Author(s)

M. S. El Naschie

Department of Physics, Faculty of Science, Alexandria University, Alexandria, Egypt.

The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.

E-Infinity, Cantorian Spacetime, Self-Similarity, M-Theory, Kaluza-Klein Space, Fuzzy Kähler Manifolds, Continued Fraction, Isomorphic Length, Geometrical Gauge Invariance

El Naschie, M. (2016) Completing Einstein’s Spacetime. Journal of Modern Physics, 7, 1972-1994. doi: 10.4236/jmp.2016.715175.