I’ve been debating for some time what to write about in my first post. As luck would have it, I discovered this recent New York Times article about Emmy Noether. Not that discovering the article was hard; it’s currently first on the list of “most emailed” articles.
I’m completely in agreement with Ransom Stephens, who said, “You can make a strong case that her theorem is the backbone on which all of modern physics is built.” Noether’s Theorem really does provide the organizing principle that underlies the Standard Model of particle physics.
Essentially, Noether’s Theorem says that there is a correspondence between symmetries and conserved quantities. For example, translational symmetry (the fact that the laws of physics don’t change as you move around in space) corresponds to conservation of momentum. Rotational symmetry (the fact that the laws of physics don’t change when you turn your head) corresponds to conservation of angular momentum. And time-translation symmetry (the fact that the laws of physics don’t change as we move forward in time) corresponds to conservation of energy.
There are conserved quantities, such as electric charge, for which the associated symmetry is not obvious. But even in those cases, there are symmetries in the mathematics. In the modern framework for describing electromagnetism, the symmetry really is built into the geometry of space. Essentially, we could think of each point of spacetime as being a tiny circle that can be rotated. And then Noether’s theorem says that conservation of electric charge corresponds to this internal point-rotation symmetry. So the key point is that Noether’s Theorem really has changed the way we view space and time. In this regard, the comparison to Einstein is well-founded.
In the future, I plan to write a series of posts that explain Noether’s theorem in more mathematical detail. But for now, welcome to my blog, and thanks for reading.