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Quantum Mechanics

Edited by Michael Cuffaro (Ludwig Maximilians Universität, München)
Assistant editors: Brian Padden, Radin Dardashti
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. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. Allen Ginsberg (1984). On a Paradox in Quantum Mechanics. Synthese 61 (3):325 - 349.
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  15. 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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  16. 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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  17. 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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  18. 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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  19. 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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  20. 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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  21. 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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  22. Roberto Giuntini, Antonio Ledda & Francesco Paoli (2007). Expanding Quasi-MV Algebras by a Quantum Operator. Studia Logica 87 (1):99 - 128.
    We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.
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  23. Gordon G. Globus (2003). Quantum Closures and Disclosures: Thinking-Together Postphenomenology and Quantum Brain Dynamics. John Benjamins.
    CHAPTER Heidegger and the Quantum Brain In any case the orientation to "I" and " consciousness" and re-presentation ...
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  24. Gordon G. Globus (2002). Ontological Implications of Quantum Brain Dynamics. In Kunio Yasue, Marj Jibu & Tarcisio Della Senta (eds.), No Matter, Never Mind. John Benjamins. 33--137.
  25. Gordon G. Globus (1998). Self, Cognition, Qualia, and World in Quantum Brain Dynamics. Journal of Consciousness Studies 5 (1):34-52.
  26. Gordon G. Globus (1996). Quantum Consciousness is Cybernetic. Psyche 2 (21).
  27. Bruce Glymour, Marcelo Sabatés & Andrew Wayne (2001). Quantum Java: The Upwards Percolation of Quantum Indeterminacy. Philosophical Studies 103 (3):271 - 283.
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  28. Clark Glymour, 5. Markov Properties and Quantum Experiments.
    Few people have thought so hard about the nature of the quantum theory as has Jeff Bub,· and so it seems appropriate to offer in his honor some reflections on that theory. My topic is an old one, the consistency of our microscopic theories with our macroscopic theories, my example, the Aspect experiments (Aspect et al., 1981, 1982, 1982a; Clauser and Shimony, l978;_Duncan and Kleinpoppen, 199,8) is familiar, and my sirnplrcation of it is borrowed. All that is new here is (...)
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  29. Clark Glymour (1971). Determinism, Ignorance, and Quantum Mechanics. Journal of Philosophy 68 (21):744-751.
    is every bit as intelligible and philosophically respectable as many other doctrines currently in favor, e.g., the doctrine that mental events are identical with brain events; the attempt to give a linguistic construal of this latter doctrine meets many of the same sorts of difficulties encountered above (see Hempel, op. cit.). Secondly, I think that evidence for universal determinism may not, as a matter of fact, be so hard to come by as one might imagine. It is a striking fact (...)
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  30. G. H. Goedecke (1984). Stochastic Electrodynamics. IV. Transitions in the Perturbed Harmonic Oscillator-Zero-Point Field System. Foundations of Physics 14 (1):41-63.
    In this fourth paper in a series on stochastic electrodynamics (SED), the harmonic oscillator-zero-point field system in the presence of an arbitrary applied classical radiation field is studied further. The exact closed-form expressions are found for the time-dependent probability that the oscillator is in the nth eigenstate of the unperturbed SED Hamiltonian H 0 , the same H 0 as that of ordinary quantum mechanics. It is shown that an eigenvalue of H 0 is the average energy that the oscillator (...)
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  31. G. H. Goedecke (1983). Stochastic Electrodynamics. I. On the Stochastic Zero-Point Field. Foundations of Physics 13 (11):1101-1119.
    This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive (...)
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  32. Joshua N. Goldberg (1994). Self-Dual Maxwell Field on a Null Surface. II. Foundations of Physics 24 (4):467-476.
    The canonical formalism for the Maxwell field on a null surface has been revisited. A new pair of gauge-independent canonical variables is introduced. It is shown that these variables are derivable from a Hamillon-Jacobi functional. The construction of the appropriate C * algebra is carried out in preparation for quantization. The resulting quantum theory is similar to a previous result. It is then shown that one can construct the T-variables of Rovelli and Smolin on the null surface. The Poisson bracket (...)
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  33. Stanford Goldman (1971). The Mechanics of Individuality in Nature. Foundations of Physics 1 (4):395-408.
    Evidence is presented to support the hypothesis that there is a set of basically similar phenomena or characteristics of physics, biology, and sociology. Six of these are identified. Five of them are usually associated with quantum mechanics. They are the existence of eigenstates, transform domains, bosons and fermions, particles and antiparticles, and complementarity. The sixth, namely alternation of generation, is usually associated with biology. The hypothesis leads to some new points of view and interpretations in biology, sociology, and physics.
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  34. Sheldon Goldstein, On a Realistic Theory for Quantum Physics.
    future evolution of the field. These ideas thou h old 'th k oug o, are ei er un nown oz misunderstood, Our point here is that a stron realistic os". g ' ' posi'.ion has consequences: it offers a completely natural..
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  35. Sheldon Goldstein, Are All Particles Identical?
    We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same particle, just as spin-up and spin-down do. The implications of this viewpoint can be best appreciated within Bohmian mechanics, a precise formulation of quantum mechanics with particle trajectories. The implementation of this viewpoint in such a theory leads to trajectories different from those of the (...)
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  36. Sheldon Goldstein, Absence of Chaos in Bohmian Dynamics.
    In a recent paper [1], O. F. de Alcantara Bonfim, J. Florencio, and F. C. S´ a Barreto claim to have found numerical evidence of chaos in the motion of a Bohmian quantum particle in a double square-well potential, for a wave function that is a superposition of five energy eigenstates. But according to the result proven here, chaos for this motion is impossible. We prove in fact that for a particle on the line in a superposition of n + (...)
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  37. Sheldon Goldstein, Bell-Type Quantum Field Theories.
    In [3] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Ψ|2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of (...)
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  38. Sheldon Goldstein, Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory.
    Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...)
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  39. Sheldon Goldstein, Quantum Hamiltonians and Stochastic Jumps.
    With many Hamiltonians one can naturally associate a |Ψ|2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it is typically a jump process on the configuration space of a variable number of particles. We define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [3] and of ourselves [11]. We introduce a formula expressing the jump rates (...)
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  40. Sheldon Goldstein (1996). Review Essay: Bohmian Mechanics and the Quantum Revolution. [REVIEW] Synthese 107 (1):145 - 165.
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  41. Sheldon Goldstein, D. Dürr, J. Taylor, R. Tumulka & and N. Zanghì, Quantum Mechanics in Multiply-Connected Spaces.
    J. Phys. A, to appear, quant-ph/0506173.
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  42. Sheldon Goldstein, D. Dürr & N. Zanghì, Bohmian Mechanics and Quantum Equilibrium.
    in Stochastic Processes, Physics and Geometry II, edited by S. Albeverio, U. Cattaneo, D. Merlini (World Scientific, Singapore, 1995) pp. 221-232.
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  43. Sheldon Goldstein & W. Struyve, On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics.
    In Bohmian mechanics the distribution |ψ|2 is regarded as the equilibrium distribution. We consider its uniqueness, finding that it is the unique equivariant distribution that is also a local functional of the wave function ψ.
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  44. Sheldon Goldstein & Roderich Tumulka, Arxiv:1003.2129v1 [Quant-Ph] 10 Mar 2010.
    The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...)
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  45. Sheldon Goldstein & Roderich Tumulka, Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John Von Neumann's 1929 Article on the Quantum Ergodic Theorem.
    The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...)
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  46. Sheldon Goldstein & Roderich Tumulka, Normal Typicality and Von Neumann's Quantum Ergodic Theorem.
    We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. The QET (...)
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  47. Sheldon Goldstein & Roderich Tumulka, On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems.
    We consider an isolated, macroscopic quantum system. Let H be a microcanonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + δE. The thermal equilibrium macro-state at energy E corresponds to a subspace Heq of H such that dim Heq/ dim H is close to 1. We say that a system with state vector ψ H is in thermal equilibrium if ψ is “close” to Heq. (...)
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  48. Ravi Gomatam, Against “Position”.
    Although quantum theory is presented as a radically non classical theory in physics, it is an open secret that our present understanding of it is based on a conceptual base borrowed from classical physics, leading to the situation that all of the radical implications of quantum theory are expressed using terminology that, in other circumstances would be considered blatantly self contradictory. To give but a few examples: wave particle duality (one and the same ontological entity can be ascribed two mutually (...)
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  49. Ravi Gomatam, Quantum Realism and Haecceity.
    Non-relativistic quantum mechanics is incompatible with our everyday or ‘classical’ intuitions about realism, not only at the microscopic level but also at the macroscopic level. The latter point is highlighted by the ‘cat paradox’ presented by Schrödinger. Since our observations are always made at the macroscopic level — even when applying the formalism to the microscopic level — the failure of classical realism at the macroscopic level is actually more fundamental and crucial.
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  50. Ravi Gomatam, Book Review. [REVIEW]
    In this book, Mara Beller, a historian and philosopher of science, undertakes to examine why and how the elusive Copenhagen interpretation came to acquire the status it has. The book appears under the series ‘Science and Its Conceptual Foundations’. The first part traces in seven chapters the early major developmental phases of QT such as matrix theory, Born’s probabilistic interpretation, Heisenberg’s uncertainty principle and Bohr’s complementarity framework. Although the historical and scientific details are authentic, the author’s presentation in this part (...)
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