The Self Similarity Equivalence Relation Connecting Newton’s Energy with Einstein’s Energy and Dark Energy

Select Volume / Issue:

• Volume 4,Issue 1, Jan. 2016

Year:

2016

Type of Publication:

Article

Keywords:

Einfinity, Einstein Self Similarity, Equivalence Relation, Fractal Scaling, Fractal Quantum Field, Golden Mean Scaling, Intermediate Asymptotic, Quantum Gravity, Random Cantor Sets, Scaling, Special Relativity, tHooft Regularization

Authors:

Mohamed S. El Naschie

Journal:

IJISM

Volume:

4

Number:

1

Pages:

42-57

Month:

January

ISSN:

2347-9051

Abstract:

In this paper we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We start 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 utilized to show how the classical Newton’s kinetic energy E = ½ mv2 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.

Full text: IJISM_507_Final.pdf [Bibtex]