8 - Noether’s First Theorem and the Energy-Momentum Tensor Ambiguity Problem

Summary

Using the converse of Noether’s first theorem, this chapter shows that the Bessel-Hagen-type transformations are uniquely selected in the case of electrodynamics, which powerfully dissolves the methodological ambiguity at hand. It then considers how this line of argument applies to a variety of other cases, including in particular the challenge of defining an energy-momentum tensor for the gravitational field in linearised gravity. Finally, the search for proper Noether energy-momentum tensors is put into context with recent claims that Noether’s theorem and its converse make statements on equivalence classes of symmetries and conservation laws. The aim is to identify clearly the limitations of this latter move, and to develop this position by contrast with recent philosophical discussions about how symmetries relate to the representational capacities of theories.