A derivation of Einstein’s vacuum field
                    equations

Reyes, Gonzalo García

doi:10.1090/crmp/053/13

Cited by 3 publications

(3 citation statements)

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“…Or are the geodesic principle and conservation condition anomalies? Some important work has already been done on this topic: Dixon (1975) has shown a sense in which the geometrized Poisson equation is the unique dynamical principle compatible with a collection of natural assumptions in Newtonian gravitation; similarly, Sachs and Wu (1973) and Reyes (2009) have shown that there is a sense in which the (vacuum form of) Einstein's equation can be derived from (in effect) the geodesic principle, among other assumptions, and Curiel (2012) has argued that there is a sense in which the Einstein tensor is the unique tensor that can appear on the left hand side of Einstein's equation, even in the non-vacuum case. Meanwhile, Duval and Künzle (1978) and Christian (1997) have argued that even though the conservation condition in geometrized Newtonian gravitation does not follow from the geometrized Poisson equation, one can nonetheless derive it from other principles, at least if one considers Lagrangian formulations of the theory.…”

Section: Explaining Inertial Motion?mentioning

confidence: 99%

Inertial Motion, Explanation, and the Foundations of Classical Spacetime Theories

Weatherall

2017

Towards a Theory of Spacetime Theories

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I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to "explain" inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of "explain" is rather different from what one might have expected. This sense of explanation is connected with a view of theories-I call it the "puzzleball view"-on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions.

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Section: Explaining Inertial Motion?mentioning

confidence: 99%

Inertial Motion, Explanation, and the Foundations of Classical Spacetime Theories

Weatherall

2017

Towards a Theory of Spacetime Theories

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“…And indeed, several mathematicians find the theory of locales to be a good replacement for the theory of topological spaces. [In fact, there is something like a first-order axiomatization of GTR, see (Reyes 2011). ]…”

Section: Fiction: Rv Confuses Theories With Theory-formulationsmentioning

confidence: 99%

Scientific Theories

Halvorson¹

2016

Oxford Handbooks Online

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Since the beginning of the twentieth century, philosophers of science have asked, “what kind of thing is a scientific theory?” The logical positivists answered: a scientific theory is a mathematical theory, plus an empirical interpretation of that theory. They also assumed that a mathematical theory is specified by a set of axioms in a formal language. Later twentieth-century philosophers questioned this account, arguing instead that a scientific theory need not include a mathematical component or that the mathematical component need not be given by a set of axioms in a formal language. In this chapter, the author surveys the various accounts of scientific theories in twentieth-century philosophy, trying to remove some misconceptions and clear the path for future research.

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“…8 For more on synthetic differential geometry, see Kock (2006); and for applications to physics, see Mac Lane (1968), Lawvere and Schanuel (1986) and, more recently, Reyes (2011). Higher gauge theory is described by Baez and Schreiber (2007).…”

Section: Structure and Equivalence In Category Theorymentioning

confidence: 99%