Symmetry and conservation laws

Abstract

Symmetry and invariance considerations, and even conservation laws, played undoubtedly an important role in the thinking of the early physicists, such as Galileo and Newton, and probably even before then. However, these considerations were not thought to be particularly important and were articulated only rarely. Newton's equations were not formulated in any special coordinate system and thus left all directions and all points in space equivalent. They were invariant under rotations and displacements, as we now say. The same applies to his gravitational law. There was little point in emphasizing this fact, and in conjuring up the possibility of laws of nature which show a lower symmetry. As to the conservation laws, the energy law was useful and was instinctively recognized in mechanics even before Galileo. The momentum and angular‐momentum conservation theorems in their full generality were not very useful even though, in the special case of central motion, they are one of Kepler's laws. Most books on mechanics, written around the turn of the century and even later, do not mention the general theorem of the conservation of angular momentum. It must have been known quite generally because those dealing with the three‐body problem, where it is useful, write it down as a matter of course. However, people did not pay very much attention to it.