A Fundamentally Fractal Universe from Einstein, Kaluza-Klein, Witten and Vafas Space-Time

Research areas:

• Volume 8,Issue 2, Sept. 2019

Year:

2019

Type of Publication:

Article

Keywords:

Fractal Cantorian Universe, Fractal Vafas Spacetime, Fractal Einstein Kaluza Klein Spacetime, Arnold Schoenberg Twelve Tones Music, Vafas F Theory in Physical Quantum Cosmology

Authors:

M. S. El Naschie

Journal:

IJAIM

Volume:

8

Number:

2

Pages:

1-11

Month:

September

ISSN:

2320-5121

Abstract:

The paper starts from A. Einstein's four-dimensional spacetime and shows that to achieve scale invariance for D(Einstein) which is equal to D(Newton) = 3 plus one, the origin of Einstein's dimension D = 4 must be extended to the scale invariant Hausdorff dimension where is the golden section. Consequently the five-dimensional spacetime of T. Kaluza and O. Klein must be analogously extended from D = 5 to . Subsequently we deduce in a systematic step by step way, the intimate relation between the k - k theory (D = 5) and its fractal version extension i.e. to E. Witten's eleven dimensional M-theory (D =11) and its fractal version with where is L. Hardy's quantum entanglement. Finally we conclude with the logical and mathematical inevitability of C. Vafa's twelve dimensional father theory and its corresponding fractal version which resonates Schoenberg's twelve- tunes music (also known as dodecaphony) with where is the E-infinity topological Unruh temperature. Last but not least, the indispensable role of the relatively modern research results on pure gravity and non-commutative spaces by numerous pioneers of theoretical and mathematical physics in elucidating all of the above is outlined at some length but not in detail i.e. presupposing a moderate familiarity with the required background in the latest research results of modern quantum physics and cosmology.

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