Links to access earlier entries in the special series on symmetry:
I, II, III, IV, V, VI
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We've now reached Part VII, the final installment of my series on symmetry. What I would like to discuss today is Noether's Theorem, which relates various kinds of symmetries to different types of conservation. As noted in this online document, the following relations follow from Noether's Theorem:
Translational symmetry means that the laws of physics are identical at all points in space, and it also implies the conservation of linear momentum. Rotational symmetry means that the laws of physics act the same in every direction, and it also implies the conservation of angular momentum. Time symmetry means that the laws of physics are eternally unchanging, and it also implies the conservation of energy.
Virtually all of the treatments of Noether's Theorem I could find online quickly turned into mathematical discussions involving calculus and other advanced concepts, such as this, this, this, and this. I took a year of college calculus, but it was 28 years ago so I couldn't really follow the mathematically based explanations. This one document, however, attempts to convey Noether's Theorem with real-life (albeit fanciful) scenarios. I found these fairly helpful.
The life of Emmy Noether (1882-1935) is also noteworthy for her overcoming of the barriers that existed at the time for women in science, including the outright opposition of male professors to women joining their ranks. She studied under many famous mathematicians such as Hermann Minkowski and David Hilbert, and her career contributions to math and physics have been praised by scholars such as Leon Lederman, Hermann Weyl, and Albert Einstein.