A Review of Applications and Results of Ε-infinity Theory

Naschie, El

doi:10.1515/ijnsns.2007.8.1.11

Cited by 92 publications

(14 citation statements)

References 56 publications

(32 reference statements)

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“…Subsequently the present author demonstrated that the Penrose fractal tiling may be viewed as a compactified Klein modular curve with 336 16 339 D k = +  degrees of freedom and that as such it is generic and represents the surface or the holographic boundary of a universe described in bulk by E8E8 exceptional Lie groups of super strings [57]. The dimensionality conservation equation connecting E8E8 with the Klein-Penrose boundary may be given in various forms of which the following is the simplest [19] [43] [49] ( ) ( ) …”

Section: Appendixmentioning

confidence: 99%

The Emergence of Spacetime from the Quantum in Three Steps

Naschie¹

2016

APM

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The paper presents a very simple and straight forward yet pure mathematical derivation of the structure of actual spacetime from quantum set theory. This is achieved by utilizing elements of the topological theory of cobordism and the Menger-Urysohn dimensional theory in conjunction with von Neumann-Connes dimensional function of Klein-Penrose modular holographic boundary of the E8E8 exceptional Lie group bulk of our universe. The final result is a lucid sharp mental picture, namely that the quantum wave is an empty set representing the surface, i.e. boundary of the zero set quantum particle and in turn quantum spacetime is simply the boundary or the surface of the quantum wave empty set. The essential difference of the quantum wave and quantum spacetime is that the wave is a simple empty set while spacetime is a multi-fractal type of infinitely many empty sets with increasing degrees of emptiness.

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Section: Appendixmentioning

confidence: 99%

The Emergence of Spacetime from the Quantum in Three Steps

Naschie¹

2016

APM

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“…In fact and as will be analysed in substantial detail in the present work, Newton's kinetic energy E = 1/2mv 2 where m is the mass and v is the velocity and probably the most famous formula in physics, with which we mean Einstein's mass-energy equation E = mc 2 where c is the speed of light (see Figure 3) differ only formally in the scale and notation used and nothing much more than that (see Figure 3 and Figure 4). Remembering that energy, entropy and information [46] [49]- [57] are without a doubt some of the most fundamental and interrelated notions in physics, then it is natural that we utilize these afore mentioned self similarity to shed light on the major problem of the measurable ordinary energy density [58]- [63] and the dark energy density [60]- [63] of the cosmos which we cannot measure at present in any direct way [57]- [63]. As mentioned earlier on, this and various related aspects [60]- [74] is the subject of the present paper which although relatively short, has the character of a survey paper due to the large number of subjects and problems we address as well as the numerous theoretical and mathematical physics references included [1]- [132].…”

Section: The Simplexity Of Quantum Complexity-an Informal Introductionmentioning

confidence: 99%

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

Naschie¹

2016

IJAA

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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 = 1/2mv 2 leads to Einstein's celebrated maximal energy equation E = mc 2 and how in turn this can be dissected into the ordinary energy density E(O) = mc 2 /22 and the dark energy density E(D) = mc 2 (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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“…12 + x if x ∈ (2,5] x − 3 if x ∈ (5,20). Here, it may be pointed out that Theorem 2.1 is not applicable to this example as S(X) is not a closed subset of X.…”

Section: Related Results In Metric Spacesmentioning

confidence: 97%

“…The theory of probabilistic metric space is of paramount importance in probabilistic functional analysis. Towards the application side, one may recall El Naschie [2] wherein he gave applications of this concept in quantum particle physics particularly in connection with both string and ε ∞ theory.…”

Section: Introductionmentioning

confidence: 99%

Common fixed points of strict contractions in Menger spaces

et al. 2011

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The aim of this paper is to prove some common fixed point theorems under certain strict contractive conditions for mappings sharing the common property (E.A) in Menger spaces. As applications to our results, we obtain the corresponding common fixed point theorems under strict contraction in metric spaces. Thus, our results generalize many known results in Menger as well as metric spaces. Some related results are also derived besides presenting several illustrative examples.

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A Review of Applications and Results of Ε-infinity Theory

Abstract: The work is basically a short review of a selection of papers published on the foundation and applications of Ε-infinity theory.

Cited by 92 publications

References 56 publications

The Emergence of Spacetime from the Quantum in Three Steps

The Emergence of Spacetime from the Quantum in Three Steps

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

Common fixed points of strict contractions in Menger spaces

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