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Thermodynamics & Symmetry



Recently, Jim Green asked who Noether was with regard to the Noether
theorems. Some answered but with incomplete accuracy so I will pass
on some more information.
1. Noether was a woman but her first name was not Emmy, her full name
was Amalie Emmy Noether, she apparently preferred to give her second name.

2. She was not a mathematical physicist, she was a pure mathematician,
perhaps the greatest woman mathematician of all time. Her father was a
well-known mathematician and her initial interest was in algebraic invariants.
Because of this interest, Hilbert and Klein hired her to work with them on
Einstein's General Relativity finding consequences of general covariance.

3. She was never in danger of receiving a Nobel prize since her interests
were purely mathematical and as everybody knows there is no prize for
mathematics. Besides, as everbody knows not even Einstein was awarded
a Nobel prize in physics for Relativity, special or general, but for his
explanation of the photoelectric effect. Contrary to an article in a
Woman's magazine I once read, Noether did not do the mathematics that
Einstein needed for General Relativity. What Einstein used went back
to Riemann, Christoffel, Ricci, and Levi-Civita and had been completed
by 1901. Einstein's gravitational equations were published in 1915.
Noether's paper was published in 1918. Noether's great work is
considered to have occured after that when she took Hilbert's axiomatic
approach to mathematics and applied it to the development of a general
theory of ideals.

4. The Noether theorems are necessary consequences when dynamical equations
follow from an action principle with a Lagrangian density. Under general
coordinate transformations certain consequences follow. If the
transformations depend on parameters then one deals with Lie groups and
the equations are called weak conservation laws. But, if the transformations
depend on arbitrary functions one deals with infinite groups and the
equations are called strong conservation laws and are in fact identities,
sometimes called Bianchi identities, and they hold even if the equations
of motion are not satisfied.

James M. Espinosa