**1. Introduction**

8 Will-be-set-by-IN-TECH

86 Quantum Gravity

several emergent gravity theories fit to the results of this work, see for instance [1–8] where

We end this work by remarking that several issues are left for future investigation. Just to name a few: The role of matter fields living in the starting gauge theory; the generalization of the present results to include metric-affine gravities before the reduction of the coframe bundle; the role of the extra matter fields in the dark matter/energy problem; explicit computations in order to make reliable predictions that fit with actual data; and so on.

Conselho Nacional de Desenvolvimento Científico e Tecnológico6 (CNPq-Brazil) is acknowledge for financial support. I also would like to express my gratitude to InTech for

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<sup>6</sup> RFS is a level PQ-2 researcher under the program *Produtividade em Pesquisa*, 304924/2009-1.

the Higgs mechanism is largely used to separate gauge and gravity phases.

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**6. Acknowledgements**

this opportunity.

**7. References**

Einstein's contribution to relativity was initially an intuitive approach based on a basic elimination of simultaneousity and a mathematical reformulation using the Lorenz transformation. In this respect Einstein just added some more physics to what Poincaré and Lorenz have done much earlier. However, it was Minkowski who introduced the geometrical ideas and the use of a four-dimensional space with time as the fourth dimension. Einstein took over Minkowski's idea and initiated what we may call the program of geometrizing physics, starting with gravity. Later on Einstein and Hilbert attempted the unification of electro-magnetism and gravity while Kaluza and Klein tried the same using an extra fifth dimension. This may have been the beginning of the higher dimensional space-time theories culminating in super strings, super gravity and the Cantorian space-time theory [1].

In special relativity there is no absolute time. We have a space and each slice has its own time. Thus each point in the Minkowski's space is specified by four coordinates, three spatial and one temporal in a four-dimensional space-time rather than the 3+1 space plus time coordinates of the classical mechanics [1].

A fundamental role in this new geometry is played by the constancy of the velocity of light that cannot be exceeded without violating the causal structure as well documented experimental facts show. A change of things began by adding quantum mechanics to special relativity.

By replacing Euclidean geometry by curved Riemannian one, Einstein was the first to give gravity a geometrical interpretation as a curvature of space-time due to matter. Einstein never fixed the topology of his theory nor did he use or was aware of the existence of nonclassical geometry which was in any case in its infancy [1-5]. The possibly only encounter of Einstein with M. S. El Naschie's Cantorian like transfinite geometry was when K. Menger presented a paper in a conference held in his honour [1, 6-17].
