Symmetry Principles and Conservation Laws

Newtonian physics is characterized by the existence of various conservation laws, that is, principles that tell us that however complicated the interactions among the components making up the system, certain quantities never change. Perhaps the most familiar such law is the conservation of the total mass of the system, or “amount of matter” in it: as described in Feynman, §3, we believe that in principle, we can always account for all the mass – if it has disappeared from one point, it must turn up somewhere else. Other important conservation laws that operate under appropriate conditions are these for the total energy, momentum and angular momentum (on which see below). We also sometimes find conservation laws for non-mechanical quantities, such as the total electric charge. An important aspect of conservation laws (or at least the ones for mechanical quantities) that gradually emerged in the nineteenth century is that, generally speaking, they are associated with some symmetry or invariance property of the physical situation (this is explained below). This connection between symmetry properties and conservation laws is, in classical physics, common to “particle” and “wave” phenomena; moreover, it has survived the violent conceptual upheavals of relativity and quantum mechanics, and I imagine that most physicists would guess that it would survive possible future upheavals. It is interesting that the idea that (for example) all positions in space are in principle equivalent, and that this equivalence leads to interesting physical consequences, is perhaps one of the most radical ways in which post-Newtonian physics breaks with Aristotle (for whom, we recall, everything had its unique “proper place”).