Symmetries and Conservation Laws

It is an interesting fact that there is a deep connection between the symmetries of the laws of physics, and the existence of conserved quantities such as total energy and momentum. Energy conservation is a direct consequence of the fact that the laws of nature do not change with time. It is therefore not something special to Newton's laws of motion, but is true for much more general physical theories. Similarly, momentum conservation derives from the simple fact that the laws of physics do not change as you move from one place to another. From our discussion in the first chapter we know that the laws of nature possess at least one more such symmetry: they do not care what direction you are looking in. If you rotate your laboratory, and everything that affects your experiment through some angle, the results of your experiment should not be affected. This symmetry of the laws of physics under rotations also gives rise to a conserved quantity. This conserved quantity is called angular momentum and arises, naturally, in the context of rotational motion of objects, which is the subject of the next Chapter.