This chapter has three main aims. First, it gives a pedagogical introduction to Noether’s two theorems and their implications for energy conservation in general relativity, which was a central point of discussion between Hilbert, Klein, Noether, and Einstein. Second, it introduces and compares two proposals for gravitational energy and momentum, one of which is very influential in physics, and neither of which has been discussed in the philosophical literature. Third, it assesses these proposals in connection with recent philosophical discussions of energy and momentum in general relativity. After briefly reviewing the debates about energy conservation between Hilbert, Klein, Noether, and Einstein, the chapter shows that Einstein’s gravitational energy-momentum pseudo-tensor, including its superpotential, is fixed, through Noether’s theorem, by the boundary terms in the action. That is, the freedom to add an arbitrary superpotential to the gravitational pseudo-tensor corresponds to the freedom to add boundary terms to the action without changing the equations of motion. This freedom is fixed in the same way for both problems. The chapter also includes a review of two proposals for energy and momentum in GR: one is a quasi-local alternative to the local expressions, and the other builds on Einstein’s local pseudo-tensor approach.

This chapter considers the metaphysics of geometric and non-geometric objects as they appear in physical theories such as general relativity, and the interactions between these considerations and the contemporary doctrines of perspectivalism and fragmentalism in the philosophy of science. Taking (following Quine) a kind’s being associated with a projectable predicate as a necessary condition for its being natural, there is a sense in which geometric objects can be assimilated to natural kinds but non-geometric objects cannot; this affords a rational reconstruction of philosophers’ and physicists’ suspicion of the latter (although this verdict can also be questioned). Even granting this, non-geometric objects can nevertheless represent real quantities in a perspectival sense-this is one way in which the perspectival realism doctrine can be endorsed. Moreover, recognising that non-geometric objects can represent real quantities in a perspectival sense affords support for fragmentalism: the view (at least in part) that frame-dependent effects are physically real. That said, one can argue that perspectivalism is superior to fragmentalism. In one sense, perspectivalism should be congenial to proponents of the ‘dynamical approach’ to spacetime theories-however, the pairing is imperfect. Endorsing perspectivalism/fragmentalism in this sense does not commit one to endorsing related-but arguably more opaque-‘structuralist’ views.