Inertia and the Conformal-Projective Decomposition for Nordström-Einstein-Fokker, Massive Scalar, Einstein, and Massive Spin 2 Gravities - a podcast by MCMP Team

J. Brian Pitts (Cambridge) gives a talk in the colloquium "On the Split Between Gravity and Inertia in Different Spacetime Theories" at the 17th UK and European Meeting on the Foundations of Physics (29-31 July, 2013) titled "Inertia and the Conformal-Projective Decomposition for Nordström-Einstein-Fokker, Massive Scalar, Einstein, and Massive Spin 2 Gravities". Abstract: The Ehlers-Pirani-Schild (EPS) construction, which derives a metric tensor from a projective connection and a conformal metric density, has sometimes been thought to undermine the conventionality of geometry. It might be of renewed interest due to the appearance of the dynamical or constructivist ap- proach to space-time geometry of Brown and Pooley. Constructivism shares with conventionalism the modally cosmopolitan awareness of a multiplicity of options, not all so tidy as to fit a unique geometry, leaving the ‘true’ geometry ambiguous. An EPS-inspired decomposition is applied to Nordström-Einstein-Fokker (massless spin 0) scalar gravity and its belatedly studied cousin, massive spin 0, which agree on the geometry seen by matter (conformally flat). For mas- sive scalar gravity, the symmetry group of the whole theory is the Poincaré group of Minkowski geometry, not the 15-parameter conformal group as in Nordström-Einstein-Fokker. By focusing only on the matter action, the EPS construction fails to notice the key geometrical diferences between massless and massive spin 0 theories and hence fails to address key issues motivating conventionalist and constructivist positions. For both massless and massive scalar gravities, inertia has an absolute core but is modifiable invariantly by gravity. The decomposition is then applied to Einstein’s General Relativity (mass-less spin 2) and its recently revived cousin(s), massive spin 2 gravity(s). Similar issues to the spin 0 comparison arise prima facie, but complicated by gauge freedom (in both cases but for different reasons) as well as the greater number of fields.

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