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

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).