Peter Woit “Not Even Wrong” is certainly right and wrong: An interview with Mohamed El Naschie

12th December, 2010.
E-infinity communication No. 52

Peter Woit “Not Even Wrong” is certainly right and wrong: An interview with Mohamed El Naschie

The following is a summary of an interview with Prof. Mohamed El Naschie conducted by Shayma, a journalist based in Cairo which will be published in full length in Arabic.
Dr. Woit’s book (published by Jonathan Cape, London (2006)) is an excellent popular account voicing strong dissent against the dominance of string theory. Never the less we think super strings are a very useful theory which has made and it still making important contributions. Dr. Woit made several important remarks and suggestions towards improving the standard model of high energy physics and reaching the number one goal of theoretical physics at present which is quantum gravity, i.e. unifying quantum mechanics and general relativity in one coherent and consistent theory. Other important aspects of modern quantum physics were omitted all together such as fractal spacetime and fractal gravity or addressed briefly and superficially like noncommutative geometry. Let us commence with the positive aspects of this important book which we believe should be read by every scientist working on modern physics.
The crucial point which Woit makes is related to the role of symmetry in quantum mechanics. He spells it out already in the introduction at the end of page 7 where he writes “The failure of the superstring theory programme can be traced to its lack of any fundamental new symmetry principle”. He then continues on page 8 by writing “…. Advances are only likely to come about if theoretist turn their attention away from this failed programme and (direct) it towards the difficult task of better understanding the symmetries of the natural world.” It is important to carefully analyze these statements of Woit summarizing all the wisdom of his book. To be sure, superstrings are making use of a very important symmetry principle which is new in physics although well known for a long time in mathematics, namely the exceptional Lie symmetry group E8. In fact superstrings take E8 E8 with dimension equal (2)(dim E8) = (20)(248) – 496. Thus this is not what Woit means. What we think he means is a completely new symmetry better suited to quantum gravity. Maybe he also means a larger group which is richer than E8. However E8 is the largest except for the monster group which is hardly understood as physics in general. If that is what Woit means then he should become a great friend of E-infinity theory and of Prof. El Naschie, that is if he took the time to read our work carefully and without prejudice. In E-infinity El Naschie, He, Crnjac and Iovane introduced much larger Lie symmetry groups than E8 by summing over all Lie symmetry groups. For instance the sum over the E-line gives a ‘fuzzy’ group, i.e. a ‘fractal’ group with 548 instead of only 496 as integer part of the dimension. During the 80’s and 90’s of the last century in what is now called the European Journal of Physics, El Naschie wrote several papers on ‘average’ symmetries. This symmetry is the symmetry of chaos and avoids the anomalies stemming from the clashes between external and internal symmetries. All that is discussed in many papers by El Naschie, particularly those related to knot theory, wild topology, von Neumann’s continuous geometry, K-theory and especially A. Connes’s noncommutative geometry and even the monster group. Woit repeats his important point regarding symmetry in the conclusion on page 266 where he write “I see as an important lesson that each generation of physicist since the advent of quantum mechanics seems to need to learn anew. This lesson is the importance of symmetry principles expressed in mathematical language of group representation theory…… The underlying source of the problems of superstring theory is that the theory is not built on a fundamental symmetry principle or expressed within the language of representation theory.” We in E-infinity theory fully endorse this point of view and believe that our reformulation of Feynman’s summing over paths theory to summing over dimensions and summing over Lie groups as well as two and three Stein spaces is the correct strategy and as such is in full harmony with the views expressed in Woit’s book.
Now we come to the point upon which we do not agree at all with Woit. E-infinity is a K-theory for spacetime. In less formal mathematical language we mainly use semi groups (being summed over groups). In popular language of computer science, we use fractal automaton. Fractal sets and K-theory are what noncommutative geometry is all about. Noncommutative geometry is not as popular as string theory. However this is not the mistake of noncommutative geometry as Woit very well knows. For this reason it is not adequate to give only a few lines in his book to noncommutative geometry. On page 256 Woit write “One other speculative research programme that deserves mention goes under the name of non-commutative geometry….”. We in E-infinity profoundly disagree. If you call noncommutative geometry speculative, what do you call superstrings with 10 spacetime dimensions of which we have only seen 3 and God knows what the fourth or the fifth could be. A. Connes is the most important mathematician alive working in physics besides Sir. R. Penrose. We are astonished about this evaluation of Woit for noncommutative geometry for another reason. In his Acknowledgement Dr. Woit thanks Sr. R. Penrose for critical help. But one of the most important and most famous contributions of Penrose is his well known Penrose tiling. This tiling is the best known example of a noncommutative space based on K-theory and it is the prototype of E-infinity space. On piece of interesting information mentioned in Woit’s book which most of us did not know is that E. Witten has no degree, not even a Bachelors in physics. He was a journalist but his father worked in relativity and was a professor. This speaks of course for Witten. However some silly people hold it against El Naschie that he is a structural engineer and has no degree in physics.
We sincerely hope there will be a new edition of Woit’s book and that noncommutative geometry, fractal spacetime and Penrose tiling will be given more attention. There are many papers published on Elsevier’s Science Direct in CS&F regarding Penrose tiling as an example for E-infinity and noncommutative geometry of which we recommend the following:
1. M.S. El Naschie: von Neumann geometry and E-infinity quantum spacetime. CS&F, Vol. 9(12), (1998), pp. 2023-2030.
2. M.S. El Naschie: Penrose universe and Cantorian spacetime as a model for noncommutative quantum geometry. CS&F, Vol. 9(6), (1998), pp. 931-933.
3. M.S. El Naschie: Penrose tiling, semi conduction and Cantorian 1/fa spectra in four and five dimensions. CS&F, Vol. 3(4), (1993), pp. 498-491.
In addition an important paper on average symmetry is
4. M.S. El Naschie: Average exceptional Lie and Coxeter group hierarchies with special reference to the standard model of high energy particle physics. CS&F, 37, (2008), pp. 662-668.