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Summary General Relativity is our best large-scale physical theory. One often investigates which philosophical consequences follow from the theory. 
Key works Sklar 1974 is an early text. Earman 1995 is the definitive modern survey of philosophical topics. Malament 2012 is a self-contained primer to the mathematical and logical foundations. 
Introductions Glymour 1972, Malament 1984, Earman & Norton 1987, Wüthrich 2009, Manchak 2009
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  1. Claes Åberg (1974). Relativity Phenomena in Set Theory. Synthese 27 (1-2):189 - 198.
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  2. 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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  3. Alexander Afriat & Ermenegildo Caccese (2010). The Relativity of Inertia and Reality of Nothing. Studies in History and Philosophy of Science Part B 41 (1):9-26.
    The determination of inertia by matter is looked at in general relativity, where inertia can be represented by affine or projective structure. The matter tensor T seems to underdetermine affine structure by ten degrees of freedom, eight of which can be eliminated by gauge choices, leaving two. Their physical meaning---which is bound up with that of gravitational waves and the pseudotensor t, and with the conservation of energy-momentum---is considered, along with the dependence of reality on invariance and of causal explanation (...)
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  4. Alexander Afriat & Ermenegildo Caccese (2010). The Relativity of Inertia and Reality of Nothing. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):9-26.
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  5. Y. Aharonov & G. Carmi (1973). Quantum Aspects of the Equivalence Principle. Foundations of Physics 3 (4):493-498.
    Two thought experiments are discussed which suggest, first, a geometric interpretation of the concept of a (say, vector) potential (i.e., as a kinematic quantity associated with a transformation between moving frames of reference suitably related to the problem) and, second, that, in a quantum treatment one should extend the notion of the equivalence principle to include not only the equivalence of inertial forces with suitable “real” forces, but also the equivalence of potentials of such inertial forces and the potentials of (...)
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  6. R. Ainscough (1922). Some Remarks on Relativity. Mind 31 (124):489-495.
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  7. Marcus Alfred, Petero Kwizera, James V. Lindesay & H. Pierre Noyes (2004). A Nonperturbative, Finite Particle Number Approach to Relativistic Scattering Theory. Foundations of Physics 34 (4):581-616.
    We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a nonperturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the nonrelativistic limit to the nonrelativistic Faddeev equations. The aim of this (...)
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  8. Marcus Alfred & James Lindesay (2003). A Test of the Calculability of a Three-Body Relativistic, Cluster Decomposable, Unitary, Covariant Scattering Theory. Foundations of Physics 33 (8):1253-1264.
    In this work a calculation of the cluster decomposable formalism for relativistic scattering as developed by Lindesay, Markevich, Noyes, and Pastrana (LMNP) is made for an ultra-light quantum model. After highlighting areas of the theory vital for calculation, a description is made of the process to go from the general theory to an eigen-integral equation for bound state problems, and calculability is demonstrated. An ultra-light quantum exchange model is then developed to examine calculability.
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  9. C. C. Allen (1933). Is the Theory of Relativity Sound? Australasian Journal of Philosophy 11 (4):293 – 299.
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  10. C. C. Allen (1933). Is the Theory of Relativity Sound? Australasian Journal of Psychology and Philosophy 11 (4):293-299.
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  11. Valia Allori (2016). Space, Time, and (How They) Matter: A Discussion About Some Metaphysical Insights Provided by Our Best Fundamental Physical Theories. In G. C. Ghirardi & S. Wuppuluri (eds.), Space, Time, and The Limits of Human Understanding. Springer. pp. 95-107.
    This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I conclude the discussion by (...)
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  12. Ben Almassi (2009). Trust in Expert Testimony: Eddington's 1919 Eclipse Expedition and the British Response to General Relativity. Studies in History and Philosophy of Science Part B 40 (1):57-67.
  13. C. Marcio do Amaral (1969). Flat-Space Metric in the Quaternion Formulation of General Relativity. Rio De Janeiro, Centro Brasileiro De Pesquisas Físicas.
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  14. Jeeva S. Anandan (1980). Quantum Interference and the Gravitational Field. In A. R. Marlow (ed.), Quantum Theory and Gravitation. Academic Press. pp. 1--157.
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  15. Jeeva Anandan & Harvey R. Brown (1995). On the Reality of Space-Time Geometry and the Wavefunction. Foundations of Physics 25 (2):349--60.
    The action-reaction principle (AR) is examined in three contexts: (1) the inertial-gravitational interaction between a particle and space-time geometry, (2) protective observation of an extended wave function of a single particle, and (3) the causal-stochastic or Bohm interpretation of quantum mechanics. A new criterion of reality is formulated using the AR principle. This criterion implies that the wave function of a single particle is real and justifies in the Bohm interpretation the dual ontology of the particle and its associated wave (...)
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  16. James L. Anderson (1971). Covariance, Invariance, and Equivalence: A Viewpoint. General Relativity and Gravitation 2:161--72.
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  17. Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely, A Logic Road From Special to General Relativity.
    We present a streamlined axiom system of special relativity in firs-order logic. From this axiom system we ``derive'' an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
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  18. Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely (2012). A Logic Road From Special Relativity to General Relativity. Synthese 186 (3):633 - 649.
    We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
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  19. Roger Bernard Angel (1970). Relativity and Covariance. Dissertation, Mcgill University (Canada)
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  20. G. S. Asanov (1983). Gravitational Field Equations Based on Finsler Geometry. Foundations of Physics 13 (5):501-527.
    The analysis of a previous paper (see Ref. 1), in which the possibility of a Finslerian generalization of the equations of motion of gravitational field sources was demonstrated, is extended by developing the Finslerian generalization of the gravitational field equations on the basis of the complete contractionK = K lj lj of the Finslerian curvature tensorK l j hk (x, y). The relevant Lagrangian is constructed by the replacement of the directional variabley i inK by a vector fieldy i (x), (...)
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  21. G. S. Asanov (1981). A Finslerian Extension of General Relativity. Foundations of Physics 11 (1-2):137-154.
    A Finslerian extension of general relativity is examined with particular emphasis on the Finslerian generalization of the equation of motion in a gravitational field. The construction of a gravitational Lagrangian density by substituting the osculating Riemannian metric tensor in the Einstein density is studied. Attention is drawn to an interesting possibility for developing the theory of test bodies against the Finslerian background.
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  22. William K. Atkins (1983). A Fundamental Quadratic Variational Principle Underlying General Relativity. Foundations of Physics 13 (5):545-552.
    The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed.
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  23. Jonathan Bain (2004). Theories of Newtonian Gravity and Empirical Indistinguishability. Studies in History and Philosophy of Modern Physics 35 (3):345--76.
    In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’’ version and a ‘‘strong’’ version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. (...)
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  24. Jonathan Bain (1998). Whitehead's Theory of Gravity. Studies in History and Philosophy of Modern Physics 29 (4):547-574.
    In 1922 in The Principle of Relativity, Whitehead presented an alternative theory of gravitation in response to Einstein’s general relativity. To the latter, he objected on philosophical grounds—specifically, that Einstein’s notion of a variable spacetime geometry contingent on the presence of matter (a) confounds theories of measurement, and, more generally, (b) is unacceptable within the bounds of a reasonable epistemology. Whitehead offered instead a theory based within a comprehensive philosophy of nature. The formulal Whitehead adopted for the gravitational field has (...)
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  25. Julian B. Barbour (1995). General Relativity as a Perfectly Machian Theory. In Julian B. Barbour & H. Pfister (eds.), Mach's Principle: From Newton's Bucket to Quantum Gravity. Birkhäuser. pp. 214--36.
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  26. C. Barceló, L. J. Garay & G. Jannes (2011). Quantum Non-Gravity and Stellar Collapse. Foundations of Physics 41 (9):1532-1541.
    Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects $E_{\rm B}$ (related to the Planck scale) and the much higher scale $E_{\rm L}$ signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: $E_{\rm L}$ is the energy scale below which a special relativistic spacetime emerges, (...)
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  27. Carlos Barceló & Gil Jannes (2008). A Real Lorentz-FitzGerald Contraction. Foundations of Physics 38 (2):191-199.
    Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and the (...)
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  28. Thomas Bartelborth (1993). Hierarchy Versus Holism: A Structuralist View on General Relativity. [REVIEW] Erkenntnis 39 (3):383 - 412.
    The philosophical debate whether the epistemological and conceptual structure of science is better characterized as hierarchical or as holistic cannot be decideda priori. A case study on general relativity should help to clarify our representation of this section of physics. For this purpose Sneed's model-theoretic approach is used to reconstruct the structure of relativity. The proposed axiomatization of general relativity takes into account approximations and utilizes local models for a realistic view on the functioning of the theory. A central objective (...)
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  29. Andreas Bartels (1987). Kausalität Ohne Vorhersagbarkeit — Eine These Des Empirismus Im Konflikt MIT der Allgemeinen Relativitätstheorie. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 18 (1-2):50-60.
    Empiricists mostly prefer an epistemic notion of causality intending thereby to avoid metaphysical entanglements. General relativity however provides examples for causality without predictability, i. e. world models in which for geometrical reasons there exist no spacelike hypersurfaces containing traces of all future events. Yet local determinism for every single event remains valid in these cases. Therefore the problem arises how to account for a causal structure that implies local but not global predictability. This problem, it is argued, cannot be solved (...)
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  30. A. O. Barut (1988). Combining Relativity and Quantum Mechanics: Schrödinger's Interpretation of Ψ. [REVIEW] Foundations of Physics 18 (1):95-105.
    The incongruence between quantum theory and relativity theory is traced to the probability interpretation of the former. The classical continium interpretation of ψ removes the difficulty. How quantum properties of matter and light, and in particular the radiative problems, like spontaneous emission and Lamb shift, may be accounted in a first quantized Maxwell-Dirac system is discussed.
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  31. Oleg Bazaluk (ed.) ( 2012). Philosophy and Cosmology 2012 (The Journal of International Society of Philosophy and Cosmology (ISPC) ). ISPC.
    The Journal «Philosophy and Cosmology» (ISSN 2307-3705) was established by Oleg Bazaluk as a press organ of International Society of Philosophy and Cosmology at 2004. This Society was established in the setting of Pereyaslav-Khmelnitskiy State Pedagogical University. Initially the Journal was printed as a special edition of Ukrainian philosophical journal «Sententiae» (Editor-in-Chief - Oleg Khoma) and covered scientific and philosophical researches of the space problematic. Since 2008, Journal «Philosophy and Cosmology» is an independent printed issue. Since 2009, together with coming (...)
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  32. R. G. Beil (2003). Finsler Geometry and Relativistic Field Theory. Foundations of Physics 33 (7):1107-1127.
    Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.
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  33. Jacob D. Bekenstein & Asaf Oron (2001). Extended Kelvin Theorem in Relativistic Magnetohydrodynamics. Foundations of Physics 31 (6):895-907.
    We prove the existence of a generalization of Kelvin's circulation theorem in general relativity which is applicable to perfect isentropic magnetohydrodynamic flow. The argument is based on a new version of the Lagrangian for perfect magnetohydrodynamics. We illustrate the new conserved circulation with the example of a relativistic magnetohydrodynamic flow possessing three symmetries.
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  34. A. B. Bell & D. M. Bell (1975). A Highly Ordered Universe. Foundations of Physics 5 (3):455-480.
    A highly ordered universe is described in terms of neutrino and electrino alone as basic particles, and length and time alone as dimensional units. New theories are obtained of particles, nuclides, atomic spectra, general relativity, and gravitation.
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  35. Gordon Belot (2013). Time in Classical and Relativistic Physics. In Adrian Bardon & Heather Dyke (eds.), A Companion to the Philosophy of Time. Blackwell. pp. 185-200.
    This is a short, nontechnical introduction to features of time in classical and relativistic physics and their representation in the four-dimensional geometry of spacetime. Topics discussed include: the relativity of simultaneity in special and general relativity; the ‘twin paradox’ and differential aging effects in special and general relativity; and time travel in general relativity.
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  36. Gordon Belot (2011). Background-Independence. General Relativity and Gravitation 43:2865-2884.
    Intuitively, a classical field theory is background-in- dependent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation (...)
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  37. Gordon Belot (2007). The Representation of Time and Change in Mechanics. In John Earman & Jeremy Butterfield (eds.), Philosophy of Physics. Elsevier. pp. 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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  38. Gordon Belot (1996). Why General Relativity Does Need an Interpretation. Philosophy of Science 63 (3):88.
    There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I illustrate (...)
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  39. Gordon Belot, John Earman & Laura Ruetsche (1999). The Hawking Information Loss Paradox: The Anatomy of a Controversy. British Journal for the Philosophy of Science 50 (2):189-229.
    Stephen Hawking has argued that universes containing evaporating black holes can evolve from pure initial states to mixed final ones. Such evolution is non-unitary and so contravenes fundamental quantum principles on which Hawking's analysis was based. It disables the retrodiction of the universe's initial state from its final one, and portends the time-asymmetry of quantum gravity. Small wonder that Hawking's paradox has met with considerable resistance. Here we use a simple result for C*-algebras to offer an argument for pure-to-mixed state (...)
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  40. Thomas Benda (2013). An Axiomatic Foundation of Relativistic Spacetime. Synthese 192 (7):1-16.
    An ab-initio foundation for relativistic spacetime is given, which is a conservative extension of Zermelo’s set theory with urelemente. Primitive entities are worldlines rather than spacetime points. Spacetime points are sets of intersecting worldlines. By the proper axioms, they form a manifold. Entities known in differential geometry, up to a metric, are defined and have the usual properties. A set-realistic point of view is adopted. The intended ontology is a set-theoretical hierarchy with a broad base of the empty set and (...)
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  41. William Bender (1958). An Introduction to Scale Coordinate Physics an Introduction to the Formalization of the Macro Operational Point of View. Burgess Pub. Co.
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  42. Peter G. Bergmann (1991). Einstein and the History of General RelativityDon Howard John Stachel. Isis 82 (4):769-769.
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  43. Peter Gabriel Bergmann (1969). The Riddle of Gravitation. London: J. Murray.
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  44. Peter Gabriel Bergmann (1942). Introduction to the Theory of Relativity. New York: Prentice-Hall.
    Comprehensive coverage of the special theory (frames of reference, Lorentz transformation, relativistic mechanics of mass points, more), the general theory ...
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  45. Alexander Blum, Roberto Lalli & Jürgen Renn (2015). The Reinvention of General Relativity: A Historiographical Framework for Assessing One Hundred Years of Curved Space-Time. Isis 106 (3):598-620.
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  46. Frank Blume (2006). A Nontemporal Probabilistic Approach to Special and General Relativity. Foundations of Physics 36 (9):1404-1440.
    We introduce a discrete probabilistic model of motion in special and general relativity that is shown to be compatible with the standard model in the statistical limit.
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  47. Hermann Bondi (1970). General Relativity as an Open Theory. In Hermann Bondi, Wolfgang Yourgrau & Allen duPont Breck (eds.), Physics, Logic, and History. New York: Plenum Press. pp. 265--276.
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  48. Hermann Bondi (1967). Assumption and Myth in Physical Theory. --. University Press.
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  49. Hermann Bondi (1964). Relativity and Common Sense. Garden City, N.Y., Anchor Books.
    Radically reoriented presentation of Einstein's Special Theory and one of most valuable popular accounts available derives relativity from Newtonian ideas, ...
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  50. Giovanni Boniolo & Fernando de Felice (2000). On the Philosophical Foundations of Measurements in General Relativity. Foundations of Physics 30 (10):1629-1641.
    In this paper, first, the question of what a measurement is in General Relativity is tackled; then, some foundational problems it involves are analysed. In particular, by recalling what a measurement is in general, we will try to precisely define what it is in General Relativity. Then, we will analyse, by means of a suitable example, some foundational problems it involves. It will be stressed that such foundational problems do not arise owing to the gauge invariance or the correlation among (...)
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