3 Symmetries in particle physics
In physics, symmetry groups are fundamental ingredients of models that describe anything from subatomic particles to the universe. One central result that connects symmetry and physics is Noether’s theorem, discovered by German mathematician Emmy Noether. This states that any symmetry of a physical system implies that there is a quantity that is conserved, meaning that it does not change. Examples in mechanics are, for instance, conservation of momentum for a system that is symmetric under translations in space, and the conservation of angular momentum for a system with rotational symmetry.
Another example of the key role of symmetry in physics is Albert Einstein’s theory of relativity. Here, Einstein starts from postulating a symmetry, namely that the physics does not change under certain changes of the coordinate system used to describe it. From this assumption of symmetry alone, he derives his famous theory, including all the mind-boggling consequences about the structure and interaction of space and time. More will be said about relativity later in this course.