We showcase a new framework for the analysis of symmetries in physical theory via the application to the problem of differentiating intuitively background dependent theories, such as diffeomorphism invariant special relativity, from intuitively background independent theories, such as general relativity. Within our framework certain structures (nomic, temporal) are classified as absolute or relative with respect to certain transformations depending on their transformation properties.
The case of particular relevance to the isolation of background independent temporal structure is ‘surplus structure’. A structure is ‘surplus structure’ with respect to a set of transformations when it is relative whilst the nomic structure is absolute. Spacetime foliation structure is surplus structure under the push-forward of diffeomorphisms in both general relativity and diffeomorphism invariant special relativity. A weak notion of background independent structure as surplus structure under the push-forward of diffeomorphisms cannot therefore be used as a means to differentiate the two theories. This accords with the magisterial analysis of Pooley (2017).
To resolve this issue we draw upon the canonical gravity formalism to suggest a stronger notion of background independent structure as surplus structure under ‘contrastive automorphisms’. These are not the push-forward of diffeomorphisms but nevertheless correspond to hypersurface deformations with respect to which the nomic structure of general relativity is absolute. Our strong notion of background independence of foliation structure can (plausibly) be isolated as the salient differentiating feature of intuitively background independent theories.
Philosophy of Physics Seminar Convenors for MT19: Tushar Menon, Adam Caulton and Chris Timpson