Reexamining the Quantum-Classical Relation: Beyond Reductionism and Pluralism

Classical mechanics and quantum mechanics are two of the most successful scientific theories ever discovered, and yet how they can describe the same world is far from clear: one theory is deterministic, the other indeterministic; one theory describes a world in which chaos is pervasive, the other a world in which chaos is absent. Focusing on the exciting field of 'quantum chaos', this book reveals that there is a subtle and complex relation between classical and quantum mechanics. It challenges the received view that classical and quantum mechanics are incommensurable, and revives another, largely forgotten tradition due to Niels Bohr and Paul Dirac. By artfully weaving together considerations from the history of science, philosophy of science, and contemporary physics, this book offers a new way of thinking about intertheory relations and scientific explanation. It will be of particular interest to historians and philosophers of science, philosophically-inclined physicists, and interested non-specialists.

[1]  James Ladyman,et al.  Remodelling Structural Realism: Quantum Physics and the Metaphysics of Structure , 2003, Synthese.

[2]  M. Redhead,et al.  Quests of a realist , 2001 .

[3]  S. Peale The rotation of Hyperion , 1984, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[4]  M. Planck The Theory of Heat Radiation , 2010 .

[5]  Michael V Berry,et al.  Regular and irregular semiclassical wavefunctions , 1977 .

[6]  P. Dirac,et al.  THE LAGRANGIAN IN QUANTUM MECHANICS. , 2022 .

[7]  Niels Bohr,et al.  ON THE NOTIONS OF CAUSALITY AND COMPLEMENTARITY1 , 1948 .

[8]  Niels Bohr,et al.  Discussion with Einstein on Epistemological Problems in Atomic Physics , 1996 .

[9]  K. Richter Semiclassical Theory of Mesoscopic Quantum Systems , 2000 .

[10]  K. Richter,et al.  The semiclassical helium atom. , 1992, Chaos.

[11]  Donald H. Menzel,et al.  The Physical Principles of the Quantum Theory , 1949, Philosophy of Science.

[12]  Alisa Bokulich,et al.  Can Classical Structures Explain Quantum Phenomena? , 2008, The British Journal for the Philosophy of Science.

[13]  M. Gutzwiller,et al.  Periodic Orbits and Classical Quantization Conditions , 1971 .

[14]  Werner Israel,et al.  An introductory survey , 1979 .

[15]  N. Bohr,et al.  On the notions of causality and complementarity. , 1950, Science.

[16]  D. Meredith Semiclassical wavefunctions of nonintegrable systems and localization on periodic orbits , 1992 .

[17]  J. Klavetter Rotation of Hyperion. II. Dynamics , 1989 .

[18]  A. Sommerfeld Zur Quantentheorie der Spektrallinien , 1916 .

[19]  Michela Massimi,et al.  Pauli's Exclusion Principle: The Origin and Validation of a Scientific Principle , 2005 .

[20]  Herbert E. Hendry On reduction , 1969 .

[21]  M. Berry Asymptotics, singularities and the reduction of theories , 1995 .

[22]  K. S. Krishnan,et al.  Thermionic Constants of Graphite , 1952, Nature.

[23]  Welch,et al.  Positive-energy structure of the diamagnetic Rydberg spectrum. , 1989, Physical review letters.

[24]  R. Liboff The correspondence principle revisited , 1984 .

[25]  Marko Robnik,et al.  Hydrogen atom in a strong magnetic field: on the existence of the third integral of motion , 1981 .

[26]  Jan Faye,et al.  Niels Bohr and contemporary philosophy , 1994 .

[27]  P. Anderson Why Decoherence has not Solved the Measurement Problem : A Response to , 2008 .

[28]  M. Friedman Explanation and Scientific Understanding , 1974 .

[29]  L. Laudan A Confutation of Convergent Realism , 1981, Philosophy of Science.

[30]  R. Jalabert,et al.  Quantum-chaotic scattering effects in semiconductor microstructures. , 1993, Chaos.

[31]  The semiclassical tool in mesoscopic physics , 1999, cond-mat/9912038.

[32]  Niels Bohr,et al.  The correspondence principle (1918-1923) , 1976 .

[33]  Gregor Wentzel,et al.  Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik , 1926 .

[34]  Philosophical Problems of Quantum Physics , 1979 .

[35]  Raymond Klibansky,et al.  Quantum Physics and Philosophy–Causality and Complementarity , 1996 .

[36]  Jean-Baptiste Lully,et al.  The collected works , 1996 .

[37]  Christopher Hitchcock,et al.  Explanatory generalizations, part II: Plumbing explanatory depth , 2003 .

[38]  A. Bokulich,et al.  Niels Bohr’s Generalization of Classical Mechanics , 2005 .

[39]  L. Ballentine,et al.  Foundations of Quantum Mechanics Since the Bell Inequalities: Selected Reprints , 1989 .

[40]  W. Heisenberg Unification of Fundamental Forces: Theory, criticism, and a philosophy , 1989 .

[41]  W. Heisenberg,et al.  La Mécanique des Quanta , 1984 .

[42]  James Ladyman,et al.  Reinflating the Semantic Approach , 1999 .

[43]  W. Heisenberg Physics and Beyond: Encounters and Conversations , 1971 .

[44]  E. Scheibe Between Rationalism and Empiricism: Selected Papers in the Philosophy of Physics , 2002 .

[45]  Margaret Morrison,et al.  Models as Mediators: Models as autonomous agents , 1999 .

[46]  Stephen H. Kellert,et al.  Scientific Pluralism. Minnesota Studies in the Philosophy of Science. Vol. 19 , 2006 .

[47]  Robert W. Batterman,et al.  The devil in the details : asymptotic reasoning in explanation, reduction, and emergence , 2002 .

[48]  Edward Mackinnon Aspects of Scientific Explanation: and Other Essays in the Philosophy of Science , 1967 .

[49]  J. Main,et al.  Quasi-Landau spectrum of the chaotic diamagnetic hydrogen atom. , 1988, Physical review letters.

[50]  R. Feynman,et al.  Space-Time Approach to Non-Relativistic Quantum Mechanics , 1948 .

[51]  J. Klavetter Rotation of Hyperion. I - Observations , 1989 .

[52]  Scott Tanona Uncertainty in Bohr's response to the Heisenberg microscope , 2004 .

[53]  J. McAllister Beauty and Revolution in Science , 1996 .

[54]  Quantum mechanics of Hyperion , 2005, quant-ph/0503170.

[55]  J. Fodor Special sciences (or: The disunity of science as a working hypothesis) , 1974, Synthese.

[56]  Niels Bohr I. On the constitution of atoms and molecules , 1913 .

[57]  J. Delos,et al.  Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. I. Physical picture and calculations. , 1988, Physical review. A, General physics.

[58]  O. Darrigol From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory , 1992 .

[59]  Léon Rosenfeld The Wave-Particle Dilemma , 1973 .

[60]  M. Berry,et al.  Semiclassically weak reflections above analytic and non-analytic potential barriers , 1982 .

[61]  Kate Moss,et al.  Approaches to reduction , 2009 .

[62]  Chet B. Opal,et al.  Chaotic rotation of Hyperion? , 1986, Nature.

[63]  J. Dupré Against Scientific Imperialism , 1994, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[64]  Stephen L. Adler,et al.  Why decoherence has not solved the measurement problem: A Response to P. W. Anderson , 2003 .

[65]  N. P. Landsman Between classical and quantum , 2005 .

[66]  Steven French,et al.  Partiality, Pursuit and Practice , 1997 .

[67]  Helge Kragh,et al.  Dirac: A Scientific Biography , 1991 .

[68]  B. O. Koopman,et al.  Hamiltonian Systems and Transformation in Hilbert Space. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[69]  H. Post Correspondence, invariance and heuristics: In praise of conservative induction , 1971 .

[70]  A. F. Foundations of Physics , 1936, Nature.

[71]  Wojciech H. Zurek Decoherence, chaos, quantum-classical correspondence, and the algorithmic arrow of time , 1998 .

[72]  D. Howard What Makes a Classical Concept Classical ? Toward a Reconstruction of Niels Bohr ' s Philosophy of Physics , 1986 .

[73]  Paul Adrien Maurice Dirac,et al.  The Evolution of the Physicist's Picture of Nature , 1963 .

[74]  A. Einstein,et al.  The Born-Einstein letters: Correspondence between Albert Einstein and Max and Hedwig Born from 1916-1955, with commentaries by Max Born; , 1971 .

[75]  Bas C. van Fraassen,et al.  The Scientific Image , 1980 .

[76]  G. Belot Chaos and Fundamentalism , 2000, Philosophy of Science.

[77]  Michael Redhead,et al.  The Intelligibility of the Universe , 2001, Royal Institute of Philosophy Supplement.

[78]  M. Chiara,et al.  Philosophy of quantum mechanics , 1982 .

[79]  Paul K. Feyerabend,et al.  Explanation, reduction, and empiricism , 1962 .

[80]  C. DeWitt-Morette,et al.  Techniques and Applications of Path Integration , 1981 .

[81]  Z. Rudnick Quantum Chaos? , 2007 .

[82]  P. Dirac XI.—The Relation between Mathematics and Physics , 1940 .

[83]  T. Kuhn,et al.  The Structure of Scientific Revolutions. , 1964 .

[84]  Otávio Bueno,et al.  Empiricism, scientific change and mathematical change , 2000 .

[85]  Daniel F. Styer,et al.  Nine formulations of quantum mechanics , 2002 .

[86]  Keith A. Markus,et al.  Making Things Happen: A Theory of Causal Explanation , 2007 .

[87]  A. Messiah Quantum Mechanics , 1961 .

[88]  Lawrence B. Sklar The Reduction(?) of Thermodynamics to Statistical Mechanics , 1999 .

[89]  Joseph B. Keller,et al.  Corrected bohr-sommerfeld quantum conditions for nonseparable systems , 1958 .

[90]  The Shaky Game: Einstein, Realism, and the Quantum Theory , 1989 .

[91]  Paul Adrien Maurice Dirac Can equations of motion be used in high‐energy physics? , 1970 .

[92]  S. Schweber QED and the Men Who Made It , 1994 .

[93]  W. Garton,et al.  Configuration interaction effect on diamagnetic phenomena in atoms: strong mixing and Landau regions , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[94]  H. Putnam Mathematics, Matter, And Method , 1975 .

[95]  D. Kleppner,et al.  EXTRACTING CLASSICAL TRAJECTORIES FROM ATOMIC SPECTRA , 1998 .

[96]  J. Emerson Chaos and quantum-classical correspondence for two- coupled spins , 2001 .

[97]  F. Weinert The Correspondence Principle and the closure of theories , 1994 .

[98]  A. Bokulich Heisenberg Meets Kuhn: Closed Theories and Paradigms* , 2006, Philosophy of Science.

[99]  F. Suppe The semantic conception of theories and scientific realism , 1989 .

[100]  K. Schwarzschild,et al.  Gesammelte Werke / Collected Works , 1992 .

[101]  P. Dirac On the Analogy Between Classical and Quantum Mechanics , 1945 .

[102]  J. Bub Quantum Dialogue: The Making of a Revolution , 2000 .

[103]  Otávio Bueno,et al.  Empirical adequacy: A partial structures approach , 1997 .

[104]  C. A. Hooker,et al.  Asymptotics, Reduction and Emergence , 2004, The British Journal for the Philosophy of Science.

[105]  J. Phillips,et al.  Beyond the Edge of Certainty, Essays in Contemporary Science and Philosophy , 1965 .

[106]  R. Batterman Quantum Chaos and Semiclassical Mechanics , 1992, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[107]  Max Jammer,et al.  The conceptual development of quantum mechanics , 1966 .

[108]  G. L. Payne,et al.  Relativistic Quantum Mechanics , 2007 .

[109]  P. Dirac The collected works of P.A.M. Dirac, 1924-1948 , 1996 .

[110]  K. Popper,et al.  Conjectures and refutations;: The growth of scientific knowledge , 1972 .

[111]  R. Batterman Response to Belot’s “Whose Devil? Which Details?”* , 2005, Philosophy of Science.

[112]  Why We Don’t Need Quantum Planetary Dynamics: Decoherence and the Correspondence Principle for Chaotic Systems , 1996, quant-ph/9612037.

[113]  Don Howard,et al.  Who Invented the “Copenhagen Interpretation”? A Study in Mythology , 2004, Philosophy of Science.

[114]  E. Scheibe The physicists' conception of progress , 1988 .

[115]  Jagdish Mehra,et al.  The Historical Development of Quantum Theory , 1982 .

[116]  J. Main,et al.  New quasi-Landau structure of highly excited atoms: The hydrogen atom. , 1986, Physical review letters.

[117]  L. Brillouin,et al.  La mécanique ondulatoire de Schrödinger; une méthode générale de resolution par approximations successives , 1926 .

[118]  W. Heisenberg,et al.  Encounters with Einstein: And Other Essays on People, Places, and Particles , 1989 .

[119]  E. Heller,et al.  Postmodern Quantum Mechanics , 1993 .

[120]  Sang Wook Kim,et al.  Decoherence from chaotic internal dynamics in two coupled {delta}-function-kicked rotors , 2003 .

[121]  Zibin,et al.  Inadequacy of Ehrenfest's theorem to characterize the classical regime. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[122]  D. Farrelly,et al.  Celestial Mechanics on a Microscopic Scale , 1991, Science.

[123]  Ernan McMullin,et al.  A Case for Scientific Realism , 2004 .

[124]  A. Bokulich Open or closed? Dirac, Heisenberg, and the relation between classical and quantum mechanics , 2004 .

[125]  J. D. Trout Scientific Explanation And The Sense Of Understanding* , 2002, Philosophy of Science.

[126]  G. Belot Whose Devil? Which Details?* , 2005, Philosophy of Science.

[127]  M. Beller The Rhetoric of Antirealism and the Copenhagen Spirit , 1996, Philosophy of Science.

[128]  Christopher Hitchcock,et al.  Explanatory Generalizations, Part I: A Counterfactual Account , 2003 .

[129]  Paul Adrien Maurice Dirac,et al.  Quantum Mechanics and a Preliminary Investigation of the Hydrogen Atom , 1926 .

[130]  S. Sridhar,et al.  Experimental observation of scarred eigenfunctions of chaotic microwave cavities. , 1991, Physical review letters.

[131]  G. S. Ezra Classical-quantum correspondence and the analysis of highly-excited states : periodic orbits , rational tori and beyond , 2003 .

[132]  John William Nicholson,et al.  The Constitution of Atoms and Molecules , 1914, Nature.

[133]  A. Sommerfeld Atomic structure and spectral lines , 1923 .

[134]  Mathias Frisch,et al.  Non‐Locality in Classical Electrodynamics , 2002, The British Journal for the Philosophy of Science.

[135]  C. Chevalley Physical Reality and Closed Theories in Werner Heisenberg’s Early Papers , 1988 .

[136]  Bas C. van Fraassen,et al.  Structure and Perspective: Philosophical Perplexity and Paradox , 1997 .

[137]  Daniel M. Greenberger,et al.  The Shaky Game: Einstein, Realism and the Quantum Theory , 1988 .

[138]  H. A. Kramers,et al.  Wellenmechanik und halbzahlige Quantisierung , 1926 .

[139]  Simon Saunders,et al.  To What Physics Corresponds , 1993 .

[140]  I. Percival,et al.  The semiclassical two-electron atom and the old quantum theory , 1980 .

[141]  陳文卿 The Statistical Interpretation of Quantum Mechanics , 1971 .

[142]  Don Howard,et al.  “Nicht Sein Kann was Nicht Sein Darf,” or the Prehistory of EPR, 1909–1935: Einstein’s Early Worries about the Quantum Mechanics of Composite Systems , 1990 .

[143]  P. Dirac Principles of Quantum Mechanics , 1982 .

[144]  Maria Luisa Dalla Chiara Scabia Logic and scientific methods : volume one of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995 , 1997 .

[145]  O'Connor,et al.  Properties of random superpositions of plane waves. , 1987, Physical review letters.

[146]  Can Bohmian trajectories account for quantum recurrences having classical periodicities , 2006, quant-ph/0607095.

[147]  D. Kleppner,et al.  Beyond Quantum Mechanics: Insights from the Work of Martin Gutzwiller , 2001 .

[148]  A. Baker Are there Genuine Mathematical Explanations of Physical Phenomena , 2005 .

[149]  K. Richter,et al.  The theory of two-electron atoms: between ground state and complete fragmentation , 2000 .

[150]  P Kitcher,et al.  1953 and all that: a tale of two sciences. , 1984, The Philosophical review.

[151]  Paul Adrien Maurice Dirac,et al.  The lorentz transformation and absolute time , 1953 .

[152]  S. French,et al.  Models, Theories, and Structures: Thirty Years on , 2000, Philosophy of Science.

[153]  W. Zurek Decoherence and the Transition from Quantum to Classical—Revisited , 2003, quant-ph/0306072.

[154]  Robert L. Weber,et al.  Sources of Quantum Mechanics , 1968 .

[155]  Otávio Bueno,et al.  What is Structural Empiricism? Scientific Change in an Empiricist Setting , 1999 .

[156]  G. H. B. Vorlesungen über die Theorie der Wärmestrahlung , 1913, Nature.

[157]  Niels Bohr,et al.  Atomic Theory and the Description of Nature , 1934 .

[158]  A. D. Stone Einstein’s Unknown Insight and the Problem of Quantizing Chaos , 2005 .

[159]  Rob Clifton,et al.  Scientific Explanation in Quantum Theory , 1998 .

[160]  W. Heisenberg,et al.  Across the Frontiers. , 1965, British medical journal.

[161]  Eric R. Scerri Has Chemistry Been at Least Approximately Reduced to Quantum Mechanics? , 1994, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[162]  D. Siegel,et al.  The collected papers of Albert Einstein. , 2007, Isis; an international review devoted to the history of science and its cultural influences.

[163]  L. Kaplan Scars in quantum chaotic wavefunctions , 1999 .

[164]  Bas C. van Fraassen,et al.  Structure: Its Shadow and Substance , 2006, The British Journal for the Philosophy of Science.

[165]  J. Mehra The physicist's conception of nature , 1973 .

[166]  A. Hoffman,et al.  Neutral models in biology , 1987 .

[167]  Hilary Putnam,et al.  Mathematics, Matter and Method: Philosophical Papers , 1979 .

[168]  W. Salmon Four decades of scientific explanation , 1989 .

[169]  Albert Einstein,et al.  Zum Quantensatz von Sommerfeld und Epstein , 1917 .

[170]  Stathis Psilos Is Structural Realism the Best of Both Worlds , 2005 .

[171]  H. Putnam,et al.  Unity of Science as a Working Hypothesis , 1958 .

[172]  J. Delos,et al.  Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. , 1987, Physical review letters.

[173]  W. Bean Physics and Philosophy, the Revolution in Modern Science. , 1959 .

[174]  S. Sarkar Models of reduction and categories of reductionism , 1992, Synthese.

[175]  I. Lakatos Falsification and the Methodology of Scientific Research Programmes , 1976 .

[176]  The Metaphysics of the Disunified World , 1994, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[177]  B. Granger Quantum and Semiclassical Scattering Matrix Theory for Atomic Photoabsorption in External Fields , 2001 .

[178]  E. Heller Qualitative properties of eigenfunctions of classically chaotic Hamiltonian systems , 1986 .

[179]  P. Dirac,et al.  Is there an Æther? , 1951, Nature.

[180]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[181]  Carl F. Craver,et al.  When mechanistic models explain , 2006, Synthese.

[182]  M. Redhead Discussion noteAsymptotic reasoning , 2004 .

[183]  Anjan Chakravartty,et al.  The Dappled World: A Study of the Boundaries of Science , 2000 .

[184]  Elliott Sober,et al.  Cartwright On Explanation And Idealization , 2002 .

[185]  W. Garton,et al.  DIAMAGNETIC ZEEMAN EFFECT AND MAGNETIC CONFIGURATION MIXING IN LONG SPECTRAL SERIES OF Ba I. , 1969 .

[186]  J. Mehra,et al.  The Quantum Theory of Planck, Einstein, Bohr and Sommerfeld: Its Foundation and the Rise of Its Difficulties 1900–1925 , 1982 .

[187]  Hans Radder,et al.  Heuristics and the Generalized Correspondence Principle , 1991, The British Journal for the Philosophy of Science.

[188]  A. Einstein On the Method of Theoretical Physics , 1934, Philosophy of Science.

[189]  W. Zurek Decoherence, einselection, and the quantum origins of the classical , 2001, quant-ph/0105127.

[190]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[191]  Thomas Nickles,et al.  Two Concepts of Intertheoretic Reduction , 1973 .

[192]  J. Woodward,et al.  Scientific Explanation and the Causal Structure of the World , 1988 .

[193]  Paul Adrien Maurice Dirac,et al.  The fundamental equations of quantum mechanics , 1925 .

[194]  Eric J. Heller,et al.  Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits , 1984 .

[195]  E. Wigner The Unreasonable Effectiveness of Mathematics in the Natural Sciences (reprint) , 1960 .

[196]  H. Feigl,et al.  Minnesota studies in the philosophy of science , 1956 .

[197]  Martin Thomson-Jones,et al.  Models and the Semantic View , 2006, Philosophy of Science.

[198]  J. Mearsheimer Structural Realism , 2006 .

[199]  A. Bokulich Paul Dirac and the Einstein-Bohr Debate , 2008, Perspectives on Science.

[200]  Paul Adrien Maurice Dirac,et al.  Classical theory of radiating electrons , 1938 .

[201]  Asher Peres,et al.  Quantum Theory: Concepts and Methods , 1994 .

[202]  Robert W. Batterman,et al.  Chaos, quantization, and the correspondence principle , 1991, Synthese.

[203]  W. Heisenberg A quantum-theoretical reinterpretation of kinematic and mechanical relations , 1925 .

[204]  Salman Habib,et al.  Decoherence, chaos, and the correspondence principle , 1998 .

[205]  Jerry A. Fodor,et al.  Special Sciences: Still Autonomous after All these Years , 2008 .

[206]  M. V. Berry,et al.  Random renormalization in the semiclassical long-time limit of a precessing spin , 1988 .

[207]  M. Berry Quantum chaology, not quantum chaos , 1989 .

[208]  M. Tabor Chaos and Integrability in Nonlinear Dynamics: An Introduction , 1989 .

[209]  N. Bohr On the Application of the Quantum Theory to Atomic Structure , 1924, Nature.

[210]  Wendy S. Parker,et al.  Does matter really matter? Computer simulations, experiments, and materiality , 2009, Synthese.

[211]  N. Bohr Atomic Theory and Mechanics , 1925, Nature.

[212]  William A. Fedak,et al.  Quantum jumps and classical harmonics , 2002 .

[213]  D. W. Noid,et al.  Highly excited states of a hydrogen atom in a strong magnetic field , 1983 .

[214]  Semiclassical cycle expansion for the helium atom , 1991 .

[215]  Steven French,et al.  Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning , 2003 .

[216]  Ron Dare,et al.  The disorder of things: Metaphysical foundations of the disunity of science , 1997 .

[217]  Michael V Berry,et al.  Some quantum-to-classical asymptotics , 1991 .

[218]  J. Delos,et al.  Correspondence principles: the relationship between classical trajectories and quantum spectral , 1988 .

[219]  C. Frank,et al.  An Uncertain Life: Uncertainty: The Life and Science of Werner Heisenberg , 1994 .

[220]  Steven French,et al.  The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics , 2004, Synthese.

[221]  T. Broadbent,et al.  Criticism and the Growth of Knowledge , 1972 .

[222]  R. Feynman The development of the space-time view of quantum electrodynamics. , 1966, Science.

[223]  Robert W. Batterman,et al.  Theories between theories: Asymptotic limiting intertheoretic relations , 1995, Synthese.

[224]  Paul K. Feyerabend Problems of empiricism , 1981 .

[225]  J. Ford,et al.  Does quantum mechanics obey the correspondence principle? Is it complete? , 1992 .

[226]  Jorge V. José,et al.  Chaos in classical and quantum mechanics , 1990 .

[227]  K. Popper,et al.  Conjectures and refutations;: The growth of scientific knowledge , 1972 .

[228]  N. Bohr The Quantum Postulate and the Recent Development of Atomic Theory , 1928, Nature.

[229]  M. Crowe Theories of the World from Antiquity to the Copernican Revolution , 1990 .

[230]  Michael V Berry,et al.  Semiclassical approximations in wave mechanics , 1972 .