On a New Elementary Particle from the Disintegration of the Symplectic &#39t Hooft-Veltman-Wilson Fractal Spacetime

doi:10.4236/WJNST.2014.44027

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On a New Elementary Particle from the Disintegration of the Symplectic &#39t Hooft-Veltman-Wilson Fractal Spacetime

Journal Article•DOI•

On a New Elementary Particle from the Disintegration of the Symplectic &#39t Hooft-Veltman-Wilson Fractal Spacetime

08 Oct 2014-World Journal of Nuclear Science and Technology (Scientific Research Publishing)-Vol. 04, Iss: 4, pp 216-221

TL;DR: In this article, the main step of the mathematical analysis in terms of elementary particles interaction is interpreted as an elementary particle with a topological mass charge equal to 0.18033989, i.e. double the magnitude of Hardy's quantum entanglement.

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Abstract: 't Hooft-Veltman Wilson dimensional regularization depends crucially upon Borel summability which entails strong links to the modern mathematical theory of transfinite sets and consequently to the fractal-Cantorian spacetime proposal of Ord-Nottale-El Naschie. Starting from the above, we interpret the main step of the mathematical analysis in terms of elementary particles interaction. Thus 't Hooft-Veltman “perturbation” parameter which measures the deviation of the regulated space from the four dimensionality of spacetime is interpreted as an elementary particle with a topological mass charge equal to 0.18033989, i.e. double the magnitude of Hardy’s quantum entanglement. In turn, Hardy’s quantum entanglement which may be interpreted geometrically as a consequence of the zero set embedded in an empty set could also be interpreted as an exchange of pseudo elementary particles with a topological mass charge equal to Hardy’s entanglement where is the Hausdorff dimension of the zero set of the corresponding 't Hooft-Veltman spacetime.

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Journal Article•DOI•

From E = mc 2 to E = mc 2 /22—A Short Account of the Most Famous Equation in Physics and Its Hidden Quantum Entanglement Origin *

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Mohamed S. El Naschie

18 Dec 2014-Journal of Quantum Information Science

TL;DR: In this paper, the authors show that all the involved physics in deriving the new quantum dissection of the famous formula of special relativity is actually a pure mathematical necessity anchored in the phenomena of volume concentration of convex manifold in high dimensional quasi Banach spaces.

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Abstract: Einstein’s energy mass formula is shown to consist of two basically quantum components E(O) = mc2/22 and E(D) = mc2(21/22). We give various arguments and derivations to expose the quantum entanglement physics residing inside a deceptively simple expression E = mc2. The true surprising aspect of the present work is however the realization that all the involved “physics” in deriving the new quantum dissection of Einstein’s famous formula of special relativity is actually a pure mathematical necessity anchored in the phenomena of volume concentration of convex manifold in high dimensional quasi Banach spaces. Only an endophysical experiment encompassing the entire universe such as COBE, WMAP, Planck and supernova analysis could have discovered dark energy and our present dissection of Einstein’s marvelous formula.

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34 citations

Cites background from "On a New Elementary Particle from t..."

...285 uation to mean that E = mc(2) is actually the sum of two parts [19]-[30]....
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Journal Article•DOI•

On a Fractal Version of Witten’s M-Theory

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Mohamed S. El Naschie

08 Apr 2016-International Journal of Astronomy and Astrophysics

TL;DR: In this article, Witten's eleven-dimensional M-theory is developed in an analogous way to a corresponding dimensional fractal version where the energy density of the cosmos is determined by a non-integer irrational Lorentzian-like factor: where is Hardy's probability of entanglement.

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Abstract: Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.

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32 citations

Cites background or methods from "On a New Elementary Particle from t..."

...How could this intricate web of delicately balanced interrelations exist without a firm “belief” in a single basic assumption namely that E-infinity and the associated golden mean transfinite computer is what nature has chosen to base itself upon [40]-[46]....
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...On the other hand, we know from E-infinity theory that 24 should be 26 + k and 336 should be 336 + 16k when transfinitely corrected to present perfect simplistic tiling of the compactified holographic boundary modelled by the compactified Klein modular curve [35]-[40]....
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...For Einstein’s isotropic spacetime 1 2 δ =  while for E-infinity like Penrose-Connes’ universe ( ) 2 1 1 10 k δ = + +  where 5 2 k φ = is ‘tHooft’s renormalon and 5 φ is Hardy’s entanglement [40] [41]....
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...Now in E-infinity theory the theoretical value is an exact transfinite number, which we give here without justification which will be given a posteriori [14]-[16] [40]-[46] ( ) ( )(4) 20 1 137 137....
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Journal Article•DOI•

The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos

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Mohamed S. El Naschie

01 Jan 2014

TL;DR: In this article, the authors gave a new confirmation of the derivation of the 95.5 per cent so-called dark energy density of the cosmos based on the Banach spaces motivated theory of convex geometry in high dimensionality.

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Abstract: Based on the Banach spaces motivated theory of convex geometry in high dimensionality we give a new confirmation of the derivation of the 95.5 per cent so called dark energy density of the cosmos. The result derives directly from the purely geometric-topological phenomenon of measure-mass concentration and gives an unqualified complete confirmation of our previous results including the hidden quantum nature of Einstein’s celebrated equation E = mc2. Thus the quantum dissection into ordinary energy of the quantum particle E(O) = mc2/22 and dark energy of the quantum wave E(D) = mc2(21/22) were validated by first a purely mathematical theorem of convex geometry and second by conservation of energy leading to E(O) + E(D) = mc2 as in Einstein’s special theory of relativity.

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22 citations

Journal Article•DOI•

Banach Spacetime-Like Dvoretzky Volume Concentration as Cosmic Holographic Dark Energy

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Mohamed S. El Naschie

02 Feb 2015

TL;DR: In this article, the authors start from the Banach spaces motivated theory of convex geometry in high dimensionality and give a new additional confirmation of previous derivations of the 96 per cent dark energy density of the cosmos.

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Abstract: We start from Banach spaces motivated theory of convex geometry in high dimensionality and give a new additional confirmation of previous derivations of the 96 per cent dark energy density of the cosmos. The result derives directly from the purely geometric-topological phenomenon of measure-mass concentration and gives an unqualified complete confirmation of our previous analysis including the hidden quantum nature of Einstein’s celebrated equation E = mc2. The straight forward relation to holographic dark energy and its endophysical nature is also outlined.

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21 citations

Cites background from "On a New Elementary Particle from t..."

...However due to self similarity we expect the above relation to hold true on all scales [4-7, 68,69]....
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...Again in the last four years numerous derivations of the preceding dissection of Einstein’s basic energy-mass relation was given by the author and his collaborators using a variety of physical and algebraic derivation and all leading to the same fundamental conclusion [4-77]....
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...‘tHooft’s dimensional regularization [4] order parameter ∈= 4 − D....
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...5% density deficit revealed that Einstein’s energy ‘density’ equation is the sum of two parts [4-15]....
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...Einstein’s most famous formula states the equivalence of matter and energy and relates them via the constant speed of light in the jewel of special relativity E = mc 2 where E is the energy, m is the mass and c is the speed of light[1-5]....
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Journal Article•DOI•

Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups

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Mohamed S. El Naschie¹•Institutions (1)

Alexandria University¹

07 Mar 2016-International Journal of Astronomy and Astrophysics

TL;DR: In this article, the authors utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space to show how the classical Newton's kinetic energy E = 1/2mv2 leads to Einstein's celebrated maximal energy equation E = mc2 and how in turn this can be dissected into the ordinary energy density E(O) =mc2/22 and the dark energy densityE(D) = mc 2(21/22) of the cosmos where m is the mass; v is the velocity and c is the speed

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Abstract: Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv2 leads to Einstein’s celebrated maximal energy equation E = mc2 and how in turn this can be dissected into the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) of the cosmos where m is the mass; v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.

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20 citations

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References

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The Renormalization group and the epsilon expansion

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Kenneth G. Wilson¹, Kenneth G. Wilson², John B. Kogut¹•Institutions (2)

Institute for Advanced Study¹, Cornell University²

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3,882 citations

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Regularization and Renormalization of Gauge Fields

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Gerard 't Hooft¹, M.J.G. Veltman¹•Institutions (1)

Utrecht University¹

01 Jul 1972-Nuclear Physics

TL;DR: In this article, a new regularization and renormalization procedure for gauge theories is presented, which is particularly well suited for the treatment of gauge theories and is transparent when anomalies such as the Bell-Jackiw-Adler anomaly may occur.

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3,722 citations

"On a New Elementary Particle from t..." refers background in this paper

...at the same time when the renormalizability of the Yang-Mills theory was discovered [2] [8]....
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Critical Exponents in 3.99 Dimensions

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Kenneth G. Wilson¹, Michael E. Fisher¹•Institutions (1)

Cornell University¹

24 Jan 1972-Physical Review Letters

TL;DR: In this paper, the critical exponents for dimension $d = 4, where d is the dimension of the dimension in the dimension space of the model, with the exponent of the critical exponent being $1+\frac{1.6} for an Ising-like model and $1 +\frac {1.5} for a more complex model.

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Abstract: Critical exponents are calculated for dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$ with $\ensuremath{\epsilon}$ small, using renormalization-group techniques. To order $\ensuremath{\epsilon}$ the exponent $\ensuremath{\gamma}$ is $1+\frac{1}{6}\ensuremath{\epsilon}$ for an Ising-like model and $1+\frac{1}{5}\ensuremath{\epsilon}$ for an $\mathrm{XY}$ model.

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"On a New Elementary Particle from t..." refers background in this paper

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Journal Article•DOI•

Dimensional regularization and the renormalization group

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Gerard 't Hooft¹•Institutions (1)

CERN¹

24 Sep 1973-Nuclear Physics

TL;DR: In this article, the behavior of a renormalized field theory under scale transformations x → λx; p → p/λ can be found in a simple way when the theory is regularized by the continuous dimension method.

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1,104 citations

"On a New Elementary Particle from t..." refers methods in this paper

...more or less a perturbation parameter [1]-[13]....
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...‘t Hooft-Veltman-Wilson dimensional regularization is a highly successful method in its analytical form as well as in the computerized counterpart extensively used in solid state physics [1]-[12]....
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Journal Article•DOI•

A review of E infinity theory and the mass spectrum of high energy particle physics

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M.S. El Naschie¹, M.S. El Naschie², M.S. El Naschie³•Institutions (3)

Université libre de Bruxelles¹, Cairo University², University of Surrey³

01 Jan 2004-Chaos Solitons & Fractals

TL;DR: In this paper, the basic conceptual framework of a new space-time theory with application to high energy particle physics is outlined, both achievements and limitations are discussed with direct reference to the mass spectrum problem.

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Abstract: The essay outlines the basic conceptual framework of a new space–time theory with application to high energy particle physics. Both achievements and limitations are discussed with direct reference to the mass spectrum problem.

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650 citations

"On a New Elementary Particle from t..." refers methods in this paper

...We stress once more that the subtlety of dimensional regularization lies in the application of Borel’s method for treating divergence and that is where Cantor sets and KAM theorem [16] enters into the subject leading to the inescapable conclusion that ‘t Hooft-Veltman-Wilson method implies a Cantorian fractal spacetime and what more exciting also to a host of exotic new elementary particles [21]-[23] as we hope to show in the following main part of the ensuing sections of the present short paper....
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...As known from E-infinity, differentiation and integration are replaced by down scaling and up scaling respectively [16]-[18]....
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...Consequently we have a highly consistent theory linking in the 16 bosonic dimensions of Heterotic superstring theory with a fractal number of generators of a fuzzy version of the electroweak Lie symmetry group SU(2) [16] [30]....
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...Scaling 2 o α down using the fundamental scaling factor φ [16] one finds the following 6 “quasi-differentiated” sequence [30]-[33]...
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...The fuzzy logic related notion of fractal counting of quantum particles which is based on fractal logic [30] was introduced some time ago in connection with the SU(3) SU(2) U(1) standard model of elementary high energy particles [16]....
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