Substantive general covariance and the Einstein-Klein dispute: A Noetherian approach

TL;DR

This paper uses Noether's second theorem to clarify the debate over conserved quantities in General Relativity, distinguishing between genuine physical charges and gauge artifacts, and relates this to background independence.

Contribution

It applies Noether's second theorem to analyze the substantive nature of general covariance and its role in defining conserved quantities in gravity theories.

Findings

Noether's second theorem helps distinguish real charges from gauge artifacts.

The analysis clarifies the role of diffeomorphism symmetry in physical charges.

Connections are made between substantive covariance and background independence.

Abstract

Famously, Klein and Einstein were embroiled in an epistolary dispute over whether General Relativity has any physically meaningful conserved quantities. In this paper, we explore the consequences of Noether's second theorem for this debate, and connect it to Einstein's search for a `substantive' version of general covariance as well as his quest to extend the Principle of Relativity. We will argue that Noether's second theorem provides a clear way to distinguish between theories in which gauge or diffeomorphism symmetry is doing real work in defining charges, as opposed to cases in which this symmetry stems from Kretchmannization. Finally, we comment on the relationship between this Noetherian form of substantive general covariance and the notion of `background independence'.