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  1. Deanna Abernethy & John R. Klauder (2005). The Distance Between Classical and Quantum Systems. Foundations of Physics 35 (5):881-895.
    In a recent paper, a “distance” function, $\cal D$ , was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a “distance”, D, which measures the distance between either pure or impure classical and quantum states. We also compare the new distance formula with the previous formula, when the latter is applicable. To illustrate these distances, we have used 2 × 2 matrix examples and two-dimensional vectors for simplicity and (...)
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  2. Carl G. Adler (1980). Why is Mechanics Based on Acceleration? Philosophy of Science 47 (1):146-152.
    The unique role of the second derivative of position with respect to time in classical mechanics is investigated. It is indicated that mechanics might have been developed around other order derivatives. Examples based on $\overset \ldots \to{x}$ and $\overset....\to{x}$ are presented. Kirchhoff's argument for using ẍ is given and generalized.
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  3. Diederik Aerts (1996). Relativity Theory: What is Reality? [REVIEW] Foundations of Physics 26 (12):1627-1644.
    In classical Newtonian physics there was a clear understanding of “what reality is.≓ Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in “the present.≓ Often it is stated that three-dimensional space and one-dimensional time hare been substituted by four-dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that which is “present,≓ cannot be retained. Is reality then the (...)
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  4. John Aidun (1982). Aristotelian Force as Newtonian Power. Philosophy of Science 49 (2):228-235.
    Aristotle's rule of proportions of the factors of motion, presented in VII 5 of the Physics, characterizes Aristotelian force. Observing that the locomotion to which Aristotle applied the Rule is the motion produced by manual labor, I develop an interpretation of the factors of motion that reveals that Aristotelian force is Newtonian power. An alternate interpretation of the Rule by Toulmin and Goodfield implicitly identifies Aristotelian force with Newtonian force. In order to account for the absence of an acceleration in (...)
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  5. E. J. Aiton (1970). Essays in the History of Mechanics. Studies in History and Philosophy of Science Part A 1 (3):265-273.
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  6. Valia Allori & Nino Zanghi (2008). On the Classical Limit of Quantum Mechanics. Foundations of Physics 10.1007/S10701-008-9259-4 39 (1):20-32.
    Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing (...)
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  7. Joseph S. Alper & Mark Bridger (1998). Newtonian Supertasks: A Critical Analysis. Synthese 114 (2):355-369.
    In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at (...)
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  8. Martin S. Altschul (1978). Coordinate Transformations and the Theory of Measurement. Foundations of Physics 8 (1-2):69-92.
    We discuss the criteria for deriving new information from coordinate transformations, focusing on the property of implementability, or measurability in practice. We contrast the role of coordinate transformations in classical and quantum physics, and demonstrate that many well-known applications fail to meet the criteria for new information. Finally, we discuss some mathematical properties of the coordinate transformations, and then relate these properties to a practical measurement scheme.
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  9. J. Anandan (1980). On the Hypotheses Underlying Physical Geometry. Foundations of Physics 10 (7-8):601-629.
    The relationship between physics and geometry is examined in classical and quantum physics based on the view that the symmetry group of physics and the automorphism group of the geometry are the same. Examination of quantum phenomena reveals that the space-time manifold is not appropriate for quantum theory. A different conception of geometry for quantum theory on the group manifold, which may be an arbitrary Lie group, is proposed. This provides a unified description of gravity and gauge fields as well (...)
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  10. James L. Anderson (1990). Newton's First Two Laws Are Not Definitions. American Journal of Physics 58 (12):1192--5.
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  11. S. M. Anlage (2000). Book Review: Quantum Chaos-An Introduction. [REVIEW] Foundations of Physics 30 (7):1135-1138.
  12. Y. Avishai & H. Ekstein (1972). Causal Independence. Foundations of Physics 2 (4):257-270.
    Causal independence of the simultaneous positions and momenta of two distinguishable particles in nonrelativistic physics and causal independence of events in two relatively spacelike regions of space-time in relativity are analyzed and discussed. This review paper formulates causal independence in a general and operational way and summarizes the inferences drawn from it in non-relativistic quantum mechanics, classical relativistic point mechanics, quantum field theory, and classical field theory. Special attention is given to the open question of the relationship between local independence (...)
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  13. Alexander Bach (1988). The Concept of Indistinguishable Particles in Classical and Quantum Physics. Foundations of Physics 18 (6):639-649.
    The consequences of the following definition of indistinguishability are analyzed. Indistinguishable classical or quantum particles are identical classical or quantum particles in a state characterized by a probability measure, a statistical operator respectively, which is invariant under any permutation of the particles. According to this definition the particles of classical Maxwell-Boltzmann statistics are indistinguishable.
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  14. Massimiliano Badino (forthcoming). Bridging Conceptual Gaps: The Kolmogorov-Sinai Entropy. Isonomía.
    The Kolmogorov-Sinai entropy is a fairly exotic mathematical concept which has recently aroused some interest on the philosophers’ part. The most salient trait of this concept is its working as a junction between such diverse ambits as statistical mechanics, information theory and algorithm theory. In this paper I argue that, in order to understand this very special feature of the Kolmogorov-Sinai entropy, is essential to reconstruct its genealogy. Somewhat surprisingly, this story takes us as far back as the beginning of (...)
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  15. C. D. Bailey (2002). The Unifying Laws of Classical Mechanics. Foundations of Physics 32 (1):159-176.
    It is shown that, at the time of Euler and Lagrange, a belief led to an assumption. The assumption is applied to derive the principle of least action from the vis viva. The assumption is also applied to derive Hamilton's principles from the vis viva. It is shown that Hamilton, in his 1834 paper, countered the assumption of the earlier mathematicians. Finally, Hamilton's law, completely independent of the principle of least action and Hamilton's principles, is obtained to verify the foregoing (...)
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  16. Cecil D. Bailey (1983). Hamilton's Law or Hamilton's Principle: A Response to Ulvi Yurtsever. [REVIEW] Foundations of Physics 13 (5):539-544.
    The law of varying action and Hamilton's principle of classical mechanics are discussed. It is now clear that the law of varying action, introduced by Hamilton in his papers of 1834 and 1935, was never recognized by either the mathematicians or other scientists who followed him. Why this occurred is discussed in this paper.
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  17. Cecil D. Bailey (1981). On a More Precise Statement of Hamilton's Principle. Foundations of Physics 11 (3-4):279-296.
    It has been recognized in the literature of the calculus of variations that the classical statement of the principle of least action (Hamilton's principle for conservative systems) is not strictly correct. Recently, mathematical proofs have been offered for what is claimed to be a more precise statement of Hamilton's principle for conservative systems. According to a widely publicized version of this more precise statement, the action integral for conservative systems is a minimum for discrete systems for small time intervals only (...)
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  18. Franz Balsiger & Alex Burri (1990). Sind Die Klassische Mechanik Und Die Spezielle Relativitätstheorie Kommensurabel? Journal for General Philosophy of Science 21 (1):157-162.
    In its first part, this paper shows why a recently made attempt to reduce the special theory of relativity to Newtonian kinematics is bound to fail. In the second part, we propose a differentiated notion of incommensurability which enables us to amend the contention that the special theory of relatively and Newtonian kinematics are “incommensurable”.
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  19. A. O. Barut & N. Ünal (1993). On Poisson Brackets and Symplectic Structures for the Classical and Quantum Zitterbewegung. Foundations of Physics 23 (11):1423-1429.
    The symplectic structures (brackets, Hamilton's equations, and Lagrange's equations) for the Dirac electron and its classical model have exactly the same form. We give explicitly the Poisson brackets in the dynamical variables (x μ,p μ,v μ,S μv). The only difference is in the normalization of the Dirac velocities γμγμ=4 which has significant consequences.
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  20. David Batchelor (2002). Erratum: “Semiclassical Models for Virtual Antiparticle Pairs, the Unit of Charge E, and the QCD Couplings Αs”. [REVIEW] Foundations of Physics 32 (2):333-333.
    New semiclassical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields ≈ℏ/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. When (...)
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  21. Robert W. Batterman (1991). Chaos, Quantization, and the Correspondence Principle. Synthese 89 (2):189 - 227.
  22. Christopher Belanger (2013). On Two Mathematical Definitions of Observational Equivalence: Manifest Isomorphism and Epsilon-Congruence Reconsidered. Studies in History and Philosophy of Science Part B 44 (2):69-76.
    In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence (...)
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  23. Ori Belkind (2007). Newton's Conceptual Argument for Absolute Space. International Studies in the Philosophy of Science 21 (3):271 – 293.
    While many take Newton's argument for absolute space to be an inference to the best explanation, some argue that Newton is primarily concerned with the proper definition of true motion, rather than with independent existence of spatial points. To an extent the latter interpretation is correct. However, all prior interpretations are mistaken in thinking that 'absolute motion' is defined as motion with respect to absolute space. Newton is also using this notion to refer to the quantity of motion (momentum). This (...)
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  24. Gordon Belot (2007). The Representation of Time and Change in Mechanics. In John Earman & Jeremy Butterfield (eds.), Philosophy of Physics. Elsevier. 133--227.
    This chapter is concerned with the representation of time and change in classical (i.e., non-quantum) physical theories. One of the main goals of the chapter is to attempt to clarify the nature and scope of the so-called problem of time: a knot of technical and interpretative problems that appear to stand in the way of attempts to quantize general relativity, and which have their roots in the general covariance of that theory. The most natural approach to these questions is via (...)
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  25. Gordon Belot & John Earman (1997). Chaos Out of Order: Quantum Mechanics, the Correspondence Principle and Chaos. Studies in History and Philosophy of Science Part B 28 (2):147-182.
  26. Gordon Belot & Lina Jansson (2010). Alisa Bokulich, Reexamining the Quantum-Classical Relation: Beyond Reductionism and Pluralism , Cambridge University Press, Cambridge (2008) ISBN 978-0-521-85720-8 Pp. X+195. [REVIEW] Studies in History and Philosophy of Science Part B 41 (1):81-83.
  27. Vieri Benci (1999). Quantum Phenomena in a Classical Model. Foundations of Physics 29 (1):1-28.
    This work is part of a program which has the aim to investigate which phenomena can be explained by nonlinear effects in classical mechanics and which ones require the new axioms of quantum mechanics. In this paper, we construct a nonlinear field equation which admits soliton solutions. These solitons exibit a dynamics which is similar to that of quantum particles.
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  28. Vieri Benci & Donato Fortunato (1998). A New Variational Principle for the Fundamental Equations of Classical Physics. Foundations of Physics 28 (2):333-352.
    In this paper we introduce a variational principle from which the fundamental equations of classical physics can be deduced. This principle permits a sort of unification of the gravitational and the electromagnetic fields. The basic point of this variational principle is that the world-line of a material point is parametrized by a parameter a which carries some physical information, namely it is related to the rest mass and to the charge. In particular, the (inertial) rest mass will not be a (...)
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  29. M. K. Bennett & D. J. Foulis (1990). Superposition in Quantum and Classical Mechanics. Foundations of Physics 20 (6):733-744.
    Using the mathematical notion of an entity to represent states in quantum and classical mechanics, we show that, in a strict sense, proper superpositions are possible in classical mechanics.
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  30. J. D. Bernal (1972). The Extension of Man: A History of Physics Before the Quantum. Cambridge,M.I.T. Press.
  31. M. Berry (2010). Alisa Bokulich * Reexamining the Quantum-Classical Relation: Beyond Reductionism and Pluralism. British Journal for the Philosophy of Science 61 (4):889-895.
  32. D. I. Blokhint͡sev (1968). The Philosophy of Quantum Mechanics. New York, Humanities.
  33. D. Bohm & B. J. Hiley (1981). On a Quantum Algebraic Approach to a Generalized Phase Space. Foundations of Physics 11 (3-4):179-203.
    We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms of a matrix algebra in a phase space. This makes clear not only the similarities of the two theories, but also certain essential differences, and lays a foundation for understanding their relationship. We use the Wigner-Moyal transformation as a change of representation in phase space, and we avoid the problem of “negative probabilities” by regarding (...)
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  34. Niels Bohr (1931). Maxwell and Modern Theoretical Physics. Nature 128:691--692.
  35. Peter Bokulich (2005). Niels Bohr's Generalization of Classical Mechanics. Foundations of Physics 35 (3):347-371.
    We clarify Bohr’s interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible.
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  36. Timothy H. Boyer (2012). The Blackbody Radiation Spectrum Follows From Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics. Foundations of Physics 42 (5):595-614.
    The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell’s equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation (...)
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  37. Stephen Breen & Peter D. Skiff (1977). Identical Motion in Relativistic Quantum and Classical Mechanics. Foundations of Physics 7 (7-8):589-596.
    The Klein-Gordon equation for the stationary state of a charged particle in a spherically symmetric scalar field is partitioned into a continuity equation and an equation similar to the Hamilton-Jacobi equation. There exists a class of potentials for which the Hamilton-Jacobi equation is exactly obtained and examples of these potentials are given. The partitionAnsatz is then applied to the Dirac equation, where an exact partition into a continuity equation and a Hamilton-Jacobi equation is obtained.
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  38. Anastasios Brenner, Paul Needham, David Stump & Robert Deltete (2011). New Perspectives on Pierre Duhem's The Aim and Structure of Physical Theory. Metascience 20 (1):1-25.
    New perspectives on Pierre Duhem’s The aim and structure of physical theory Content Type Journal Article DOI 10.1007/s11016-010-9467-3 Authors Anastasios Brenner, Department of Philosophy, Paul Valéry University-Montpellier III, Route De Mende, 34199 Montpellier cedex 5, France Paul Needham, Department of Philosophy, University of Stockholm, 10691 Stockholm, Sweden David J. Stump, Department of Philosophy, University of San Francisco, 2130 Fulton Street, San Francisco, CA 94117, USA Robert Deltete, Department of Philosophy, Seattle University, 901 12th Avenue, Seattle, WA 98122-1090, USA Journal Metascience (...)
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  39. Giorgio Brida, Maria Bondani, Ivo P. Degiovanni, Marco Genovese, Matteo G. A. Paris, Ivano Ruo Berchera & Valentina Schettini (2011). On the Discrimination Between Classical and Quantum States. Foundations of Physics 41 (3):305-316.
    With the purpose of introducing a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we address three quantumness quantifiers for bipartite optical systems: one is based on sub-shot-noise correlations, one is related to antibunching and one springs from entanglement determination. The specific cases of parametric downconversion seeded by thermal, coherent and squeezed states are discussed in detail.
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  40. John S. Briggs & Jan M. Rost (2001). On the Derivation of the Time-Dependent Equation of Schrödinger. Foundations of Physics 31 (4):693-712.
    Few have done more than Martin Gutzwiller to clarify the connection between classical time-dependent motion and the time-independent states of quantum systems. Hence it seems appropriate to include the following discussion of the origins of the time-dependent Schrödinger equation in this volume dedicated to him.
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  41. Jeffrey Bub (1970). Book Review:The Philosophy of Quantum Mechanics D. I. Blokhintsev. [REVIEW] Philosophy of Science 37 (1):153-.
  42. G. Buchdahl (1951). Science and Logic: Some Thoughts on Newton's Second Law of Motion in Classical Mechanics. British Journal for the Philosophy of Science 2 (7):217-235.
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  43. Agung Budiyono (2010). On Quantum-Classical Transition of a Single Particle. Foundations of Physics 40 (8):1117-1133.
    We discuss the issue of quantum-classical transition in a system of a single particle with and without external potential. This is done by elaborating the notion of self-trapped wave function recently developed by the author. For a free particle, we show that there is a subset of self-trapped wave functions which is particle-like. Namely, the spatially localized wave packet is moving uniformly with undistorted shape as if the whole wave packet is indeed a classical free particle. The length of the (...)
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  44. Jeremy Butterfield (2006). Against Pointillisme About Mechanics. British Journal for the Philosophy of Science 57 (4):709-753.
    This paper forms part of a wider campaign: to deny em pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, (...)
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  45. Jeremy Butterfield, Against Pointillisme About Geometry.
    This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the structure of space and-or spacetime itself, especially a paper by Bricker (1993). (...)
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  46. Jeremy Butterfield, On Symmetry and Conserved Quantities in Classical Mechanics.
    This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic coordinates, (...)
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  47. Jeremy Butterfield, On Symplectic Reduction in Classical Mechanics.
    This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light on philosophical (...)
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  48. Jeremy Butterfield, Some Aspects of Modality in Analytical Mechanics.
    This paper discusses some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to David Lewis' work on modality, especially on counterfactuals. The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. The structure of this set of ensembles remains to be explored by philosophers. The second is the way the Lagrangian and Hamiltonian approaches' variational (...)
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  49. Jeremy Butterfield, On Hamilton-Jacobi Theory as a Classical Root of Quantum Theory.
    This paper gives a technically elementary treatment of some aspects of <span class='Hi'>Hamilton</span>-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the optico-mechanical analogy and the transition to quantum mechanics. Finally, I report recent work of Holland providing a Hamiltonian formulation of the pilot-wave theory.
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  50. Craig Callender (1995). The Metaphysics of Time Reversal: Hutchison on Classical Mechanics. British Journal for the Philosophy of Science 46 (3):331-340.
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