Re: Hilbert's Foundation of Physics

Hi Pete
I think that Noether had to straighten out both Einstein and 
Hilbert==>

"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." 
http://cwp.library.ucla.edu/articles/noether.asg/noether.html

Search on "Bianchi" to find this
"Theorem II applies when the action is an invariant of an infinite 
Lie group. The statement of the theorem for this case is very general 
and, aside from its application to general relativity, it applies in 
a wide variety of other cases. For example, quantum chromodynamics 
and other gauge field theories are theories to which it applies. From 
theorem II, one has identities beteen Lagrange functions and their 
derivatives. See Appendix B. These identities Noether 
calls 'dependencies'. Generally they are covariant with respect to 
the group. For example, the Bianchi identities in the general theory 
of relativity are examples of such 'dependencies'."

Best - John B.

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