E-infinity Theory Research Articles

Advanced prerequisite for E-infinity theory

Abstract This is the third of a series of papers written with the primary aim of communicating necessary theoretical background knowledge required for an in-depth study of E-infinity theory. Compared to the previous two papers [El Naschie MS. Elementary prerequisites for E-infinity (Recommended background readings in nonlinear dynamics, geometry and topology). Chaos, Solitons & Fractals 2006;30(3):579–605; El Naschie MS. Intermediate prerequisites for E-infinity theory. Chaos, Solitons & Fractals 2006;30(3):622–8], the present one may be described as advanced.

Intermediate prerequisites for E-infinity theory (Further recommended reading in nonlinear dynamics and mathematical physics)

Abstract The paper presents an intermediate level prerequisite for understanding E -infinity theory as applied to particle physics. It is the sequel to an earlier elementary level prerequisite paper (El Naschie MS. Elementary prerequisite for E -infinity. Chaos, Solitons & Fractals 2006;30(3):579–605). The work ends with a somewhat detailed discussion of the role which a Lagrangian type formulation could play in E -infinity theory.

Topics in the mathematical physics of E-infinity theory

Abstract This is the fourth contribution in a series of papers aimed at directing the attention of the prospective E-infinity researcher to the most important mathematical background and sources needed for an easy understanding and successful application of this theory. The present paper is mainly concerned with the mathematical physics relevant to E-infinity theory with emphasis on super Yang–Mills theory and superstrings.

E-Infinity theory and the Higgs field

E-Infinity theory predicts nine more elementary particles to be discovered in a standard model including the Higgs bosons. In addition a Higgs field is supposed to endow the particles with mass. This field must interact with the three nongravitational forces, i.e., the electromagnetic force, the weak force, and the strong force, therefore we could have four spin zero massive Higgs particles, namely two neutral (H ð0Þ

3-Adic Cantor function on local fields and its p-adic derivative

Abstract The problem of “rate of change” for fractal functions is a very important one in the study of local fields. In 1992, Su Weiyi has given a definition of derivative by virtue of pseudo-differential operators [Su W. Pseudo-differential operators and derivatives on locally compact Vilenkin groups. Sci China [series A] 1992;35(7A):826–36. Su W. Gibbs–Butzer derivatives and the applications. Numer Funct Anal Optimiz 1995;16(5&6):805–24. [2] , [3] ]. In Qiu Hua and Su Weiyi [Weierstrass-like functions on local fields and their p-adic derivatives. Chaos, Solitons & Fractals 2006;28(4):958–65. [8] ], we have introduced a kind of Weierstrass-like functions in p-series local fields and discussed their p-adic derivatives. In this paper, the 3-adic Cantor function on 3-series field is constructed, and its 3-adic derivative is evaluated, it has at most ln 2 ln 3 order. Moreover, we introduce the definition of the Hausdorff dimension [Falconer KJ. Fractal geometry: mathematical foundations and applications. New York: Wiley; 1990. [1] ] of the image of a complex function defined on local fields. Then we conclude that the Hausdorff dimensions of the 3-adic Cantor function and its derivatives and integrals on 3-series field are all equal to 1. There are various applications of Cantor sets in mechanics and physics. For instance, E-infinity theory [El Naschie MS. A guide to the mathematics of E-infinity Cantorian spacetime theory. Chaos, Solitons & Fractals 2005;25(5):955–64. El Naschie MS. Dimensions and Cantor spectra. Chaos, Solitons & Fractals 1994;4(11):2121–32. El Naschie MS. Einstein’s dream and fractal geometry. Chaos, Solitons & Fractals 2005;24(1):1–5. El Naschie MS. The concepts of E infinity: an elementary introduction to the Cantorian-fractal theory of quantum physics. Chaos, Solitons & Fractals 2004;22(2):495–511. [9] , [10] , [11] , [12] ] is based on random Cantor set which takes the golden mean dimension 5 - 1 2 as shown by El Naschie.

E-infinity theory—Some recent results and new interpretations

Abstract The present work consists mainly of a collection of recently obtained results and various new interpretations of earlier conclusions pertinent to the applications of E-infinity theory in high energy particle physics. No particular order has been followed in our presentation and the main motivation is to put things together in a convenient form for later reference and systematic use.

Is gravity less fundamental than elementary particles theory? Critical remarks on holography and E-infinity theory

Abstract This work is concerned with showing, using various arguments, the possibility of giving an interpretation of the fundamental interactions conveying a mental picture in which gravity and general relativity would appear to be less fundamental than high energy particle physics.

On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles

This short paper outlines the basic topological features of two new fuzzy Kahler manifolds in duality. Relation to E-infinity theory of the compactified Klein modular space in connection with ’t Hooft holographic principles is briefly discussed.

Superstring theory: What it cannot do but E-infinity could

Superstring theory is by far the most popular mathematical theory for quantum gravity ever devised. It also has genuine successes in numerous respects and helped initiate and develop other theories. However, there are numerous short comings and some fundamental problems which superstring theory, as it stands today, cannot solve in a satisfactory way. In the present note we examine whether E-infinity theory could be drawn into complimenting superstring and Brane theory to reach a more satisfactory resolution of these outstanding problems.

Fractal black holes and information

If nature is fractal as it evidently is, at classical resolution and if it is suspected to also be fractal at the quantum resolution as it is now a days generally believed to be, then we must have over looked at least two points or so in our physical model building of mini black holes. To start with at such ultra high resolution, the mini black hole geometry must be a fractal. Consequently we have zero volume and only a fractal surface area. Second because we cannot take the differential limit for the ℓp2 covering the transfinite surface area, there will be many gaps between the (ℓp)2 tilings. In other words we must introduce transfinite corrections to the final result. Proceeding this way the information entropy unit of a black hole should bea=I=(7+ϕ3)(10)-66cm2=7.23606799(10)-66cm2The nearest classical result to the above is that obtained by Gerard ‘t Hoofta=I=(0.724)(10)-65cm2The paper ends with a general discussion of E-infinity theory and its possible relation with ‘t Hooft’s holographic principle and his gluons–quark strings.

Application of E-infinity theory to turbulence

Abstract El-Naschie’s E-infinity theory is applied to turbulence. The Hausdorff-fractal dimension for turbulent flow is defined, the critical values for laminar flow (D = 3.98) and turbulent flow (D = 4.23) are obtained, and the fractal dimension for fully developed turbulent flow is D > 6.8. It is also shown that the Navier–Stokes equations are invalid for an exact model of turbulent flow and that two-dimensional planar turbulence does not exist in nature.

A tale of two Kleins unified in strings and E-infinity theory

A tale of two Kleins unified in strings and E-infinity theory

Application of E-infinity theory to biology

Abstract Albert Einstein combined continuous space and time into his special relativity, El-Naschie discovered the transfinite discontinuity of space–time in his E -infinity theory where infinity of dimensions was created. We find a partner of both space–time and E -infinity in biology. In our theory, the number of cells in an organism endows an additional dimension in biology, leading to explanation of many complex phenomena.

Elementary particle mass, subquark model and E-infinity theory

Abstract With the use of the perturbation method and E -infinity theory, we have derived the mass formula for elementary particles; m k = m 0 k ( ϕ ) λ k ( ϕ ) δ k ( ϕ ). By using this formula, we have calculated the mass of quarks, leptons and weak bosons on the basis of subquark model, and obtained the nice agreement with experiments. We have shown that the hierarchy structure of leptons is reduced to the mass formula obtained in this paper. We have also given some discussions on the related problems, such as the sum rules and the mass of Higgs bosons.

The mass spectrum of hadrons and E-infinity theory

Abstract With the use of quantum mechanics and E-infinity theory, we have derived the mass formula for elementary particles; mk = m0k(ϕ)λk(ϕ)δk(ϕ). By using this formula, we have calculated the mass of octet baryons and nonet mesons on the basis of quark model, and obtained the nice agreement with experiments. We have shown that the multiplet structure of baryons and mesons is reduced to the mass formula obtained in this paper. We have also given several discussions on the related problems of hadron masses, such as the sum rules and the mass of heavier hadrons.

From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold

Abstract Starting from the two-slit experiment we show that the so-called particle–wave duality could be resolved amicably by assuming space–time to be a fuzzy K3 manifold akin to that of E-Infinity theory. Subsequently, we show how many of the fundamental constants of nature such as the electromagnetic fine structure as well as the quantum gravity coupling may be deduced from the topology and geometry of the space–time manifold.

Kähler-like manifolds, Weyl spinor particles and E-infinity high energy physics

Abstract The Kahler-like fuzzy manifold of E-infinity theory is introduced. The Betti numbers and other topological invariants of this manifold are determined. In particular it is found that the Euler characteristic is equal to 26 + k = 26.18033989 while the absolute value of the inverse signature is equal to the electromagnetic fine structure times D(10) = 10. The relation to Weyl spinor is discussed.

Gödel universe, dualities and high energy particles in E-infinity

The paper discusses possible connections between Gödel’s classical solution of Einstein’s field equations and E-infinity theory of high energy particles. The role of T-duality and P-Adic expansion in establishing such a connection is discussed.

A P-Brane vindication of the two Higgs-doublet minimally super-symmetric standard model and related issues

The two-Higgs doublet MSSM predicts three neutral and two charged Higgs particles. The present work gives a vindication of this model based on a P-Brane model in eleven dimensions. Subsequently, we give alternative derivations using various ideas from the theory of maximally symmetric spaces and E-Infinity theory.

On a connection between Stieltjes continued fraction, KAM theory and E-infinity theory

In the present work we establish a connection between El Naschie's E-infinity theory and Stieltjes solution of the problem on the distribution of mass along a line and KAM theory following Gantmacher and Krein mechanical interpretation of Stieltjes' classical research on the subject.