“...the paper does describe new discoveries of new applications for chaos and fractals in the very unlikely area of high-energy particle physics.”

I think there may be several reasons why this particular paper is highly cited. However, the main reason, which may apply to various papers that I have written in the field, is most probably connected to the subject itself. My paper brings together two fields that are rarely allowed to come together, even though they could benefit tremendously from cross-fertilization. The two subjects are high-energy particle physics on the one side and nonlinear dynamics, complexity theory, chaos, and fractals on the other. Leading particle physicists rarely have deep knowledge of fractals and nonlinear dynamics. To be candid, they rarely take this mathematical subject seriously. By contrast, people working in nonlinear dynamics and complexity theory are usually mathematicians and applied mechanicians dealing with classical physics with little, if any, interest in particle physics. There are of course exceptions, for instance, Nobel Laureate Gerrard ‘t Hooft who is, although very conservative, extremely open minded, which is quite a rare combination. Theoretical physicists are conservative by nature and it is important to be that way, but one also has to be open minded about things in maths which may seem at the beginning to be esoteric, such as the Cantor sets that I use. However, what could be more esoteric than the real outcome of real experiments in quantum particle physics. Another example of an experimentalist with enthusiasm for nonlinear dynamics and chaos is Nobel Laureate Gerd Binnig, who has encouraged me in many ways. I have intentionally omitted mentioning my teacher and mentor, the late Nobel Laureate Ilya Prigogine, because he was immersed in nonlinear dynamics and may have been biased towards it. Those are all the exceptions; the usual leading particle physicist is totally disinterested in chaos and fractals, and the usual leading nonlinear dynamacist usually applies his knowledge in classical fields and never has the time to be trained in particle physics. However, it is my belief as well as the belief of a growing minority that without an expertise in nonlinear dynamics, chaos, and fractals, the two excellent theories for quantum gravity, namely string theory and loop-quantum mechanics, will only partially solve the problem. Another reason for the high citation of my paper may be the review character and its somewhat informal user-friendly language as well as the many colored illustrations included.

Yes, the paper does describe new discoveries of new applications for chaos and fractals in the very unlikely area of high-energy particle physics. Using many methods and tools borrowed from complexity theory, chaos, and fractals, we can better understand the role of the symplictic vacuum in creating particles. In this way we understand the Higgs boson, quantum gravity, and the unification of all fundamental forces. Of course I am building on pioneering work done by many other people but the new ingredient, chaos and fractals, gave me a new geometry, and using this geometry we were in a position to understand, for instance, why we have so many particles and why the elementary particles have the masses they have.

I was originally trained as an engineer, but I came to know Prof. Carl F. Weizker in Germany and got interested in the work of W. Heisenberg as an engineering student in the early ‘60s. Later on I received a Ph.D. at University College, London where I worked on elastic stability and buckling of shells. I subsequently started moving toward applied mathematics working in R. Thom’s catastrophe theory, bifurcation, and nonlinear dynamics. While experimenting with spatial chaos I discovered that I could use chaos, fractals, and complexity theory to solve difficult problems in quantum mechanics with amazing simplicity. That was when I changed completely to physics and studied particle physics on my own, with the help of some of my friends. Then I realized that the mass spectrum of high-energy particle physics could be solved as a scaling problem in an infinite dimensional but hierarchal fractal space-time.

Einstein’s theory deals with the very large, i.e., planets, stars, and galaxies. By contrast quantum mechanics and particle physics deals with the very small, i.e., atoms, electrons, protons, and quarks. Einstein formulated his general theory of gravity in four-dimensional, curved space-time. Quantum mechanics, on the other hand, is formulated in the smooth space plus time as a parameter, exactly as in Newton’s classical mechanics. This is a contradiction which showed itself in the fact that we could not bring Einstein’s theory to be unified with quantum mechanics, like Maxwell when he unified electricity and magnetism in the theory of electromagnetism. However if we postulate a geometry which is so wild that it looks more like a stormy ocean to be the geometry of space-time, then both Einstein’s theory and quantum particle physics will fit in. That is more or less what I have done. The ideas come from many other scientists like Wheeler, Penrose, Finkelstein, and many others. Yet to have a pictorial model is one thing and to make calculations is another thing. By introducing very simple sets, called Cantor sets, I was able to make precise calculations and exact predictions of things that were previously done by hand based on measurements in laboratories. So by introducing a space-time which is not only four-dimensional but also infinite-dimensional, and by using hyperbolic random fractals, I was able to precisely model this stormy ocean in which relativity and quantum mechanics can live side by side. I hasten to say that all these results would not have been possible without the pioneering work done in many other theories, particularly string theory as developed by Green, Gross, and Witten as well as loop quantum mechanics, noncommutative geometry, and twistor theory, to mention only a few.