Emmy Noether. A not well known female scientist

ORIGINAL: Yonatan Zunger

Portrait of Emmy Noether.  (1910). nhn.ou.edu/

There are some people who are simply insufficiently famous, and Emmy Noether is one of them. Now, mathematicians may claim her as one of their own, merely because she was a professor of mathematics for several decades and made more foundational and revolutionary contributions to the study of groups, rings, and algebras than I could easily list in a post, pioneering numerous basic techniques and having important mathematical structures named after her. But all of this manages to pale next to her contribution to physics; and being an ex-physicist, and thus feeling no reason not to be horribly biased about this, I want to tell you about Noether's Theorem: her 1915 proof that is, perhaps, the single most important result in mathematical physics. And when I say the single most important result, I mean not only that most of modern physics is built on top of it, but working theoretical physicists actually use this theorem several times a day.

Her theorem relates two seemingly unrelated things: symmetries and conserved charges. A physical system has a symmetry if there's some way to transform it which leaves all of its behavior the same. For example, if you took the entire Solar System and moved it three feet to the left, nobody could tell the difference. Similarly, if you rotated a sphere around any of its axes, nothing about them would change. Some symmetries are discrete, which means that they can only take on a fixed set of jumps: for example, you can rotate a square by 0°, 90°, 180°, or 270° and it will look the same, but if you rotate it by 260° it will look different. Other symmetries are continuous, which means that there's a continuous range of transformations you can make: e.g., you can rotate a circle by any angle, rotate a sphere by any angle along three different axes, or translate (shift) a physical system by any distance along any of three axes, or forward and backwards in time. Noether's Theorem actually applies to both kinds of symmetry, but the continuous ones are the most interesting ones.

There's an obvious reason that symmetry is important in physics: it tells you about things you can ignore, and strip out of your calculation, e.g. the overall angle of your experiment.