Friday, December 14, 2007

How Long Must We Sing This Song?

Need I say more?
Noether's Theorem can go eff itself. Even if Noether was a chick. And there are never any chick theorems in physics. I dare you to check out the proof here. Part (c) of Problem #3 on my PHYS 701 final will be on this principle. Be sad for me. Be scared for me. Most of all, be glad you are not me.

"Noether's theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. For example, the conservation of energy is a consequence of the fact that all laws of physics (including the values of the physical constants) are invariant under translation through time; they do not change as time passes.

Noether's theorem, published in 1918, holds for all physical laws based upon the action principle. It is named after the early 20th century mathematician Emmy Noether. Noether's theorem is a relationship of classical mechanics between pairs of conjugate variables—if the action is invariant under a shift in one of the two physical variables, then the equations of motion resulting from holding that action stationary conserve the value of the other of the pair of variables. These conjugate pairs also play a crucial role in quantum theory—they are the pairs of variables that are related by the Heisenberg uncertainty principle (such as position and momentum, time and energy, angle and angular momentum, etc)."

(From Wikipedia, who I wish would do my final for me)

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