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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 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. 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. Margarita A. Man’ko & Vladimir I. Man’ko (2011). Probability Description and Entropy of Classical and Quantum Systems. Foundations of Physics 41 (3):330-344.
    Tomographic approach to describing both the states in classical statistical mechanics and the states in quantum mechanics using the fair probability distributions is reviewed. The entropy associated with the probability distribution (tomographic entropy) for classical and quantum systems is studied. The experimental possibility to check the inequalities like the position–momentum uncertainty relations and entropic uncertainty relations are considered.
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  4. P. Marcer & E. Mitchell (2001). What is Consciousness? An Essay on the Relativistic Quantum Holographic Model of the Brain/Mind, Working by Phase Conjugate Adaptive Resonance. In P. Loockvane (ed.), The Physical Nature of Consciousness. John Benjamins.
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  5. Jean-Paul Marchand (1997). A Minimal Phenomenology for Decay and Resonance. Foundations of Physics 27 (2):215-226.
    We discuss in what sense the decay-scattering system is a minimal phenomenological theory for particle decay and resonance scattering.
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  6. Jean-Paul Marchand (1977). Relative Coarse-Graining. Foundations of Physics 7 (1-2):35-49.
    The problem of statistical inference based on a partial measurement (“coarse-graining”) requires the specification of an a priori distribution. We reformulate the ordinary theory such as to encompass systematically a wide range of a priori distributions (“relative coarse-graining”). This is done in a mathematical setting which admits an interpretation in both classical probability and quantum mechanics. The formalism is illustrated in a few simple examples, such as the die whose geometrical shape is known, the spin in thermal equilibrium with an (...)
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  7. Henry Margenau (1967). Quantum Mechanics, Free Will, and Determinism. Journal of Philosophy 64 (21):714-725.
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  8. Henry Margenau (1963). Measurements and Quantum States: Part I. Philosophy of Science 30 (1):1-16.
    Although there is a complete consensus among working physicists with respect to the practical and operational meanings of quantum states, and also a rather loosely formulated general philosophic view called the Copenhagen interpretation, a great deal of confusion and divergence of opinions exist as to the details of the measurement process and its effects upon quantum states. This paper reviews the current expositions of the measurement problem, limiting itself for lack of space primarily to the writings of physicists; it calls (...)
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  9. Henry Margenau (1963). Measurements and Quantum States: Part II. Philosophy of Science 30 (2):138-157.
    This is the second, mathematically more detailed part of a paper consisting of two articles, the first having appeared in the immediately preceding issue of this Journal. It shows that a measurement converts a pure case into a mixture with reducible probabilities. The measurement as such permits no inference whatever as to the state of the physical system subjected to measurement after the measurement has been performed. But because the probabilities after the act are classical and therefore reducible, it is (...)
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  10. Henry Margenau (1949). Reality in Quantum Mechanics. Philosophy of Science 16 (4):287-302.
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  11. Henry Margenau (1932). Probability and Causality in Quantum Physics. The Monist 42 (2):161-188.
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  12. Henry Margenau & John Compton (1949). Report on Recent Developments in the Philosophy of Quantum Mechanics. Synthese 8 (1):260 - 271.
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  13. Henry Margenau & James L. Park (1973). The Physics and the Semantics of Quantum Measurement. Foundations of Physics 3 (1):19-28.
    In a recent paper, Prugovečki offered a theory of simultaneous measurements based upon an axiomatic description of the measurement act which excludes certain illustrations of simultaneous measurement previously discussed by the present writers. In this article, the fundamental conceptions of state preparation, state determination, and measurement which underlie our research are compared to Prugovečki's interpretations of the analogous constructs in his theory of measurement.
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  14. M. S. Marinov & Bilha Segev (1997). Causality and Time Dependence in Quantum Tunneling. Foundations of Physics 27 (1):113-132.
    Quantal penetration through a (stationary) one-dimensional potential barrier is considered as a time evolution of an initially prepared wave packet. The large-time asymptotics of the process is concerned. Locality of the potential imposes certain analytical properties of the interaction amplitudes in the energy representation. The results are presented in terms of development of the phase-space (Wigner's) quasi-distribution. The phase-space evolution kernel is constructed, and it is shown that in the presence of a positive potential no part of the distribution is (...)
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  15. Ned Markosian (1995). On the Argument From Quantum Cosmology Against Theism. Analysis 55 (4):247 - 251.
    In a recent Analysis article, Quentin Smith argues that classical theism is inconsistent with certain consequences of Stephen Hawking's quantum cosmology.1 Although I am not a theist, it seems to me that Smith's argument fails to establish its conclusion. The purpose of this paper is to show what is wrong with Smith's argument. According to Smith, Hawking's cosmological theory includes what Smith calls "Hawking's wave function law." Hawking's wave function law (hereafter, "HL") apparently has, among its consequences, the following claim. (...)
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  16. A. R. Marlow (ed.) (1980). Quantum Theory and Gravitation. Academic Press.
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  17. A. R. Marlow (ed.) (1978). Mathematical Foundations of Quantum Theory. Academic Press.
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  18. O. J. E. Maroney (2005). The Density Matrix in the de Broglie--Bohm Approach. Foundations of Physics 35 (3):493-510.
    If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie--Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which Bell [Int. (...)
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  19. I. N. Marshall (1995). Some Phenomenological Implications of a Quantum Model of Consciousness. Minds and Machines 5 (4):609-20.
    We contrast person-centered categories with objective categories related to physics: consciousness vs. mechanism, observer vs. observed, agency vs. event causation. semantics vs. syntax, beliefs and desires vs. dispositions. How are these two sets of categories related? This talk will discuss just one such dichotomy: consciousness vs. mechanism. Two extreme views are dualism and reductionism. An intermediate view is emergence. Here, consciousness is part of the natural order (as against dualism), but consciousness is not definable only in terms of physical mass, (...)
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  20. Trevor Marshall & Emilio Santos (1988). Stochastic Optics: A Reaffirmation of the Wave Nature of Light. [REVIEW] Foundations of Physics 18 (2):185-223.
    Quantum optics does not give a local explanation of the coincidence counts in spatially separated photodetectors. This is the case for a wide variety of phenomena, including the anticorrelated counting rates in the two channels of a beam splitter, the coincident counting rates of the two “photons” in an atomic cascade, and the “antibunching” observed in resonance fluorescence.We propose a local realist theory that explains all of these data in a consistent manner. The theory uses a completely classical description of (...)
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  21. Iain Martel, The Principle of the Common Cause, the Causal Markov Condition, and Quantum Mechanics: Comments on Cartwright.
    Nancy Cartwright believes that we live in a Dappled World– a world in which theories, principles, and methods applicable in one domain may be inapplicable in others; in which there are no universal principles. One of the targets of Cartwright’s arguments for this conclusion is the Causal Markov condition, a condition which has been proposed as a universal condition on causal structures.1 The Causal Markov condition, Cartwright argues, is applicable only in a limited domain of special cases, and thus cannot (...)
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  22. Hans Martens & Willem M. De Muynck (1990). Nonideal Quantum Measurements. Foundations of Physics 20 (3):255-281.
    A partial ordering in the class of observables (∼ positive operator-valued measures, introduced by Davies and by Ludwig) is explored. The ordering is interpreted as a form of nonideality, and it allows one to compare ideal and nonideal versions of the same observable. Optimality is defined as maximality in the sense of the ordering. The framework gives a generalization of the usual (implicit) definition of self-adjoint operators as optimal observables (von Neumann), but it can, in contrast to this latter definition, (...)
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  23. Hans Martens & Willem M. De Muynck (1990). The Inaccuracy Principle. Foundations of Physics 20 (4):357-380.
    The problem of joint measurement of incompatible observables is investigated. Measurements are represented by positive operator-valued measures. A quantitative notion of inaccuracy is defined. It is shown that within this framework joint inaccurate measurements are possible for arbitrary maximal projection-valued measures on finite-dimensional spaces. The accuracy of such measurements is limited, as is shown by an inaccuracy inequality we derive. This new type of uncertainty relation can be unambiguously interpreted as referring to measurement precision rather than preparative quality. Several recent (...)
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  24. Sergio Martinez (1990). A Search for the Physical Content of Luders' Rule. Synthese 82 (1):97 - 125.
    An interpretation of quantum mechanics that rejects hidden variables has to say something about the way measurement can be understood as a transformation on states of individual systems, and that leads to the core of the interpretive problems posed by Luders' projection rule: What, if any, is its physical content? In this paper I explore one suggestion which is implicit in usual interpretations of the rule and show that this view does not stand on solid ground. In the process, important (...)
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  25. Bahram Mashhoon (1986). General Covariance and Quantum Theory. Foundations of Physics 16 (7):619-635.
    The extension of the principle of relativity to general coordinate systems is based on the hypothesis that an accelerated observer is locally equivalent to a hypothetical inertial observer with the same velocity as the noninertial observer. This hypothesis of locality is expected to be valid for classical particle phenomena as well as for classical wave phenomena but only in the short-wavelength approximation. The generally covariant theory is therefore expected to be in conflict with the quantum theory which is based on (...)
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  26. V. S. Mashkevich (1985). Quantum Statistical Dynamics: Statistics Origin, Measurement, and Irreversibility. [REVIEW] Foundations of Physics 15 (1):1-33.
    It is shown that in the quantum theory of systems with a finite number of degrees of freedom which employs a set of algebraic states, a statistical element introduced by averaging the mean values of operators over the distribution of continuous quantities (a spectrum point of a canonical operator and time) is conserved for the limiting transition to the δ distribution. On that basis, quantum statistical dynamics, i.e., a theory in which dynamics (time evolution) includes a statistical element, is advanced. (...)
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  27. Sergei G. Matinyan & Berndt Müller (1997). Quantum Fluctuations and Dynamical Chaos: An Effective Potential Approach. [REVIEW] Foundations of Physics 27 (9):1237-1255.
    We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos, and we speculate that monopole condensation can have the same effect in non-Abelian gauge theories.
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  28. L. S. Mayants (1977). On Some Peculiarities of Quantum Mechanics. Foundations of Physics 7 (1-2):3-28.
    General regularities related toLagrangian andHamiltonian equations are revealed. Probability distributions for functions ofHamiltonian random variables are considered. It is shown that all probability distributions of this kind are fully determined by the probability distributions for the random variables satisfying the corresponding Lagrangian equations. Some formulas related tocanonically conjugate operators are given. The similarity of these formulas to those related to Hamiltonian random variables is demonstrated. The “quantum approach” to the treatment of Hamiltonian random variables is discussed, and the origin of (...)
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  29. L. S. Mayants (1976). On Transformations of Physical Systems. Foundations of Physics 6 (5):485-510.
    A universal, unified theory of transformations of physical systems based on the propositions of probabilistic physics is developed. This is applied to the treatment of decay processes and intramolecular rearrangements. Some general features of decay processes are elucidated. A critical analysis of the conventional quantum theories of decay and of Slater's quantum theory of intramolecular rearrangements is given. It is explained why, despite the incorrectness of the decay theories in principle, they can give correct estimations of decay rate constants. The (...)
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  30. D. Mayr (1981). Comment on Putnam's 'Quantum Mechanics and the Observer'. Erkenntnis 16 (2):221 - 225.
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  31. Gordon McCabe (2005). The Structure and Interpretation of Cosmology: Part II. The Concept of Creation in Inflation and Quantum Cosmology. Studies in History and Philosophy of Science Part B 36 (1):67-102.
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  32. Gordon McCabe (1992). Quantum Implications. Cogito 6 (2):106-108.
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  33. Storrs McCall (2001). Axiomatic Quantum Theory. Journal of Philosophical Logic 30 (5):465-477.
    The basis of a rigorous formal axiomatization of quantum mechanics is constructed, built upon Dirac's bra-ket notation. The system is three-sorted, with separate variables for scalars, vectors and operators. First-order quantification over all three types of variable is permitted. Economy in the axioms is effected by, e.g., assigning a single logical function * to transform (i) a scalar into its complex conjugate, (ii) a ket vector into a bra and a bra into a ket, (iii) an operator into its adjoint. (...)
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  34. Storrs McCall (2000). QM and STR: The Combining of Quantum Mechanics and Relativity Theory. Philosophy of Science 67 (3):548.
    Combining quantum mechanics with special relativity requires (i) that a spacetime representation of quantum states be found; (ii) that such states, represented as extended along equal-time hyperplanes, be invariant when transformed from one frame to another; and (iii) that collapses of states be instantaneous in every frame. These requirements are met using branching spacetime, in which probabilities of outcomes are represented by the numerical proportions of branches on which the outcomes occur. Quantum states of systems are then identified with the (...)
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  35. J. P. McEvoy (1997/1996). Introducing Quantum Theory. Distributed to the Trade in the United States by National Book Network.
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  36. James H. McGrath (1980). Book Review:The Logico-Algebraic Approach to Quantum Mechanics. Volume II: Contemporary Consolidation C. A. Hooker. [REVIEW] Philosophy of Science 47 (4):660-.
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  37. James H. McGrath (1978). Book Review:The Logico-Algebraic Approach to Quantum Mechanics. Volume I: Historical Evolution C. A. Hooker. [REVIEW] Philosophy of Science 45 (1):145-.
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  38. Leemon McHenry (2002). Whitehead, Quantum Mechanics and Local Realism. Process Studies 31 (1):164-170.
  39. John L. McKnight (1957). The Quantum Theoretical Concept of Measurement. Philosophy of Science 24 (4):321-330.
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  40. John Lacy McKnight (1958). An Extended Latency Interpretation of Quantum Mechanical Measurement. Philosophy of Science 25 (3):209-222.
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  41. Jagdish Mehra (1988). Erwin Schrödinger and the Rise of Wave Mechanics. III. Early Response and Applications. Foundations of Physics 18 (2):107-184.
    This article (Part III) deals with the early applications of wave mechanics to atomic problems—including the demonstration of the formal mathematical equivalence of wave mechanics with the quantum mechanics of Born, Heisenberg, and Jordan, and that of Dirac—by Schrödinger himself and others. The new theory was immediately accepted by the scientific community.
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  42. Jagdish Mehra (1987). Erwin Schrödinger and the Rise of Wave Mechanics. I. Schrödinger's Scientific Work Before the Creation of Wave Mechanics. Foundations of Physics 17 (11):1051-1112.
    This article is in three parts. Part I gives an account of Erwin Schrödinger's growing up and studies in Vienna, his scientific work—first in Vienna from 1911 to 1920, then in Zurich from 1920 to 1925—on the dielectric properties of matter, atmospheric electricity and radioactivity, general relativity, color theory and physiological optics, and on kinetic theory and statistical mechanics. Part II deals with the creation of the theory of wave mechanics by Schrödinger in Zurich during the early months of 1926; (...)
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  43. Jagdish Mehra (1987). Erwin Schrödinger and the Rise of Wave Mechanics. II. The Creation of Wave Mechanics. Foundations of Physics 17 (12):1141-1188.
    This article (Part II) deals with the creation of the theory of wave mechanics by Erwin Schrödinger in Zurich during the early months of 1926; he laid the foundations of this theory in his first two communications toAnnalen der Physik. The background of Schrödinger's work on, and his actual creation of, wave mechanics are analyzed.
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  44. Jagdish Mehra (1987). Niels Bohr's Discussions with Albert Einstein, Werner Heisenberg, and Erwin Schrödinger: The Origins of the Principles of Uncertainty and Complementarity. Foundations of Physics 17 (5):461-506.
    In this paper, the main outlines of the discussions between Niels Bohr with Albert Einstein, Werner Heisenberg, and Erwin Schrödinger during 1920–1927 are treated. From the formulation of quantum mechanics in 1925–1926 and wave mechanics in 1926, there emerged Born's statistical interpretation of the wave function in summer 1926, and on the basis of the quantum mechanical transformation theory—formulated in fall 1926 by Dirac, London, and Jordan—Heisenberg formulated the uncertainty principle in early 1927. At the Volta Conference in Como in (...)
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  45. Jagdish Mehra (1974). The Quantum Principle: Its Interpretation and Epistemology. D. Reidel.
  46. Jagdish Mehra (ed.) (1973). The Physicist's Conception of Nature. Boston,Reidel.
    Development of the Physicist's Conception of Nature P. A. M. Dime When one looks back over the development of physics, one sees that it can be pictured as a ...
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  47. Jagdish Mehra & Helmut Rechenberg (1999). Planck's Half-Quanta: A History of the Concept of Zero-Point Energy. [REVIEW] Foundations of Physics 29 (1):91-132.
    Max Planck introduced the concept of zero-point energy in spring 1911. In the early struggles to establish the concept of the energy-quantum, it provided a helpful heuristic principle, to guide as well as supplement the efforts of some leading physicists in understanding the laws that applied in the atomic domain. The history and growth of this concept, and its application in the general development of quantum theory during the past many decades are studied under three principal headings: (1) The Birth (...)
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  48. Miguel Ferrero Melgar (1988). The Philosophy of Erwin Schrödinger: A Diachronic View of Schrödinger's Thoughts. [REVIEW] Foundations of Physics 18 (3):357-371.
    There is no agreement within the scientific community about the philosophy of Schrödinger. Some people think that he was a realist, while others defend him as an idealist. In this paper we study a number of Schrödinger's works and we show that the epithets of realist and idealist do not do him justice. Toward the end we conclude that it would be more adequate to place him in the trend known as the philosophy of immanence.
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  49. G. F. Melloy (2002). The Generalized Representation of Particle Localization in Quantum Mechanics. Foundations of Physics 32 (4):503-530.
    It has been shown earlier that while strict localization of the free Dirac particle is not describable within the usual mathematical formalism, it is possible to describe sequences of positive-energy states whose spread Δ x =〈(x−x 0)2〉 about any given point x 0 approaches zero, where x is Dirac's position operator. The concept of a generalized function is extended here to allow for the succinct description of localized states in terms of “Asymptotic Localizing Functions.” Localization of both the nonrelativistic particle (...)
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  50. Olaf Melsheimer (1983). Quantum Statistical Mechanics as a Construction of an Embedding Scheme. Foundations of Physics 13 (7):745-758.
    The aim of the present paper is to show that the formalism of equilibrium quantum statistical mechanics can fully be incorporated into Ludwig's embedding scheme for classical theories in many-body quantum mechanics. A construction procedure based on a recently developed reconstruction procedure for the so-called macro-observable is presented which leads to the explicit determination of the set of classical ensembles compatible with the embedding scheme.
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