach to a quantum theory of gravity, there are found indications that there may exist no such (...)
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  17. Han Geurdes, Field Equations, Quantum Mechanics and Geotropism.
    The biochemistry of geotropism in plants and gravisensing in e.g. cyanobacteria or paramacia is still not well understood today [1]. Perhaps there are more ways than one for organisms to sense gravity. The two best known relatively old explanations for gravity sensing are sensing through the redistribution of cellular starch statoliths and sensing through redistribution of auxin. The starch containing statoliths in a gravity field produce pressure on the endoplasmic reticulum of the cell. This enables the cell to sense direction. (...)
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  18. Han Geurdes, On an Intrinsic Quantum Theoretical Structure Inside Einstein's Gravity Field Equations.
    As is well known, Einstein was dissatisfied with the foundation of quantum theory and sought to find a basis for it that would have satisfied his need for a causal explanation. In this paper this abandoned idea is investigated. It is found that it is mathematically not dead at all. More in particular: a quantum mechanical U(1) gauge invariant Dirac equation can be derived from Einstein's gravity field equations. We ask ourselves what it means for physics, the history of physics (...)
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  19. Ashot S. Gevorkyan (2011). Nonrelativistic Quantum Mechanics with Fundamental Environment. Foundations of Physics 41 (3):509-515.
    Spontaneous transitions between bound states of an atomic system, “Lamb Shift” of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations (fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system “quantum system (QS) + FE” is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ (...)
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  20. G. C. Ghirardi, R. Grassi & F. Benatti (1995). Describing the Macroscopic World: Closing the Circle Within the Dynamical Reduction Program. [REVIEW] Foundations of Physics 25 (1):5-38.
    With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe systems within a genuine Hilbert space framework, the peculiar features of the spontaneous reduction models limit drastically the states which are dynamically stable. (...)
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  21. G. C. Ghirardi, A. Rimini & T. Weber (1988). The Puzzling Entanglement of Schrödinger's Wave Function. Foundations of Physics 18 (1):1-27.
    A brief review of the conceptual difficulties met by the quantum formalism is presented. The main attempts to overcome these difficulties are considered and their limitations are pointed out. A recent proposal based on the assumption of the occurrence of a specific type of wave function collapse is discussed and its consequences for the above-mentioned problems are analyzed.
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  22. G. C. Ghirardi, A. Rimini & T. Weber (1980). A General Argument Against Superluminal Transmission Through the Quantum Mechanical Measurement Process. Lettere Al Nuovo Cimento 27:294--298.
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  23. G. Ghirardi & M. Jammer (1996). II International Symposium on Fundamental Problems in Quantum Physics. Foundations of Physics 26 (2).
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  24. GianCarlo Ghirardi (2011). Vedral, V.: Decoding Reality: The Universe as Quantum Information. [REVIEW] Foundations of Physics 41 (4):637-639.
  25. GianCarlo Ghirardi (2008). Reconsidering Mermin's “In Praise of Measurement”. Foundations of Physics 38 (11):1011-1019.
    We critically analyze a recent paper by D. Mermin and we compare his statements with Bell’s position on the problems he is discussing.
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  26. GianCarlo Ghirardi (2005). Quantum Theory as an Emergent Phenomenon: The Statistical. Philosophy of Science 72 (4):642-645.
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  27. GianCarlo Ghirardi (2002). Making Quantum Theory Compatible with Realism. Foundations of Science 7 (1-2):11-47.
    After a brief account of theway quantum theory deals with naturalprocesses, the crucial problem that such atheory meets, the measurement or, better, themacro-objectification problem is discussed.The embarrassing aspects of the occurrence ofentangled states involving macroscopic systemsare analyzed in details. The famous example ofSchroedinger's cat is presented and it ispointed out how the combined interplay of thesuperposition principle and the ensuingentanglement raises some serious difficultiesin working out a satisfactory quantum worldview, agreeing with our definiteperceptions. The orthodox solution to themacro-objectification problem, i.e. (...)
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  28. Giancarlo Ghirardi (1996). Quantum Dynamical Reduction and Reality: Replacing Probability Densities with Densities in Real Space. [REVIEW] Erkenntnis 45 (2-3):349 - 365.
    Consideration is given to recent attempts to solve the objectification problem of quantum mechanics by considering nonlinear and stochastic modifications of Schrödinger's evolution equation. Such theories agree with all predictions of standard quantum mechanics concerning microsystems but forbid the occurrence of superpositions of macroscopically different states. It is shown that the appropriate interpretation for such theories is obtained by replacing the probability densities of standard quantum mechanics with mass densities in real space. Criteria allowing a precise characterization of the idea (...)
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  29. GianCarlo Ghirardi & Raffaele Romano (2013). About Possible Extensions of Quantum Theory. Foundations of Physics 43 (7):881-894.
    Recently it has been claimed that no extension of quantum theory can have improved predictive power, the statement following, according to the authors, from the assumptions of free will and of the correctness of quantum predictions concerning the correlations of measurement outcomes. Here we prove that the argument is basically flawed by an inappropriate use of the assumption of free will. In particular, among other implications, the claim, if correct, would imply that Bohmian Mechanics is incompatible with free will. This (...)
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  30. Partha Ghose (2002). A Continuous Transition Between Quantum and Classical Mechanics. I. Foundations of Physics 32 (6):871-892.
    In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of mechanics which provides a continuous transition between quantum and classical mechanics via environment-induced decoherence.
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  31. Partha Ghose (1996). Relativistic Quantum Mechanics of Spin-0 and Spin-1 Bosons. Foundations of Physics 26 (11):1441-1455.
    It is shown that below the threshold of pair creation, a consistent quantum mechanical interpretation of relativistic spin-0 and spin-1 particles (both massive and mussless) ispossible based an the Hamiltonian-Schrödinger form of the firstorder Kemmer equation together with a first-class constraint. The crucial element is the identification of a conserved four-vector current associated with the equation of motion, whose time component is proportional to the energy density which is constrainedto be positive definite for allsolutions. Consequently, the antiparticles must be interpreted (...)
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  32. Partha Ghose & Dipankar Home (1995). An Analysis of the Aharonov-Anandan-Vaidman Model. Foundations of Physics 25 (7):1105-1109.
    We argue that the Aharonov-Anandan-Vaidman model, by using the notion of so-called “protective measurements,” cannot claim to have dispensed with the ldcollapse of the wave function,” because it does not succeed in avoiding the quantum measurement problem. Its claim to be able to distinguish between two nonorthogonal states is also critically examined.
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  33. Partha Ghose & Manoj K. Samal (2002). A Continuous Transition Between Quantum and Classical Mechanics. II. Foundations of Physics 32 (6):893-906.
    Examples are worked out using a new equation proposed in the previous paper to show that it has new physical predictions for mesoscopic systems.
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  34. Francesco Giacosa (2012). Non-Exponential Decay in Quantum Field Theory and in Quantum Mechanics: The Case of Two (or More) Decay Channels. Foundations of Physics 42 (10):1262-1299.
    We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of non-exponential decay in QFT and QM, we evaluate in both cases the decay probability that the unstable particle decays in a given channel in the time interval between t and t+dt. An important quantity is the ratio of the probability of decay (...)
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  35. Irene Giardina & Alberto Rimini (1996). On the Existence of Inequivalent Quasideterministic Domains. Foundations of Physics 26 (8):973-987.
    In the framework of the history approach to quantum mechanics and, in particular, of the formulation of Gell-Mann and Hartle, the question of the existence of inequivalent decoherent sets of histories is reconsidered. A simple but acceptably realistic model of the dynamics of the universe is proposed and a particular set of histories is shown to be decoherent. By suitable tranformations of this set, a family of sets of histories is then generated, such that the sets, first, are decoherent on (...)
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  36. P. F. Gibbins & D. B. Pearson (1981). The Distributive Law in the Two-Slit Experiment. Foundations of Physics 11 (9-10):797-803.
    It is shown that the lattice-theoretic distributive law does not fail to hold in the two slit-experiment for the general case offinite slit widths and for a position measurement which localizes the observed particle to afinite region of the screen. Comments are made on previous and less general discussions of the case considered.
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  37. Steven B. Giddings (2013). Is String Theory a Theory of Quantum Gravity? Foundations of Physics 43 (1):115-139.
    Some problems in finding a complete quantum theory incorporating gravity are discussed. One is that of giving a consistent unitary description of high-energy scattering. Another is that of giving a consistent quantum description of cosmology, with appropriate observables. While string theory addresses some problems of quantum gravity, its ability to resolve these remains unclear. Answers may require new mechanisms and constructs, whether within string theory, or in another framework.
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  38. Robin Giles (1979). The Concept of a Proposition in Classical and Quantum Physics. Studia Logica 38 (4):337 - 353.
    A proposition is associated in classical mechanics with a subset of phase space, in quantum logic with a projection in Hilbert space, and in both cases with a 2-valued observable or test. A theoretical statement typically assigns a probability to such a pure test. However, since a pure test is an idealization not realizable experimentally, it is necessary — to give such a statement a practical meaning — to describe how it can be approximated by feasible tests. This gives rise (...)
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  39. Tepper L. Gill (1998). Canonical Proper-Time Dirac Theory. Foundations of Physics 28 (10):1561-1575.
    In this paper, we report on a new approach to relativistic quantum theory. The classical theory is derived from a new implementation of the first two postulates of Einstein, which fixes the proper-time of the physical system of interest for all observers. This approach leads to a new group that we call the proper-time group. We then construct a canonical contact transformation on extended phase space to identify the canonical Hamiltonian associated with the proper-time variable. On quantization we get a (...)
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  40. Daniel T. Gillespie (1995). Incompatibility of the Schrödinger Equation with Langevin and Fokker-Planck Equations. Foundations of Physics 25 (7):1041-1053.
    Quantum mechanics posits that the wave function of a one-particle system evolves with time according to the Schrödinger equation, and furthermore has a square modulus that serves as a probability density function for the position of the particle. It is natural to wonder if this stochastic characterization of the particle's position can be framed as a univariate continuous Markov process, sometimes also called a classical diffusion process, whose temporal evolution is governed by the classically transparent equations of Langevin and Fokker-Planck. (...)
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  41. Edward J. Gillis (2011). Causality, Measurement, and Elementary Interactions. Foundations of Physics 41 (12):1757-1785.
    Signal causality, the prohibition of superluminal information transmission, is the fundamental property shared by quantum measurement theory and relativity, and it is the key to understanding the connection between nonlocal measurement effects and elementary interactions. To prevent those effects from transmitting information between the generating and observing process, they must be induced by the kinds of entangling interactions that constitute measurements, as implied in the Projection Postulate. They must also be nondeterministic as reflected in the Born Probability Rule. The nondeterminism (...)
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  42. R. Gilmore, H. G. Solari & S. K. Kim (1993). Algebraic Description of the Quantum Defect. Foundations of Physics 23 (6):873-879.
    A simple model for the description of atomic and ionic species with spectra exhibiting a quantum defect is solved using the Lie algebra su(1, 1). The quantum defect of bound states is related to the phase shift of scattering states. The resonances are discussed in terms of the nonunitary representations of this algebra.
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  43. Allen Ginsberg (1984). On a Paradox in Quantum Mechanics. Synthese 61 (3):325 - 349.
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  44. Allen Ginsberg (1981). Quantum Theory and the Identity of Indiscernibles Revisited. Philosophy of Science 48 (3):487-491.
    In this paper I defend the claim that quantum theory, Specifically quantum field theory (qft), Is incompatible with leibniz's principle of the identity of indiscernibles. This is in response to r. Barnette's criticism ("philosophy of science" 45:466-470) of an argument given by alberto cortes ("philosophy of science" 43:491-505) intended to establish this claim. I show that, Using the qft point of view, Cortes' argument can be restated in a way that leaves it immune to barnette's criticism.
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  45. N. Gisin (1983). Dissipative Quantum Dynamics for Systems Periodic in Time. Foundations of Physics 13 (7):643-654.
    A model of dissipative quantum dynamics (with a nonlinear friction term) is applied to systems periodic in time. The model is compared with the standard approaches based on the Floquet theorem. It is shown that for weak frictions the asymptotic states of the dynamics we propose are the periodic steady states which are usually postulated to be the states relevant for the statistical mechanics of time-periodic systems. A solution to the problem of nonuniqueness of the “quasienergies” is proposed. The implication (...)
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  46. Nicolas Gisin (2012). Non-Realism: Deep Thought or a Soft Option? Foundations of Physics 42 (1):80-85.
    The claim that the observation of a violation of a Bell inequality leads to an alleged alternative between nonlocality and non-realism is annoying because of the vagueness of the second term.
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  47. Domenico Giulini (2008). Electron Spin or “Classically Non-Describable Two-Valuedness”. Studies in History and Philosophy of Science Part B 39 (3):557-578.
    In December 1924 Wolfgang Pauli proposed the idea of an inner degree of freedom of the electron, which he insisted should be thought of as genuinely quantum mechanical in nature. Shortly thereafter Ralph Kronig and, independently, Samuel Goudsmit and George Uhlenbeck took up a less radical stance by suggesting that this degree of freedom somehow corresponded to an inner rotational motion, though it was unclear from the very beginning how literal one was actually supposed to take this picture, since it (...)
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  48. Domenico Giulini, Concepts of Symmetry in the Work of Wolfgang Pauli.
    "Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which differ in meaning as well as their mathematical consequences. Symmetries of crystals, for example, generally express a different kind of invariance than gauge symmetries, though in specific situations the distinctions may become quite subtle. I will review some of the various (...)
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  49. Domenico Giulini, Superselection Rules.
    This note provides a summary of the meaning of the term `Superselection Rule' in Quantum Mechanics and Quantum-Field Theory. It is a contribution to the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, edited by Friedel Weinert, Klaus Hentschel, Daniel Greenberger, and Brigitte Falkenburg, to be published by Springer Verlag.
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  50. Roberto Giuntini (1996). Quantum MV Algebras. Studia Logica 56 (3):393 - 417.
    We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.
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