Self-similar cosmological model: Technical details, predictions, unresolved issues, and implications

Discrete Scale Relativity and SX Phoenicis Variable Stars

“…The arguments presented below are based on the Self-Similar 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. Briefly, the discrete self-similar paradigm focuses on nature's fundamental organizational principles and symmetries, emphasizing nature's intrinsic hierarchical organization of systems from the smallest observable subatomic particles to the largest observable superclusters of galaxies.…”

“…A third general principle of the new paradigm is that the cosmological Scales are rigorously self-similar to one another, such that for each class of fundamental particles, composite systems or physical phenomena on a given Scale there is a corresponding class of particles, systems or phenomena on all other cosmological Scales. Specific self-similar 3 analogues from different Scales have rigorously analogous morphologies, kinematics and dynamics. When the general self-similarity among the discrete Scales is exact, the paradigm is referred to as Discrete Scale Relativity 5 and nature's global space-time geometry manifests a new universal symmetry principle: discrete self-similarity or discrete scale invariance.…”

“…The self-similar scaling constants Λ and D have been determined empirically and are equal to ≅ 5.2 x 10 17 and ≅ 3.174, respectively. 2,3 The value of Λ D is 1.70 x 10 56 . Different cosmological Scales are designated by the discrete index Ψ (≡ …, -2, -1, 0, 1, 2, …) and the Atomic, Stellar and Galactic Scales are usually assigned Ψ = -1, Ψ = 0 and Ψ = +1, respectively.…”

The Hidden Meaning of Planck’s Constant

“…The discrete fractal paradigm focuses on nature's fundamental organizational principles and symmetries, and is referred to as the Self-Similar Cosmological Paradigm. [2] It emphasizes nature's hierarchical organization of systems from the smallest observable subatomic particles to the largest observable superclusters of galaxies. The new fractal paradigm also highlights the fact that nature's global hierarchy is highly stratified into discrete Scales, of which we can currently observe the Atomic, Stellar and Galactic Scales.…”

“…Based upon decades of studying the scaling relationships among analogue systems from the Atomic, Stellar and Galactic Scales, [2] a close approximation to nature's actual Scale transformation equations for the length (L), time (T) and mass (M) parameters of analogue systems on neighboring cosmological Scales Ψ and Ψ-1 are as follows.…”