Suppose that one thinks that certain symmetries of a theory reveal "surplus structure". What would a formalism without that surplus structure look like? The conventional answer is that it would be a reduced theory: a theory which tra cs only in structures invariant under the relevant symmetry. In this paper, I argue that there is a neglected alternative: one can work with a sophisticated version of the theory, in which the symmetries act as isomorphisms.

There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation (i.e., Newton-Cartan theory). We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized (gauge-free) theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation.Email address: weatherj@uci.edu (James Owen Weatherall) 1 See, for instance, Misner et al. (1973, pp. 466-468), for a classic argument that there cannot be a local notion of energy associated with gravitation in general relativity; see also Choquet-Brouhat (1983), Goldberg (1980, and Curiel (2017) for other arguments and discussion.

This paper gives an explicit presentation of Newtonian gravitation on the backdrop of Maxwell spacetime, giving a sense in which acceleration is relative in gravitational theory. However, caution is needed: assessing whether this is a robust or interesting sense of the relativity of acceleration depends upon some subtle technical issues, and upon substantive philosophical questions over how to identify the spacetime structure of a theory. (London, ON) and Foundations of Physics Conference (London, UK) for questions and feedback; and to several anonymous referees for very helpful and detailed comments.

In this paper, I consider the role of exact symmetries in theories of physics, working throughout with the example of gravitation set in Newtonian spacetime. First, I spend some time setting up a means of thinking about symmetries in this context; second, I consider arguments from the seeming undetectability of absolute velocities to an anti-realism about velocities; and finally, I claim that the structure of the theory licences (and perhaps requires) us to interpret models which differ only with regards to the absolute velocities of objects as depicting the same physical state of affairs. In defending this last claim, I consider how ideas and resources from the philosophy of language may usefully be brought to bear on this topic.