zbMATH — the first resource for mathematics

VAK, vacuum fluctuation and the mass spectrum of high energy particle physics. (English) Zbl 1034.81515
Summary: We introduce a fundamental hypothesis identifying quantum vacuum fluctuation with the vague attractor of Kolmogorov, the so-called VAK. This Hamiltonian conterpart of a dissipative attractor is then modelled by $$\varepsilon^{(\infty)}$$, topology as a “limit set” of a wild dynamics generated by Möbius-like transformation of space. We proceed as follows: First we give an introduction to the $$\varepsilon^{(\infty)}$$ quantum spacetime theory from the point of view of nonlinear dynamics, complexity, string and KAM theory. Subsequently we give without proof several theorems and conjectures that we consider to be fundamental to the foundation of any general theory for high energy particles interaction. The final picture seems to be a synthesis between compactified Kleinian groups acting on an essentially nonlinear dynamics of a KAM system which enables us to give a very accurate estimation of the mass spectrum of the standard model, and further still we are granted a glimpse into the physics of grand unification as well as quantum gravity. It is concluded that VAK in the infinite dimensions of $$\varepsilon^{(\infty)}$$ is a valid model for stable quantum states.

MSC:
 81R60 Noncommutative geometry in quantum theory 81Q50 Quantum chaos 81V35 Nuclear physics 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
Full Text:
References:
 [1] El Naschie, M.S., Superstrings, knots and non-commutative geometry in ε(∞) space, Int. J. theor. phys., 37, 12, (1998) · Zbl 0935.58005 [2] El Naschie, M.S., Modular groups in Cantorian ε(∞), high-energy physics, Chaos, solitons & fractals, 16, 353-366, (2003) · Zbl 1035.83503 [3] Marek-Crnjac, L., On mass spectrum of elementary particles of the standard model using el naschie’s Golden field theory, Chaos, solitons & fractals, 15, 611-618, (2003) · Zbl 1033.81521 [4] Ord, G., Classical particles and the Dirac equation with an electro-magnetic force, Chaos, solitons & fractals, 8, 5, 727-741, (1997) · Zbl 0940.81003 [5] Arnold, V.I., Geometrical methods in the theory of ordinary differential equations, (1983), Springer-Verlag New York · Zbl 0507.34003 [6] Mumford, D.; Series, C.; Wright, D., (2002), Indra’s Pearls Cambridge [7] El Naschie, M.S.; Rossler, O.; Prigogine, I., Quantum mechanics, diffusion and chaotic fractals, (1995), Elsevier Science-Pergamon Press Oxford · Zbl 0830.58001 [8] El Naschie, M.S., On the exact mass spectrum of quarks, Chaos, solitons & fractals, 14, 369-376, (2002) [9] El Naschie MS, Nottale L, Al Athel S, Ord G. Fractal spacetime and Cantorian geometry in quantum mechanics, Special Issue of Chaos, Solitons & Fractals, 1996;7(6) [10] Beck, C., Spatio-temporal chaos and vacuum fluctuations of quantized fields, (2002), World Scientific Singapore · Zbl 1066.81621 [11] Kilmister CW. Eddington’s search for a fundamental theory. Cambridge, 1994 [12] ’t Hooft G. In search of the ultimate building blocks. Cambridge, 1997 · Zbl 1344.81006 [13] El Naschie, M.S., Stress, stability & chaos, (1990), McGraw Hill London · Zbl 0729.73919 [14] Binnig G. Aus dem Nichts Piper, Munich, 1989 [15] Guckenheim, J.; Holmes, P., Nonlinear oscillation, dynamical systems and bifurcation of vector fields, (1983), Springer New York [16] Abraham, R.; Mardsen, J., Foundation of mechanics, (1978), Benjamin London
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.