The Inception of the Noether Theorems

Abstract

Emmy Noether’s two theorems on the relation between symmetries and conservation laws were a response to the mathematical problems that arose when Einstein proposed the generally covariant equations of general relativity, and when Hilbert and Klein pursued research related to the new physical theory. They served both to elucidate the problem of the conservation of the energy-momentum tensor in that new theory, and to reconcile formulations of the law of conservation of energy that had appeared, a priori, to be quite distinct. Her first theorem also offered a vast generalization of the conservation theorems in mechanics and in the special theory of relativity that had been known at the time. Using Lie’s theory of continuous groups of transformations, she presented remarkably general results for the problem of applying the theory of differential invariants to the variational equations of physics.