Symmetries and invariances in classical physics

This Chapter discusses the role of symmetry in classical physics. We begin, in Section 2, with the distinction between symmetries of objects and of laws, and that between symmetry principles and symmetry arguments, including a discussion of Curie’s principle. Section 3 discusses the important connection between symmetries, as studied in physics, and the mathematical techniques of group theory. We offer a brief history of how group theory was applied first to geometry and then to physics in the course of the nineteenth century, preluding to the central importance acquired by group theoretical techniques in contemporary physics. Section 4 offers an account of what is meant by symmetry in physics, and a taxonomy of the different types of symmetry that are found within physics. In Sections 5 and 6 we discuss some applications of symmetries in classical physics, beginning with transformation theory in classical mechanics, and then turning to Einstein’s Special and General Theories of Relativity. We focus on the roles and meaning of symmetries in these theories, and this leads into the discussion of Noether’s theorems in Section 7. Finally, in Section 8, we offer some concluding remarks concerning the place, role and interpretation of symmetries in classical physics.