E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws
Abstract
Emmy Noether proved two deep theorems, and their converses, on the connection between symmetries and conservation laws. Because these theorems are not in the mainstream of her scholarly work, which was the development of modern abstract algebra, it is of some historical interest to examine how she came to make these discoveries. The present paper is an historical account of the circumstances in which she discovered and proved these theorems which physicists refer to collectively as Noether's Theorem. The work was done soon after Hilbert's discovery of the variational principle which gives the field equations of general relativity. The failure of local energy conservation in the general theory was a problem that concerned people at that time, among them David Hilbert, Felix Klein, and Albert Einstein. Noether's theorems solved this problem. With her characteristically deep insight and thorough analysis, in solving that problem she discovered very general theorems that have profoundly influenced modern physics.
 Publication:

arXiv eprints
 Pub Date:
 July 1998
 arXiv:
 arXiv:physics/9807044
 Bibcode:
 1998physics...7044B
 Keywords:

 Physics  History of Physics;
 Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 21 pages including English translations of quotations from correspondence between Felix Klein and David Hilbert and from notes of Felix Klein. The failure of local energy conservation in the theory of general relativity is central to this paper. Latex file. Metric tensor explicitly given in Footnote 7 of replacement paper