Application of Symmetry

Abstract

In this chapter we continue developing the general symmetry formalism that we started developing in the preceding chapter. Here we study the theory and practice of the application of symmetry in science. The practice is based on the symmetry principle, stating roughly that the effect is at least as symmetric as the cause, and the theory is the proof of that principle. The proof starts with a discussion of the concept of causal relation, followed by a clarification of certain points concerning the nature of science, from which we are led to the equivalence principle, stating roughly that equivalent causes imply equivalent effects. The symmetry principle follows almost immediately from the equivalence principle. In the application of symmetry in science the symmetry principle can be used in two ways: minimalistically, to set a lower bound on the symmetry of the effect, and maximalistically, to set an upper bound on the symmetry of the cause. Numerous examples are presented. The application of symmetry in quantum systems is briefly discussed.