The first E8 proposal for complete unification of all fundamental forces

12th December, 2010.
E-infinity communication No. 53

The first E8 proposal for complete unification of all fundamental forces

It is abundantly clear from a quick study of the large body of literature published by Mohamed El Naschie, Ji-Huan He, L. Marek-Crnjac and many of those working on E-infinity theory that the first implicit proposal for unification using E8 exceptional Lie group was published around 2005 or even earlier. The exact date needs time to nail down more accurately because of the large volume of papers by the prolific author. In a paper entitled “Determining the number of Hiss particles starting from general relativity and various other field theories” which was published in CS&F, 23, (2005), pp. 711-725 El Naschie set outs to explain the idea of unification in paragraph 11 which is labeled Discussion and Conclusion on pages 724 and 725.
In what follows we give a summary of what was said on this subject. At that time El Naschie chose to call his idea, conservation of the dimensional symmetry. He wrote that in what was a rudimentary form simply equating Dim E8E8 to N(R(8)) plus alpha bar naught of electromagnetism, that is to say 137 plus N(R(4)). With R(8) he means the number of independent components of a Riemannian tensor in eight dimensions. These are 336 before compactification and 338.885438, nearly equal 339 after compactification. They are the net difference between the compactified dimensions of E8E8, namely 496 ̶ k2 = 495.9674775 and the compactified dimensions of E6E6 which are equal to 156 + 6k = 157.0820393 when symmetry is broken and E8E8 goes to E6E6 of the exceptional E-line of those important Lie symmetry groups. It is historically interesting to note that at this time El Naschie did not use ‘t Hooft’s holographic boundary where all the 339 particles of the 496 bulk lives. Thus El Naschie used a kind of super gravity argument at that time. He then adds the usual 20 representing the independent components of the Einstein gravity. There are exactly 20 for the case of four dimensions. Thus he has in essence equated the 496 dimensions of the E8E8 bulk with N(R(8)) plus alpha bar naught of electromagnetism plus N(R(4)) = 339 + 137 + 20. This is exactly equal 496 when we consider the integer approximation. In later publications the said 20 were interpreted as the number of isometries of pure gravity in 8 dimensions and the 339 as the number of elementary particles living on the holographic boundary. This is a real unification attempt using the E8E8 group and is many years before any similar attempt by anyone and definitely years before G. Lisi. It is also interesting to note that calculation without compactification leading to 336 instead of 339 particles was interpreted in this particular article as suggesting the existence of 3 Higgs particles H(+), H( ̶ ) and H(0) to make up the deficit of 339 ̶ 336 = 3. El Naschie for some reason never repeated this interesting interpretation again as far as we are aware.