Application of Symmetry

Abstract

This chapter deals with the application of the symmetry principle. In its minimalistic use, the symmetry principle sets a lower bound on the symmetry of an effect, since, according to the principle, the symmetry of an effect cannot be less than that of its cause. Examples of minimalistic use of the symmetry principle are examined. Some of the examples involve physical systems, while others are mathematical. The physical cases have the character of problem solving for a unique solution, and the solution isfully or partially found by applying the symmetry of the cause to the effect. The mathematical examples serve to examine how to deal with situations in which a problem possesses more than one solution. In such cases it is the family of all solutions that serves as the effect and must exhibit the symmetry of the cause (and possibly more). In its maximalistic use, the symmetry principle sets an upper bound on the symmetry of a cause, since, by the symmetry principle, the cause cannot be more symmetric than its effect. Maximalistic use is characteristic of basic science research, in which the effect is given and its cause must be found. For a cause to be as simple as possible, it must be as symmetric as possible, and its maximal allowed symmetry is that of the effect. The examples are from the fields of nuclear physics and the physics of elementary particles and their interactions.