Symmetry at the foundations of quantum theory

Abstract

Symmetry in its essence is the possibility of making a change that leaves some aspect of the situation unchanged, or, most succinctly, symmetry is immunity to possible change. This is the conceptual formulation of symmetry. It might also be called the qualitative formulation of symmetry, in contrast to the group-theoretical formulation, which might be called the quantitative formulation of symmetry, in contrast to the group-theoretical formulation, which might be called the quantitative formulation of symmetry. The latter is expressed in terms of transformations (or operations), transformation groups, equivalence relations, equivalence classes, symmetry transformations (or symmetry operations), and symmetry groups, and can be developed from the conceptual formulation. For the description and treatment of many applications of symmetry in physics the group-theoretical formulation is the appropriate one. But for the account of the fundamental manifestations of symmetry in physics it is the conceptual formulation that is the more suitable. Symmetry implications of the postulates of quantum theory are investigated.