Abstract

Discrete Scale Relativity proposes a new symmetry principle called discrete cosmological self-similarity which relates each class of systems and phenomena on a given Scale of nature's discrete cosmological hierarchy to the equivalent class of analogue systems and phenomena on any other Scale. The new symmetry principle can be understood in terms of discrete scale invariance involving the spatial, temporal and dynamic parameters of all systems and phenomena. This new paradigm predicts a rigorous discrete self-similarity between Stellar Scale variable stars and Atomic Scale excited atoms undergoing energy-level transitions and subthreshold oscillations. Previously, methods for demonstrating and testing the proposed symmetry principle have been applied to RR Lyrae, ? Scuti and ZZ Ceti variable stars. In the present paper we apply the same analytical methods and diagnostic tests to a new class of variable stars: SX Phoenicis variables. Double-mode pulsators are shown to provide an especially useful means of testing the uniqueness and rigor of the conceptual principles and discrete self-similar scaling of Discrete Scale Relativity.