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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. Erik M. Alfsen & Frederic W. Shultz (2003). Geometry of State Spaces of Operator Algebras. Monograph Collection (Matt - Pseudo).
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  2. A. D. Alhaidari (2014). Renormalization of the Strongly Attractive Inverse Square Potential: Taming the Singularity. Foundations of Physics 44 (10):1049-1058.
    Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle’s state as it approaches the origin when the attractive coupling parameter is greater than the critical value of 1/4. Due to this unphysical divergence in oscillations, we are proposing that the interaction gets screened at short distances making the coupling parameter acquire an effective (renormalized) value that falls within the weak range 0–1/4. This prevents the oscillations (...)
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  3. Robert Alicki (2009). Quantum Decay Cannot Be Completely Reversed: The 5% Rule. In Institute of Physics Krzysztof Stefanski (ed.), Open Systems and Information Dynamics. World Scientific Publishing Company 16--01.
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  4. Valia Allori, Mauro Dorato, Federico Laudisa & Nino Zanghi (eds.) (2005). La Natura Delle Cose: Introduzione Ai Fondamenti E Alla Filosofia Della Fisica. Carocci.
    The year 2005 has been named the World Year of Physics in recognition of the 100th anniversary of Albert Einstein's "Miracle Year," in which he published four landmark papers which had deep and great influence on the last and the current century: quantum theory, general relativity, and statistical mechanics. Despite the enormous importance that Einstein’s discoveries played in these theories, most physicists adopt a version of quantum theory which is incompatible with the idea that motivated Einstein in the first place. (...)
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  5. J. Almog (1978). Perhaps , New logical foundations are needed for quantum mechanics. Logique Et Analyse 21 (82):251.
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  6. Ramón Alvarado (1995). Dialogic Interpretation of Social Worlds. Semiotics:51-59.
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  7. Ramón Alvarado (1995). Dialogic Interpretation of Social Worlds. Semiotics:51-59.
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  8. Ramón Alvarado (1995). Dialogic Interpretation of Social Worlds. Semiotics:51-59.
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  9. Vitorino de Sousa Alves (1961). L. de Broglie e a Interpretação das Leis Microfísicas. Revista Portuguesa de Filosofia 17 (1):62 - 76.
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  10. David Albert Alyssa Ney (ed.) (2013). The Wave Function: Essays in the Metaphysics of Quantum Mechanics.
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  11. Richard L. Amoroso (2012). PHYSICAL PARAMETERS OF MIND-BODY INTERACTION: BREAKING THE 1ST PERSON 3RD PERSON BARRIER. Journal of Nonlocality 1 (01).
    This physics note entails a summary of an extended form of Eccles-Cartesian Interactive Dualism mind-body-multiverse paradigm called Noetic Field Theory: The Quantization of Mind (NFT), distinguished as a paradigm because it is comprehensive and empirically testable. NFT posits not only that the brain is not the seat of awareness but also that neither classical nor quantum mechanics are sufficient to describe mind as the required regime entails the new physics associated with Unified Field, UF Mechanics. This means that the brain (...)
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  12. J. Anandan (1986). Gravitational Effects on Charged Quantum Systems. In Roger Penrose & C. J. Isham (eds.), Quantum Concepts in Space and Time. New York ;Oxford University Press 1--57.
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  13. Jeeva S. Anandan (1996). Reality and Geometry in Quantum Theory.
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  14. Jeeva S. Anandan (1980). Quantum Interference and the Gravitational Field. In A. R. Marlow (ed.), Quantum Theory and Gravitation. Academic Press 1--157.
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  15. Panagiotes S. Anastasiades (2002). The Theory of Information Reversal. Acm Sigcas Computers and Society 32 (2):10-16.
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  16. Leonard Angel (2002). Zeno's Arrow, Newton's Mechanics, and Bell's Inequalities. British Journal for the Philosophy of Science 53 (2):161-182.
    A model of a new version of Zeno's arrow paradox is presented in a plausible extension of Newtonian collision mechanics. In exploring various avenues for resolution of the paradox, it becomes evident that a prerelativistic classical physical topology which is locally deterministic can mechanically generate nonclassical ontological properties such as the appearance of a particle in many places at once. It can also mimic some properties of quantum physics, including unprepared spatially-separated correlations. 1 Zeno's arrow paradox 2 Newtonian collision mechanics (...)
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  17. Douglas Anger (1988). The Balance Equation: Part 2. Derivation of the Balance Equation for Response-Specific Inhibition. Bulletin of the Psychonomic Society 26 (1):55-58.
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  18. C. Antonopoulos (1998). Bohr's Reply to EPR: A Zenonian Version of Complementarity. Idealistic Studies 27 (3):165-192.
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  19. C. Antonopoulos (1997). A Schism in Quantum Physics or How Locality May Be Salvaged. Philosophia Naturalis 34 (1):33-69.
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  20. C. Antonopoulos (1996). Bohr on Nonlocality: The Facts and the Fiction. Philosophia Naturalis 33 (2):205-241.
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  21. Constantin Antonopoulos (1997). Bohr's Reply to EPR. Idealistic Studies 27 (3):165-192.
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  22. Constantin Antonopoulos (1997). Time as Non-Observational Knowledge: How to Straighten Out Δeδt≥H. International Studies in the Philosophy of Science 11 (2):165 – 183.
    The Energy-Time Uncertainty (ETU) has always been a problem-ridden relation, its problems stemming uniquely from the perplexing question of how to understand this mysterious Δ t . On the face of it (and, indeed, far deeper than that), we always know what time it is. Few theorists were ignorant of the fact that time in quantum mechanics is exogenously defined, in no ways intrinsically related to the system. Time in quantum theory is an independent parameter, which simply means independently known (...)
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  23. Arjun Appadurai (1995). The Production of Locality. In Richard Fardon (ed.), Counterworks: Managing the Diversity of Knowledge. Routledge 204--225.
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  24. Juan Sebastián Ardenghi (2009). Mecánica cuántica. Theoria 24 (1):5-28.
    RESUMEN: El propósito del presente trabajo consiste en analizar los vínculos entre la interpretación modal-hamiltoniana de la mecánica cuántica y las transformaciones de Galileo, a fin de poner de manifiesto que el grupo de tales transformaciones permite reformular la regla de actualización de un modo más básico desde un punto de vista teórico, aplicable a otras teorías cuánticas. Además se argumentará que, bajo esta nueva forma, la regla de actualización manifiesta explícitamente su invariancia frente al grupo de Galileo.ABSTRACT: The purpose (...)
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  25. Jonas Becker Arenhart & Décio Krause (2014). From Primitive Identity to the Non-Individuality of Quantum Objects. Studies in History and Philosophy of Science Part B 46 (2):273-282.
    We consider the claim by Dorato and Morganti 591–610) that primitive individuality should be attributed to the entities dealt with by non-relativistic quantum mechanics. There are two central ingredients in the proposal: in the case of non-relativistic quantum mechanics, individuality should be taken as a primitive notion and primitive individuality is naturalistically acceptable. We argue that, strictly understood, naturalism faces difficulties in helping to provide a theory with a unique principle of individuation. We also hold that even when taken in (...)
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  26. Camilo Argoty & Alexander Berenstein (2009). Hilbert Spaces Expanded with a Unitary Operator. Mathematical Logic Quarterly 55 (1):37-50.
    We study Hilbert spaces expanded with a unitary operator with a countable spectrum. We show that the theory of such a structure is ω -stable and admits quantifier elimination.
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  27. Angus Armitage (1950). “Borell's Hypothesis” and the Rise of Celestial Mechanics. Annals of Science 6 (3):268-282.
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  28. R. A. Aronov (1970). Toward a Logic of the Microworld. Russian Studies in Philosophy 9 (3):212-217.
    The discovery of the microworld presented a serious trial for many systems of views held by mankind, including its logic. This world was found to lack the familiar solid bodies, the unchanging particles and interrelations between them, the reflection of which, in one way or another, is the logic of the macroscopic world. What elementary particle physics encountered in the microscopic world seemed illogical: the rest-mass of a particle equals zero; a part that is not smaller than the whole; a (...)
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  29. J. L. Aronson (1973). Methodological Foundations of Relativistic Mechanics. Studi Internazionali Di Filosofia 5:282-283.
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  30. Abhay Ashtekar (1986). Self-Duality and Spinorial Techniques in the Canonical Approach to Quantum Gravity. In Roger Penrose & C. J. Isham (eds.), Quantum Concepts in Space and Time. New York ;Oxford University Press 1--302.
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  31. Richard N. Aslin & József Fiser (2005). Behavioral Paradigms and Their Measurement Outcomes. Trends in Cognitive Sciences 9 (3):92-98.
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  32. H. G. Äsop, Fabeln: Greichisch - Deutsch.
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  33. Andre Koch Torres Assis & J. Guala-Valverde (2000). Mass in Relational Mechanics. Apeiron 7:131-132.
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  34. Diana Athill (2003). Andre Deutsch The Great Persuader. Logos 14 (4):174-180.
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  35. Michael Atiyah (1991). Topology of the Vacuum. In Simon Saunders & Harvey R. Brown (eds.), The Philosophy of Vacuum. Oxford University Press
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  36. David Atkinson, Joint Probabilities Reproducing Three EPR Experiments On Two Qubits.
    An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states.
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  37. H. Atmanspacher, H. Romer & H. Wallach (2006). Weak Quantum Theory: Formal Framework and Selected Applications. Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond. Foundations of Physics 32:379-406.
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  38. Harald Atmanspacher & G. J. Dalenoort (1994). Inside Versus Outside Endo- and Exo-Concepts of Observation and Knowledge in Physics, Philosophy, and Cognitive Science.
  39. G. Auletta & V. Fano (2004). Recensioni/Reviews-Foundations and Interpretation of Quantum Mechanics. In the Light of a Critical-Historical Analysis of the Problems and of the Synthesis of the Results. Epistemologia 27 (1):157-160.
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  40. Gennaro Auletta (2006). The Ontology Suggested by Quantum Mechanics. In Paolo Valore (ed.), Topics on General and Formal Ontology. Polimetrica International Scientific Publisher 161.
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  41. V. L. Auslender, A. A. Bryazgin, V. G. Cheskidov, I. V. Gornakov, B. L. Faktorovich, E. N. Kokin, M. V. Korobeynikov, G. I. Kuznetsov, A. N. Lukin & I. G. Makarov (2005). Electron Accelerator for Energy Up to 5.0 MeV and Beam Power Up to 50 kW. In Alan F. Blackwell & David MacKay (eds.), Power. Cambridge University Press 15.
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  43. William Harvey Austin (1967). Complementarity and Paradox. Dissertation, Yale University
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  45. J. H. B. (1962). From Dualism to Unity in Quantum Physics. [REVIEW] Review of Metaphysics 15 (4):676-676.
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  46. L. K. B. (1957). The Language of Modern Physics. Review of Metaphysics 10 (4):720-721.
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  47. Yossi Bachar, Rafael I. Arshansky, Lawrence P. Horwitz & Igal Aharonovich (2014). Lorentz Invariant Berry Phase for a Perturbed Relativistic Four Dimensional Harmonic Oscillator. Foundations of Physics 44 (11):1156-1167.
    We show the existence of Lorentz invariant Berry phases generated, in the Stueckelberg–Horwitz–Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.
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  48. Manuel Bächtold (2008). Bohr (1885-1962): Bohr, Whitehead, and the Interpretation of Quantum Mechanics. In Weber (ed.), Handbook of Whiteheadian Process Thought. 353--361.
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  49. J. C. Baez (2006). Quantum Quandaries: A Category-Theoretic Perspective. In Dean Rickles, Steven French & Juha T. Saatsi (eds.), The Structural Foundations of Quantum Gravity. Clarendon Press
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  50. S. N. Bagchi & G. P. Das (1965). A Rigorous Analytic Solution of Nonlinear Differential Equation of the Poisson-Bolitzmann Type. In Karl W. Linsenmann (ed.), Proceedings. St. Louis, Lutheran Academy for Scholarship 29--28.
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