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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. Satoshi Iriyama & Masanori Ohya (2011). Quantum Mutual Entropy Defined by Liftings. Foundations of Physics 41 (3):406-413.
    A lifting is a map from the state of a system to that of a compound system, which was introduced in Accardi and Ohya (Appl. Math. Optim. 39:33–59, 1999). The lifting can be applied to various physical processes.In this paper, we defined a quantum mutual entropy by the lifting. The usual quantum mutual entropy satisfies the Shannon inequality (Ohya in IEEE Trans. Inf. Theory 29(5):770–774, 1983), but the mutual entropy defined through the lifting does not satisfy this inequality unless some (...)
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  4. C. J. Isham (2005). Quantising on a Category. Foundations of Physics 35 (2):271-297.
    We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose ‘configuration space’ (or history-theory analogue) is the set of objects Ob(Q) in a category Q. We develop a scheme based on constructing (...)
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  5. Jamal Nazrul Islam (1994). The Schrödinger Equation in Quantum Field Theory. Foundations of Physics 24 (5):593-630.
    Some aspects of the Schrödinger equation in quantum field theory are considered in this article. The emphasis is on the Schrödinger functional equation for Yang-Mills theory, arising mainly out of Feynman's work on (2+1)-dimensional Yang-Mills theory, which he studied with a view to explaining the confinement of gluons. The author extended Feynman's work in two earlier papers, and the present article is partly a review of Feynman's and the author's work and some further extension of the latter. The primary motivation (...)
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  6. T. J. (2001). Testing Quantum Mechanics on New Ground. Studies in History and Philosophy of Science Part B 32 (1):131-134.
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  7. J. M. Jauch (1974). The Quantum Probability Calculus. Synthese 29 (1-4):131 - 154.
  8. Wei Min Jin (2000). From Time Inversion to Nonlinear QED. Foundations of Physics 30 (11):1943-1973.
    In Minkowski flat space-time, it is perceived that time inversion is unitary rather than antiunitary, with energy being a time vector changing sign under time inversion. The Dirac equation, in the case of electromagnetic interaction, is not invariant under unitary time inversion, giving rise to a “Klein paradox.” To render unitary time inversion invariance, a nonlinear wave equation is constructed, in which the “Klein paradox” disappears. In the case of Coulomb interaction, the revised nonlinear equation can be linearized to give (...)
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  9. Philip R. Johnson & B. L. Hu (2005). Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect. [REVIEW] Foundations of Physics 35 (7):1117-1147.
    We present a stochastic theory for the nonequilibriurn dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We summarize (1) the steps leading to a derivation of a modified Abraham-Lorentz-Dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre-acceleration patholigies, and (2) the transformation to a stochastic effective action, which generates Abraham-Lorentz-Dirac-Langevin equations depicting the fluctuations of a particle’s (...)
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  10. Brian D. Josephson (1988). Limits to the Universality of Quantum Mechanics. Foundations of Physics 18 (12):1195-1204.
    Niels Bohr's arguments indicating the non-applicability of quantum methodology to the study of the ultimate details of life, given in his bookAtomic Physics and Human Knowledge, conflict with the commonly held opposite view. The bases for the usual beliefs are examined and shown to have little validity; significant differences do exist between the living organism and the type of system studied successfully in the physics laboratory. Dealing with living organisms in quantum-mechanical terms with the same degree of rigor as is (...)
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  11. Richard Jozsa & Noah Linden (2003). On the Role of Entanglement in Quantum-Computational Speed-Up. Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 459:2011--2032.
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  12. K. Just & L. S. The (1986). Canonical Quantization Without Conjugate Momenta. Foundations of Physics 16 (11):1127-1141.
    In the traditional form of canonical quantization, certain field components (not having “conjugate” momenta) must be regarded as noncanonical. This long-known distinction enters modern gauge theories, when they are canonically quantized as by Kugo and Ojima. We avoid that peculiarity by not using any conjugate “momenta” at all. In our formulation, canonical quantization can be related to Feynman's path integral.
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  13. Leonid A. Khalfin (1997). Unconditional Tests of Fundamental Discrete Symmetries CP, T, CPT in Rigorous Quantum Dynamics Beyond the Approximate Lee-Oehme-Yang Theory. Foundations of Physics 27 (11):1549-1570.
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  14. H. Kleinert (2014). Quantum Field Theory of Black-Swan Events. Foundations of Physics 44 (5):546-556.
    Free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. They describe Gaussian random walks with collisions. By contrast, the fields of strongly interacting particles are governed by effective actions, whose extremum yields fractional field equations. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, earthquakes, (...)
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  15. D. Kolak & J. Symons (eds.) (2004). Quantifiers, Questions and Quantum Physics. Springer.
    This book includes a comprehensive overview of Hintikka's philosophy by Dan Kolak and John Symons and an annotated bibliography of Hintikka's work.
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  16. Fred Kronz (2008). Non-Monotonic Probability Theory for N-State Quantum Systems. Studies in History and Philosophy of Science Part B 39 (2):259-272.
    In previous work, a non-standard theory of probability was formulated and used to systematize interference effects involving the simplest type of quantum systems. The main result here is a self-contained, non-trivial generalization of that theory to capture interference effects involving a much broader range of quantum systems. The discussion also focuses on interpretive matters having to do with the actual/virtual distinction, non-locality, and conditional probabilities.
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  17. Alexey Kryukov, Geometric Derivation of Quantum Uncertainty.
    Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation follows from the following stronger statement: Of all parallelograms with given sides the rectangle has the largest area.
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  18. Alexey Kryukov (2004). On the Problem of Emergence of Classical Space—Time: The Quantum-Mechanical Approach. Foundations of Physics 34 (8):1225-1248.
    The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization (...)
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  19. Alexey Kryukov (2003). Coordinate Formalism on Abstract Hilbert Space: Kinematics of a Quantum Measurement. [REVIEW] Foundations of Physics 33 (3):407-443.
    Coordinate form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. The unitary evolution and the non-unitary collapse processes are interpreted as isometric functional transformations. Several experiments are analyzed in the new context.
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  20. Alexey Kryukov, Coordinate Formalism on Hilbert Manifolds: String Bases of Eigenvectors.
    Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square integrable functions (...)
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  21. Alexey A. Kryukov (2006). Quantum Mechanics on Hilbert Manifolds: The Principle of Functional Relativity. [REVIEW] Foundations of Physics 36 (2):175-226.
    Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces of functions. The principle of functional relativity is introduced which states that quantum theory (QT) is indeed a functional tensor theory, i.e., it can be described by functional tensor (...)
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  22. C. N. Ktorides & L. C. Papaloucas (1987). A Special Construction of Berezin'sL-Kernel. Foundations of Physics 17 (2):201-207.
    We consider Berezin's algebraic considerations regarding the quantization of phase space polynomials. After making a connection with Prugovečki's stochastic quantization approach, we give a particular construction of Berezin's L-Kernel in terms of Prugovečki's ξ-functions.
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  23. Shoju Kudaka (1999). Modified Busch-Type Measurements and the Universal Conservation Laws. Foundations of Physics 29 (9):1371-1388.
    P. Busch has formulated a particular measurement process in order to show that predictable position measurements are impossible in general. Here we apply his formulation to studying the characteristics of various quantum measurements under the limitations which are imposed by the universal conservation laws and prove some theorems related to Busch's theorem. A simple approximate model measuring momentum is analyzed to investigate the roles of energy and momentum conservation. The results reveal the importance of the role of Galilei's principle of (...)
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  24. Wilfried Kuhn (1988). Analysis of the Development of Wave Mechanics: Aspects From the History of Physics and the Philosophy of Science. [REVIEW] Foundations of Physics 18 (3):379-399.
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  25. Manjit Kumar (2009). Quantum: Einstein, Bohr, and the Great Debate About the Nature of Reality. Hachette India.
    The reluctant revolutionary -- The patent slave -- The golden Dane -- The quantum atom -- When Einstein met Bohr -- The prince of duality -- Spin doctors -- The quantum magician -- A late erotic outburst -- Uncertainty in Copenhagen -- Solvay 1927 -- Einstein forgets relativity -- Quantum reality -- For whom Bell's theorem tolls -- The quantum demon.
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  26. Hans Kummer (1991). The Foundation of Quantum Theory and Noncommutative Spectral Theory. Part I. Foundations of Physics 21 (9):1021-1069.
    The present paper is the first part of a work which follows up on H. Kummer: “A constructive approach to the foundations of quantum mechanics,”Found. Phys. 17, 1–63 (1987). In that paper we deduced the JB-algebra structure of the space of observables (=detector space) of quantum mechanics within an axiomatic theory which uses the concept of a filter as primitive under the restrictive assumption that the detector space is finite-dimensional. This additional hypothesis will be dropped in the present paper.It turns (...)
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  27. Hans Kummer (1991). The Foundation of Quantum Theory and Noncommutative Spectral Theory: Part II. [REVIEW] Foundations of Physics 21 (10):1183-1236.
    The present paper comprises Sects. 5–8 of a work which proposes an axiomatic approach to quantum mechanics in which the concept of a filter is the central primitive concept. Having layed down the foundations in the first part of this work (which appeared in the last issue of this journal and comprises Sects. 0–4), we arrived at a dual pair 〈Y, M〉 consisting of abase norm space Y and anorder unit space M, being in order and norm duality with respect (...)
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  28. Hans Kummer (1987). A Constructive Approach to the Foundations of Quantum Mechanics. Foundations of Physics 17 (1):1-62.
    An axiomatic theory is formulated which describes a class of “yes-no” experiments, involving a fixed basic source, a fixed basic detector, and various filters. It is assumed that all filters considered can be constructed from a setP of primitive filters by composition and stochastic selection. Two physically plausible axioms are formulated which allow us to define the concept of asystem in the present context (cf. Definition2.4). To each system we can attach anorder unit module ( $^\circ \hat V, ^\circ \hat (...)
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  29. M. A. Kurkov & V. A. Franke (2011). Local Fields Without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation. Foundations of Physics 41 (5):820-842.
    Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. One may assume the existence of such fields only if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT-invariance. Restrictions on mass-spectrum of CPT-violating fields are (...)
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  30. Fred Kuttner (2008). Response to Nauenberg's “Critique of Quantum Enigma: Physics Encounters Consciousness”. [REVIEW] Foundations of Physics 38 (2):188-190.
    Nauenberg’s extended critique of Quantum Enigma rests on fundamental misunderstandings.
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  31. A. Kyrala (1974). Selection Rules, Causality, and Unitarity in Statistical and Quantum Physics. Foundations of Physics 4 (1):31-51.
    The integrodifferential equations satisfied by the statistical frequency functions for physical systems undergoing stochastic transitions are derived by application of a causality principle and selection rules to the Markov chain equations. The result equations can be viewed as generalizations of the diffusion equation, but, unlike the latter, they have a direct bearing onactive transport problems in biophysics andcondensation aggregation problems of astrophysics and phase transition theory. Simple specific examples of the effects of severe selection rules, such as the relaxational Boltzmann (...)
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  32. Jan Lacki (2004). The Puzzle of Canonical Transformations in Early Quantum Mechanics. Studies in History and Philosophy of Science Part B 35 (3):317-344.
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  33. James Ladyman & Tomasz Bigaj (2010). The Principle of the Identity of Indiscernibles and Quantum Mechanics. Philosophy of Science 77 (1):117-136.
    It is argued that recent discussion of the principle of the identity of indiscernibles (PII) and quantum mechanics has lost sight of the broader philosophical motivation and significance of PII and that the `received view' of the status of PII in the light of quantum mechanics survives recent criticisms of it by Muller, Saunders, and Seevinck.
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  34. Pekka Lahti & Juha-Pekka Pellonpää (2010). On the Complementarity of the Quadrature Observables. Foundations of Physics 40 (9-10):1419-1428.
    In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon transform of a phase space distribution of the covariant phase space (...)
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  35. V. Lakshminarayanan (2005). Book Review:Quantum Mechanics: Theory and Applications. By Ajoy K. Ghatak and S. Lokanathan, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004, Xlviii+858 Pp., $303.00/ $99.00 (Hardcover/Softcover). ISBN 1-4020-1850-9. [REVIEW] Foundations of Physics 35 (6):1107-1109.
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  36. F. Laloë & W. J. Mullin (2012). Quantum Properties of a Single Beam Splitter. Foundations of Physics 42 (1):53-67.
    When a single beam-splitter receives two beams of bosons described by Fock states (Bose-Einstein condensates at very low temperatures), interesting generalizations of the two-photon Hong-Ou-Mandel effect take place for larger number of particles. The distributions of particles at two detectors behind the beam splitter can be understood as resulting from the combination of two effects, the spontaneous phase appearing during quantum measurement, and the quantum angle. The latter introduces quantum “population oscillations”, which can be seen as a generalized Hong-Ou-Mandel effect, (...)
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  37. M. C. Land (1998). Part 1. Proceedings First International Conference on Parametrized Relativistic Quantum Theory-the Classical Coulomb Problem in Pre-Maxwell Electrodynamics. Foundations of Physics 28 (9):1489-1498.
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  38. M. C. Land, R. I. Arshansky & L. P. Horwitz (1994). Selection Rules for Dipole Radiation From a Relativistic Bound State. Foundations of Physics 24 (4):563-578.
    Recently, in the framework of a relativistic quantum theory with invariant evolution parameter, solutions have been found for the two-body bound state, whose mass spectrum agrees with the nonrelativistic Schrödinger energy spectrum. In this paper, we study the radiative transitions of these states in the dipole approximation and find that the selection rules are identical with those of the usual nonrelativistic theory, expressed in a manifestly covariant form. In addition to the transverse and longitudinal polarizations of the nonrelativistic theory, we (...)
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  39. Alfred Landé (1986). The Laws Behind the Quantum Laws. British Journal for the Philosophy of Science 37 (1):43-50.
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  40. Alfred Landé (1976). The Laws Behind the Quantum Laws. British Journal for the Philosophy of Science 27 (1):43-50.
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  41. Alfred Lande (1971). The Decline and Fall of Quantum Dualism. Philosophy of Science 38 (2):221 - 223.
    The Bohr-Heisenberg doctrine of wave-particle duality has been attacked in the past for its methodical defects, over-complication, internal contradictions, its positivistic phenomenalism, etc. The present investigation shows that duality, the doctrine of equivalence of the particle picture and the wave picture of matter, is untenable since its wave part leads to empirically wrong results in the relativistic domain, and violates the postulate of independence of the arbitrary choice of reference system in the non-relativistic realm. Therefore, when methodical objections were never (...)
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  42. Alfred Landé (1971). The Decline and Fall of Quantum Dualism. Philosophy of Science 38 (2):221-223.
    The Bohr-Heisenberg doctrine of wave-particle duality has been attacked in the past for its methodical defects, over-complication, internal contradictions, its positivistic phenomenalism, etc. The present investigation shows that duality, the doctrine of equivalence of the particle picture and the wave picture of matter, is untenable since its wave part leads to empirically wrong results in the relativistic domain, and violates the postulate of independence of the arbitrary choice of reference system in the non-relativistic realm. Therefore, when methodical objections were never (...)
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  43. Alfred Landé (1965). Why Do Quantum Theorists Ignore the Quantum Theory? British Journal for the Philosophy of Science 15 (60):307-313.
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  44. Alfred Lande (1962). The Case Against Quantum Duality. Philosophy of Science 29 (1):1 - 6.
    (1) The idea that diffraction of matter particles can only be understood in terms of a temporary wave transformation or 'double manifestation' is an uneconomical ad hoc hypothesis, shattered already in 1923 by the unitary quantum theory of diffraction of Duane which in 1926 became part of the quantum mechanics, with a statistical interpretation of wave-like appearances. (2) Bohr's re-interpretation of Heisenberg's uncertainty of prediction as an indeterminacy of existence rests on an illegitimate literal translation of a wave result into (...)
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  45. Alfred Landé (1962). The Case Against Quantum Duality. Philosophy of Science 29 (1):1-6.
    (1) The idea that diffraction of matter particles can only be understood in terms of a temporary wave transformation or 'double manifestation' is an uneconomical ad hoc hypothesis, shattered already in 1923 by the unitary quantum theory of diffraction of Duane which in 1926 became part of the quantum mechanics, with a statistical interpretation of wave-like appearances. (2) Bohr's re-interpretation of Heisenberg's uncertainty of prediction as an indeterminacy of existence rests on an illegitimate literal translation of a wave result into (...)
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  46. Alfred Landé (1959). From Dualism to Unity in Quantum Mechanics. British Journal for the Philosophy of Science 10 (37):16-24.
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  47. Alfred Lande (1957). Non-Quantal Foundations of Quantum Theory. Philosophy of Science 24 (4):309 - 320.
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  48. Alfred Landé (1957). Non-Quantal Foundations of Quantum Theory. Philosophy of Science 24 (4):309-320.
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  49. Alfred Lande (1953). Continuity, A Key to Quantum Mechanics. Philosophy of Science 20 (2):101 - 109.
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  50. Alfred Landé (1953). Continuity, a Key to Quantum Mechanics. Philosophy of Science 20 (2):101-109.
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