‘t Hooft dilaton proposal and the inbuilt natural conformal invariance of E-infinity and Nottale scale relativity

6th December, 2010
E-infinity Communication No. 43

‘t Hooft dilaton proposal and the inbuilt natural conformal invariance of E-infinity and Nottale scale relativity

Nobel Laureate Professor Gerard ‘t Hooft is one of a handful of leading mainstream physicists who have an enduring interest in reforming quantum field theory and therefore by necessity amending the basic structure of quantum mechanics itself. This interest continued despite considerable criticism from many other leading scientists, for instance Nobel Laureate D. Gross who recently said in an article entitled “The major unknown in particle physics and cosmology” with respect to ‘t Hooft’s deterministic quantum mechanics that if we were to go back to deterministic classical theory, things would only get worse. In our view this is a total misunderstanding of what ‘t Hooft is trying to do as well as a total misunderstanding of classical mechanics. Classical mechanics is generically deterministically chaotic. In fact this is a well known result of the major work of Poincaré on the three body problems. The four body problem is even worse and at the time of writing there is no computer in the universe which is large enough to even start numerically integrating the problem of how five planets move under mutual influence. It was in fact Nobel Laureate Max Born, the teacher of Werner Heisenberg who disputed that classical mechanics is deterministic. A very readable and relatively short paper discussing the work of Max Born and contrasting ‘t Hooft’s work on deterministic quantum mechanics with Mohamed El Naschie’s work on E-infinity theory is “Deterministic quantum mechanics versus classical mechanical indeterminism”, published in Int. J. of Nonlinear Sci. & Num. Simulation, 8(1), 5-10 (2007). The article of Max Born is “Ist die Klassische Mechanik tatsächlich deterministisch?”, published in Physikalishe Blätter II, pp. 49 (1955). A second paper by El Naschie is in the same volume where Prof. ‘t Hooft’s paper is published entitled “What is quantum mechanics?”, pp. 84-102. The volume is a publication of the American Inst. of Physics, Vol. 905 (2007). El Naschie’s paper is entitled “Deterministic quantum mechanics versus classical mechanical indeterminism and nonlinear dynamics”, pp. 56-66. In our opinion the most important new developments in the work of ‘t Hooft is that he seems to have discovered fractals and consequently El Naschie’s zero and empty transfinite-fractal sets for quantum field theory. In his 2008 paper “Locally finite model for gravity”, published on arXiv: 0804.0328U1[gr-qc]2, April, 2008 he clearly says in the abstract that the model is not finite because the solutions tend to generate infinite fractals. Furthermore in Fig. 2 on page 5 his deficit and surplus angles are the reason for introducing fractal simplicticity a la Mohamed El Naschie and thus Cantor dust and fractals. In fact it is the dilaton, which is known from all superstring theories which bring the scale invariance of the fractal geometry of Nottale and El Naschie through a backdoor into ‘t Hooft’s quantum field theoretical model. He admits trouble due to the negative sign of the new field but that is a little price to pay to enter into the paradise of zero and empty transfinite-fractal sets which are the basic building blocks of spacetime and consequently of E-infinity. We hope ‘t Hooft remains in Cantor paradise with D. Hilbert.