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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 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. D. Han, Y. S. Kim & Marilyn E. Noz (1981). Physical Principles in Quantum Field Theory and in Covariant Harmonic Oscillator Formalism. Foundations of Physics 11 (11-12):895-905.
    It is shown that both covariant harmonic oscillator formalism and quantum field theory are based on common physical principles which include Poincaré covariance, Heisenberg's space-momentum uncertainty relation, and Dirac's “C-number” time-energy uncertainty relation. It is shown in particular that the oscillator wave functions are derivable from the physical principles which are used in the derivation of the Klein-Nishina formula.
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  4. 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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  5. 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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  6. Nicolaas P. Landsman, Between Classical and Quantum.
    The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...)
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  7. G. Lanyi (2003). Thermal Equilibrium Between Radiation and Matter. Foundations of Physics 33 (3):511-528.
    In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that the (...)
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  8. J. Larsson (2008). Quantum Mechanics at the Crossroads, James Evans, Alan S. Thorndike. Springer, Berlin (2007). 249pp., Hardcover, US$ 69.95, ISBN: 978-3-540-32663-. [REVIEW] Studies in History and Philosophy of Science Part B 39 (1):229-230.
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  9. Kathryn Blackmond Laskey (2006). Quantum Physical Symbol Systems. Journal of Logic, Language and Information 15 (1-2):109-154.
    Because intelligent agents employ physically embodied cognitive systems to reason about the world, their cognitive abilities are constrained by the laws of physics. Scientists have used digital computers to develop and validate theories of physically embodied cognition. Computational theories of intelligence have advanced our understanding of the nature of intelligence and have yielded practically useful systems exhibiting some degree of intelligence. However, the view of cognition as algorithms running on digital computers rests on implicit assumptions about the physical world that (...)
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  10. Ervin Laszlo (2006). Quantum and Consciousness: In Search of a New Paradigm. Zygon 41 (3):533-541.
  11. Federico Laudisa (2014). On Leggett Theories: A Reply. Foundations of Physics 44 (3):296-304.
    In his 2013 Foundations of Physics paper Mathias Egg claims to show that my critical arguments toward the foundational significance of Leggett’s non-local theories are misguided. The main motivation is that my argument would connect too strongly the Leggett original motivation for introducing this new class of theories with the foundational significance of these theories per se. Egg basically aims to show that, although it can be conceded that the Leggett original motivation relies on a mistaken view of the original (...)
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  12. Federico Laudisa, Relational Quantum Mechanics. Stanford Encyclopedia of Philosophy.
    Relational quantum mechanics is an interpretation of quantum theory which discards the notions of absolute state of a system, absolute value of its physical quantities, or absolute event. The theory describes only the way systems affect each other in the course of physical interactions. State and physical quantities refer always to the interaction, or the relation, between two systems. Nevertheless, the theory is assumed to be complete. The physical content of quantum theory is understood as expressing the net of relations (...)
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  13. Hans Laue (1981). Quantum Mechanics Without the Position Operator. Foundations of Physics 11 (1-2):37-46.
    The formula for the differential scattering cross section in quantum mechanics is derived without the usual assumption that the square of the ψ-function is a position probability density for particles. It is argued that position, like time, may be basically a macroscopic parameter rather than a random variable for microparticles.
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  14. Charles D. Laughlin & C. Jason Throop (2001). Imagination and Reality: On the Relations Between Myth, Consciousness, and the Quantum Sea. Zygon 36 (4):709-736.
  15. Roberto Laura & Leonardo Vanni (2009). Time Translation of Quantum Properties. Foundations of Physics 39 (2):160-173.
    Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving properties at different times. We compare our results with the theory of consistent histories.
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  16. K. V. Laurikainen (1990). Quantum Physics, Philosophy, and the Image of God: Insights From Wolfgang Pauli. Zygon 25 (4):391-404.
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  17. B. H. Lavenda (1987). Classical Variational Derivation and Physical Interpretation of Dirac's Equation. Foundations of Physics 17 (3):221-237.
    A simple random walk model has been shown by Gaveauet al. to give rise to the Klein-Gordon equation under analytic continuation. This absolutely most probable path implies that the components of the Dirac wave function have a common phase; the influence of spin on the motion is neglected. There is a nonclassical path of relative maximum likelihood which satisfies the constraint that the probability density coincide with the quantum mechanical definition. In three space dimensions, and in the presence of electromagnetic (...)
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  18. Shaughan Lavine (1991). Is Quantum Mechanics an Atomistic Theory? Synthese 89 (2):253 - 271.
    If quantum mechanics (QM) is to be taken as an atomistic theory with the elementary particles as atoms (an ATEP), then the elementary particlcs must be individuals. There must then be, for each elementary particle a, a property being identical with a that a alone has. But according to QM, elementary particles of the same kind share all physical properties. Thus, if QM is an ATEP, identity is a metaphysical but not a physical property. That has unpalatable consequences. Dropping the (...)
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  19. D. A. Lavis (2004). The Spin-Echo System Reconsidered. Foundations of Physics 34 (4):669-688.
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  20. Soazig Le Bihan, Understanding Quantum Phenomena.
    It so happens that classical physical theories can be interpreted as a representation of local interactions between systems with determinate properties. Orthodox quantum mechanics, which is one of our most experimentally well-confirmed theories, is notoriously resistant to being interpreted in terms of the above framework. Bell-type theorems and Bell-type experiments have made such an interpretation impossible. In the early sixties, John Bell demonstrated that any theory that represents its domain in terms of the above framework satisfies a set of inequalities, (...)
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  21. Robert A. Leacock (1987). The Physical Properties of Linear and Action-Angle Coordinates in Classical and Quantum Mechanics. Foundations of Physics 17 (8):799-807.
    The quantum harmonic oscillator is described in terms of two basic sets of coordinates: linear coordinates x, px and angular coordinates eiφ, Pφ (action-angle variables). The angular “coordinate” eiφ is assumed unitary, the conjugate momentum pφ is assumed Hermitian, and eiφ and pφ are assumed to be a canonical pair. Two transformations are defined connecting the angular coordinates to the linear coordinates. It is found that x, px can be physical, i.e., Hermitian and canonical, only under constraints on the pφ (...)
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  22. Boris Leaf (1982). The Continuous Spectra of Quantum Operators. Foundations of Physics 12 (6):583-606.
    The linear vector space for the quantum description of a physical system is formulated as the intersection of the domains of Hermiticity of the observables characterizing the system. It is shown that on a continuous interval of its spectrum every Hermitian operator on a Hilbert space of one degree of freedom is a generalized coordinate with a conjugate generalized momentum. Every continuous spectral interval of a Hermitian operator is the limit of a discrete spectrum in the same interval. This result (...)
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  23. Hai-Woong Lee (1992). Wigner Trajectories of a Gaussian Wave Packet Perturbed by a Weak Potential. Foundations of Physics 22 (8):995-1010.
    Trajectories along which phase-space points of the Wigner distribution function move are computed for a Gaussian wave packet moving under the influence of a weak perturbative potential. The potentials considered are a potential step, a potential barrier, and a periodic potential. Trajectories computed exhibit the complex, nonlocal nature of quantum dynamics. It is seen that quantum interference, which takes place in the time development of the wave packet, is taken care of in a simple way by the Wigner trajectory method (...)
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  24. Jae-Weon Lee (2011). Quantum Mechanics Emerges From Information Theory Applied to Causal Horizons. Foundations of Physics 41 (4):744-753.
    It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde’s entropic gravity theory is also investigated.
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  25. V. J. Lee (1980). Physical Foundations of Quantum Theory: Stochastic Formulation and Proposed Experimental Test. [REVIEW] Foundations of Physics 10 (1-2):77-107.
    The time-dependent Schrödinger equation has been derived from three assumptions within the domain of classical and stochastic mechanics. The continuity equation isnot used in deriving the basic equations of the stochastic theory as in the literature. They are obtained by representing Newton's second law in a time-inversion consistent equation. Integrating the latter, we obtain the stochastic Hamilton-Jacobi equation. The Schrödinger equation is a result of a transformation of the Hamilton-Jacobi equation and linearization by assigning the arbitrary constant ħ=2mD. An experiment (...)
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  26. Stephen Leeds (1984). Chance, Realism, Quantum Mechanics. Journal of Philosophy 81 (10):567-578.
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  27. A. J. Leggett (1999). Part I. Invited Papers Dedicated to Daniel Greenberger-Some Thought-Experiments Involving Macrosysterns as Illustrations of Various Interpretations of Quantum Mechanics. Foundations of Physics 29 (3):445-456.
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  28. A. J. Leggett (1995). Is “Relative Quantum Phase” Transitive? Foundations of Physics 25 (1):113-122.
    I discuss the question: Is it possible to prepare, by purely thermodynamic means, an ensemble described by a quantum state having a definite phase relation between two component states which have never been in direct contact? Resolution of this question requires us to take explicit account of the nature of the correlations between the system and its thermal environment.
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  29. V. F. Lenzen (1962). Book Review:From Dualism to Unity in Quantum Physics Alfred Lande. [REVIEW] Philosophy of Science 29 (2):213-.
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  30. Victor F. Lenzen (1949). Concepts and Reality in Quantum Mechanics. Philosophy of Science 16 (4):279-286.
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  31. E. A. Liberman & S. V. Minina (1997). Cell Molecular Quantum Computer and Principles of New Science. World Futures 50 (1):583-590.
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  32. Richard Lieu (2001). Microscopic Relativity: The Basic Theory. [REVIEW] Foundations of Physics 31 (8):1233-1250.
    In effort to investigate how quantum physics might modify Einstein's Theory of Relativity at speeds v→c, the relationship between space-time coordinates of different reference frames is revisited by introducing only one new parameter xo, a fundamental constant for the quantization of space. The starting point is three criteria: (a) real space-time data are conditioned by standard quantum effects on measurements; (b) since currently used apparatus are only capable of probing the aggregate behavior of these quanta the relevant model is one (...)
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  33. Shih-Yuin Lin & B. L. Hu (2007). New Insights Into Uniformly Accelerated Detector in a Quantum Field. Foundations of Physics 37 (4-5):480-490.
    We obtained an exact solution for a uniformly accelerated Unruh–DeWitt detector interacting with a massless scalar field in (3 + 1) dimensions which enables us to study the entire evolution of the total system, from the initial transient to late-time steady state. We find that the conventional transition probability of the detector from its initial ground state to excited states, as derived from time-dependent perturbation theory over an infinitely long duration of interaction, is valid only in the transient stage and (...)
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  34. James Lindesay (2012). Self-Consistent Solutions of Canonical Proper Self-Gravitating Quantum Systems. Foundations of Physics 42 (12):1573-1585.
    Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have appropriate correspondence with Newtonian gravitation. The results are consistent with known experimental results that indicate the maintenance of the quantum coherence of gravitating systems, as expected through the equivalence principle.
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  35. James Lindesay & Tepper Gill (2004). Canonical Proper Time Formulation for Physical Systems. Foundations of Physics 34 (1):169-182.
    The canonical proper time formulation of relativistic dynamics provides a framework from which one can describe the dynamics of classical and quantum systems using the clock of those very systems. The framework utilizes a canonical transformation on the time variable that is used to describe the dynamics, and does not transform other dynamical variables such as momenta or positions. This means that the time scales of the dynamics are described in terms of the natural local time coordinates, which is the (...)
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  36. James Lindesay & H. Pierre Noyes (2004). Nonperturbative, Unitary Quantum-Particle Scattering Amplitudes From Three-Particle Equations. Foundations of Physics 34 (10):1573-1606.
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  37. Øystein Linnebo & F. A. Muller (2013). On Witness-Discernibility of Elementary Particles. Erkenntnis 78 (5):1133-1142.
    In the context of discussions about the nature of ‘identical particles’ and the status of Leibniz’s Principle of the Identity of Indiscernibles in Quantum Mechanics, a novel kind of physical discernibility has recently been proposed, which we call witness-discernibility. We inquire into how witness-discernibility relates to known kinds of discernibility. Our conclusion will be that for a wide variety of cases, including the intended quantum-mechanical ones, witness-discernibility collapses extensionally to absolute discernibility, that is, to discernibility by properties.
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  38. Abninder Litt, Chris Eliasmith, Fred Kroon, Steven Weinstein & Paul Thagard (2006). Is the Brain a Quantum Computer? Cognitive Science 30 (3):593-603.
  39. Chuang Liu (1996). Potential, Propensity, and Categorical Realism. Erkenntnis 45 (1):45 - 68.
    I argue that categorical realism, contrary to what most believe today, holds for quantum (and indeed for all) objects and substances. The main argument consists of two steps: (i) the recent experimental verification of the AB effect gives strong empirical evidence for taking quantum potentials as physically real (or substantival), which suggests a change of the data upon which any viable interpretation of quantum theory must rely, and (ii) quantum potentials may be consistently taken as the categorical properties of quantum (...)
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  40. Chuang Liu & Gerard G. Emch (2005). Explaining Quantum Spontaneous Symmetry Breaking. Studies in History and Philosophy of Science Part B 36 (1):137-163.
    Two alternative accounts of quantum spontaneous symmetry breaking (SSB) are compared and one of them, the decompositional account in the algebraic approach, is argued to be superior for understanding quantum SSB. Two exactly solvable models are given as applications of our account -- the Weiss-Heisenberg model for ferromagnetism and the BCS model for superconductivity. Finally, the decompositional account is shown to be more conducive to the causal explanation of quantum SSB.
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  41. Stathis Livadas (2012). The Expressional Limits of Formal Language in the Notion of Quantum Observation. Axiomathes 22 (1):147-169.
    In this article I deal with the notion of observation, from a phenomenologically motivated point of view, and its representation mainly by means of the formal language of quantum mechanics. In doing so, I have taken the notion of observation in two diverse contexts. In one context as a notion related with objects of a logical-mathematical theory taken as registered facts of phenomenological perception ( Wahrnehmung ) inasmuch as this phenomenological idea can also be linked with a process of measurement (...)
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  42. Hugh Lloyd-Jones (1962). Quantum Mutatus Alfred Körte: Die hellenistische Dichtung. Zweite, vollständig neubearbeitete Auflage von Paul Händel. (Kröners Taschenausgabe, 47.) Pp. xi+363. Stuttgart: Kröner, 1961. Cloth, DM. 11. [REVIEW] The Classical Review 12 (03):245-246.
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  43. Georges Lochak (1981). Irreversibility in Physics: Reflections on the Evolution of Ideas in Mechanics and on the Actual Crisis in Physics. [REVIEW] Foundations of Physics 11 (7-8):593-621.
    The author proposes to show that the actual crisis in microphysics is principally due to the fact that, as quantum mechanics is a theory of stationary states and reversible movements, it fundamentally ignores the notion of a transitory process. The essential characteristic of quantum theories is the result of an evolution of more than two centuries; a period of development essentially devoted to the description of stationary and reversible phenomena. The author's point of view, which reflects that of the school (...)
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  44. James A. Lock (1982). The Transformation Properties of World Lines in Relativistic Quantum Mechanical Hamiltonian Models. Foundations of Physics 12 (8):743-757.
    The supposition of the manifest covariance of average trajectory world lines is violated in Hamiltonian formulations of relativistic quantum mechanics. This is due to the nonlinear appearance of particle dynamical variable operators in the Heisenberg picture boosted position, velocity, and momentum operators. The magnitude of this deviation from world line manifest covariance is found to be exceedingly small for a number of common time of flight experiments.
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  45. Michael Lockwood (2003). Consciousness and the Quantum World: Putting Qualia on the Map. In Quentin Smith & Aleksandar Jokic (eds.), Consciousness: New Philosophical Perspectives. Oxford University Press. 447.
  46. Michael Lockwood (1989). Mind, Brain, and the Quantum: The Compound 'I'. B. Blackwell.
  47. Barry M. Loewer (1996). Freedom From Physics: Quantum Mechanics and Free Will. Philosophical Topics 24 (2):91-112.
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  48. Olimpia Lombardi, Sebastian Fortin & Mario Castagnino (2012). The Problem of Identifying the System and the Environment in the Phenomenon of Decoherence. In. In Henk W. de Regt (ed.), Epsa Philosophy of Science: Amsterdam 2009. Springer. 161--174.
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  49. Gui Lu Long, Yi-Fan Zhou, Jia-Qi Jin, Yang Sun & Hai-Woong Lee (2006). Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix. Foundations of Physics 36 (8):1217-1243.
    We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief (...)
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  50. William J. Long (2006). Quantum Theory and Neuroplasticity: Implications for Social Theory. Journal of Theoretical and Philosophical Psychology 26 (1-2):78-94.
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