When I gave a public lecture at the Perimeter Institute for Theoretical Physics in April, I mentioned Noether’s theorem in an answer to a question, to the delight of my hosts. Unknown to me at the time, Noether is a key figure for the Institute, and the dinner afterwards included members of the Emmy Noether Council. Noether was a mathematician rather than a physicist, but her theorem, which states that for every continuous symmetry in nature, there is a conservation law, is now part of the bedrock of physics.
A “continuous symmetry” of some system means a variable that can be changed to any value without affecting the system. For example the laws of physics don’t depend on where you are. There is a continuous symmetry with respect to changes of location. Noether’s theorem says that because of this, there must be a conserved quantity.
That quantity is actually momentum. So from an assumption that the laws of physics are the same wherever you are, Noether’s theorem basically allows us to prove, amongst other things, Newton’s First Law: An object will remain at rest or moving with a constant velocity unless acted on by an external force. This is a very powerful principle, with many further profound consequences, and is one of the foundation stones of the Standard Model of particle physics¹. These ideas were needed before moving on to gauge symmetries, broken symmetries and the Higgs boson.
Tonight, mathematician Peter Olver will explore Noether’s life and career, and delve into the curious history of her famous theorem, and her other work. Physicist Ruth Gregory will look at the lasting impact of Noether’s theorem, and how it connects with the Standard Model and Einstein’s general relativity.
As usual, the lectures will be available here live (1am UK time!) and recordings will appear soon afterwards. Tomorrow there is a lecture on Relativity, which I will also post.
¹There’s actually a whole chapter on this in my book Smashing Physics/Most Wanted Particle.
