Symmetry and Equivalence

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent (in the sense of being equally well- or ill-suited to represent any given situation, relative to any reasonable interpretation). A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is no such concept. The present paper arrives at a cautiously pessimistic conclusion