The Honourable Schoolboy





http://en.wikipedia.org/wiki/Emmy_Noether

Outstanding. Brilliant.

Maths & Physics, viz.

Physics[edit]

Main articles: Noether's theorem, Conservation law (physics) and Constant of motion

Noether was brought to Göttingen in 1915 by David Hilbert and Felix Klein, who wanted her expertise in invariant theory to help them in understanding general relativity, a geometrical theory of gravitation developed mainly by Albert Einstein. Hilbert had observed that the conservation of energy seemed to be violated in general relativity, due to the fact that gravitational energy could itself gravitate. Noether provided the resolution of this paradox, and a fundamental tool of modern theoretical physics, with Noether's first theorem, which she proved in 1915, but did not publish until 1918.^[102] She not only solved the problem for general relativity, but also determined the conserved quantities for every system of physical laws that possesses some continuous symmetry.

Upon receiving her work, Einstein wrote to Hilbert: "Yesterday I received from Miss Noether a very interesting paper on invariants. I'm impressed that such things can be understood in such a general way. The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff."^[103]

For illustration, if a physical system behaves the same, regardless of how it is oriented in space, the physical laws that govern it are rotationally symmetric; from this symmetry, Noether's theorem shows the angular momentum of the system must be conserved.^[104]The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. Rather, the symmetry of the physical laws governing the system is responsible for the conservation law. As another example, if a physical experiment has the same outcome at any place and at any time, then its laws are symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the conservation laws of linear momentum andenergy within this system, respectively.

Noether's theorem has become a fundamental tool of modern theoretical physics, both because of the insight it gives into conservation laws, and also, as a practical calculation tool.^[4] Her theorem allows researchers to determine the conserved quantities from the observed symmetries of a physical system. Conversely, it facilitates the description of a physical system based on classes of hypothetical physical laws. For illustration, suppose that a new physical phenomenon is discovered. Noether's theorem provides a test for theoretical models of the phenomenon: if the theory has a continuous symmetry, then Noether's theorem guarantees that the theory has a conserved quantity, and for the theory to be correct, this conservation must be observable in experiments.