General covariance from the perspective of Noether´´ s Theorems

Abstract

Questions concerning the meaning of the principle of general covariance and, perhaps to a lesser extent, its precise historical role in the development of Einstein's general theory of relativity (GR), never quite seem to go away. General covariance is a bit like the principle of equivalence: much cited, often misunderstood, and a noble, if treacherous, source of occupation for the philosopher of physics. After all, in the process of developing GR, Einstein himself got seriously confused about it in a number of ways, and his mature writings never laid the matter to rest. Our own ideas on the topic were largely the byproduct of immersion in the 1918 theorems of Emmy Noether, whose work was inspired by the attempt amongst the Gottingen mathematicians to understand the technical role of general covariance in the variational approach to GR