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 sub-threshold oscillations. Previously, methods for demonstrating and testing the proposed symmetry principle have been applied to RR Lyrae, δ 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. These research efforts will help theoretical physicists to understand the fundamental discrete self-similarity of nature, and to model both stellar and atomic systems with one unified physics.
Highlights
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 arguments presented below are based on the SelfSimilar Cosmological Paradigm (SSCP) [1,2,3,4,5,6] which has been developed over a period of more than 30 years, and can be unambiguously tested via its definitive predictions [1,4] concerning the nature of the galactic dark matter
Discrete Scale Relativity hypothesizes that each welldefined class of systems on a given cosmological scale has a discrete self-similar class of analogue systems on any other cosmological scales x
Summary
The arguments presented below are based on the SelfSimilar Cosmological Paradigm (SSCP) [1,2,3,4,5,6] which has been developed over a period of more than 30 years, and can be unambiguously tested via its definitive predictions [1,4] concerning the nature of the galactic dark matter. While the observable portion of the entire hierarchy encompasses nearly 80 orders of magnitude in mass, three relatively narrow mass ranges, each extending for only about 5 orders of magnitude, account for ≥ 99% of all mass observed in the cosmos These dominant mass ranges: roughly 10–27 g to 10–22 g, 1028 g to 1033 g and 1038 g to 1043 g, are referred to as the Atomic, Stellar and Galactic Scales, respectively. OLDERSHAW and Galactic Scales [1,2,3,4,5,6], a close approximation to nature’s discrete self-similar scale transformation equations for the length (L), time (T) and mass (M) parameters of analogue systems on neighboring cosmological scales and –1, as well as for all dimensional constants, are as follows. Perhaps the single most thorough and accessible resource for exploring the SSCP and Discrete Scale Relativity is the author’s website [6]
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