2002/03/31 by Carlos Castro
Physics and Astronomy · #hep-th
published as Chaos Solitons Fractals 14 (2002) 1341-1351 · 14 pages, plain Tex, Revised. An appendix with additional Comments on arithmetic QFT and other topics has been added. References are added
arxiv created 2002/04/30 · arxiv updated 2009/11/30
Beginning with the most general fractal strings/sprays construction recently expounded in the book by Lapidus and Frankenhuysen, it is shown how the complexified extension of El Naschie's Cantorian-Fractal spacetime model belongs to a very special class of families of fractal strings/sprays whose scaling ratios are given by suitable pinary (pinary, p prime) powers of the Golden Mean. We then proceed to show why the logarithmic periodicity laws in Nature are direct physical consequences of the complex dimensions associated with these fractal strings/sprays. We proceed with a discussion on quasi-crystals with p-adic internal symmetries, von Neumann's Continuous Geometry, the role of wild topology in fractal strings/sprays, the Banach-Tarski paradox, tesselations of the hyperbolic plane, quark confinement and the Mersenne-prime hierarchy of bit-string physics in determining the fundamental physical constants in Nature.