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On a connection between the VAK, knot theory and El Naschie’s theory of the mass spectrum of the high energy elementary particles

Authors
Journal
Chaos Solitons & Fractals
0960-0779
Publisher
Elsevier
Publication Date
Volume
19
Issue
3
Identifiers
DOI: 10.1016/s0960-0779(03)00253-4
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract In the present work we give an introduction to the ε (∞) Cantorian space–time theory. In this theory every particle can be interpreted as a scaling of another particle. Some particles are a scaling of the proton and are expressed in terms of φ and α 0 . Following the VAK suggestion of El Naschie, the limit sets of Kleinian groups are Cantor sets with Hausdorff dimension φ or a derivative of φ such as 1/ φ, 1/ φ 2, 1/ φ 3, etc. Consequently and using ε (∞) theory, the mass spectrum of elementary particles may be found from the limit set of the Möbius–Klein geometry of quantum space–time as a function of the golden mean φ=( 5 −1)/2=0.618033989 as discussed recently by Datta (see Chaos, Solitons & Fractals 17 (2003) 621–630).

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