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H. Gomes

Publications and source records attributed to H. Gomes.

3 recordsLinked to original sources

Functionalism as a Species of Reduction

This is the first of four papers prompted by a recent literature about a doctrine dubbed spacetime functionalism. This paper gives our general framework for discussing functionalism. Following Lewis, we take it as a species of reduction. We start by expounding reduction in a broadly Nagelian sense. Then we argue that Lewis's functionalism is an improvement on Nagelian reduction. This paper thereby sets the scene for the other papers, which will apply our framework to theories of space and time. Overall, we come to praise spacetime functionalism, not to bury it. But we criticize the recent philosophical literature for failing to stress: (i) functionalism's being a species of reduction (in particular: reduction of chrono-geometry to the physics of matter and radiation); (ii) functionalism's idea of specifying several concepts simultaneously by their roles; (iii) functionalism's providing bridge laws that are mandatory, not optional: they are statements of identity (or co-extension) that are conclusions of a deductive argument; and once we infer them, we have a reduction in a Nagelian sense. On the other hand, some of the older philosophical literature, and the mathematical physics literature, is faithful to these ideas (i) to (iii). In various papers, falling under various research programmes, the unique definability of a chrono-geometric concept (or concepts) in terms of matter and radiation, and a corresponding bridge law and reduction, is secured by a precise theorem. Hence our desire to celebrate these results as rigorous renditions of spacetime functionalism.

physics.hist-ph

Lorentz Invariance in Shape Dynamics

Shape dynamics is a reframing of canonical general relativity in which time reparametrization invariance is "traded" for a local conformal invariance. We explore the emergence of Lorentz invariance in this model in three contexts: as a maximal symmetry, an asymptotic symmetry, and a local invariance.

gr-qc

Frequently asked questions about Shape Dynamics

Barbour's interpretation of Mach's principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, "shapes." Recently, it was shown that the dynamics of General Relativity can indeed be formulated as the dynamics of shapes. This new Shape Dynamics theory, unlike earlier proposals by Barbour and his collaborators, implements local spatial conformal invariance as a gauge symmetry that replaces refoliation invariance in General Relativity. It is the purpose of this paper to answer frequent questions about (new) Shape Dynamics, such as its relation to Poincaré invariance, General Relativity, Constant Mean (extrinsic) Curvature gauge, earlier Shape Dynamics, and finally the conformal approach to the initial value problem of General Relativity. Some of these relations can be clarified by considering a simple model: free electrodynamics and its dual shift symmetric formulation. This model also serves as an example where symmetry trading is used for usual gauge theories.

gr-qc