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Fractal Strings as the Basis of Cantorian-Fractal Spacetime and the Fine Structure Constant

Carlos Castro
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Abstract

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.

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Carlos Castro. 2002-04-30. Fractal Strings as the Basis of Cantorian-Fractal Spacetime and the Fine Structure Constant. https://arxiv.org/abs/hep-th/0203086

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