Complexity in Spacetime and Gravitation i. FromChaos to Superchaos

We intend to show in this paper that the two fundamental concepts of the GrandUnification and the Chaos Theory are essential constituent elements of a theory of everythingand appertain, in fact, to the overall domain of complexity in space, time and gravitation. Theauthors hope that the present paper may offer suggestions for the necessary methodology in theanalysis of complex problems. Following a short review of the main concepts describingconventional complexity, we introduce as an example of a possible development in standardparadigms, a new type of Rayleigh–Bénard instability which maybe generated in the interior of a gravitating body and may be the cause of earthquakephenomena. We define the new terminologies of constructive and destructiveresonances in relation to the stability of the solar system. We attempt to find a physicalargument in support of the invariant character of a gravitational chaos. Within the frame of aRiemannian spacetime we obtain also a mathematical formulation of El Naschies conjecture: gravity is caused by an average deviation of fractal time from linear uniform time. Westudy also in some detail the physics of black holes because black holes offer perfect laboratoriesfor all manifestations of complexities and simplicities. We stress that singularities as well aschaos demonstrate an invariant character. Even the Schwarzschild radius, which was initiallyconsidered to be merely a coordinate singularity, is found to retain or deepen its physicalsignificance by diffeomorphisms. Symmetry principles in particle physics and continuousattempts to find a fundamental and unique constituent (strings, p-branes, etc.) of matter arereviewed and their link with complexity, dimensionality of spacetime and chaos is indicated.Particular attention is paid to spontaneous symmetry breaking and the Higgs mechanism in thecontext of a cascade of concepts: classical lattice gas, Ising model, order–disorder transition,inflationary scenario, and the universe as a lattice. This cascade tends to confirm the universalityof the lattice structure of the universe. In the final section of this first part of the paper wepropose a novel multi-spherical cosmic fractal as a model of homogeneous andisotropic cosmologies. If chaos is generated at the level of a background-arena in spacetime, thenadditional chaotic manifestations generated in this arena represent chaos on a higher level orscale. The suggestion is offered that a chaos on a higher level called superchaos interlaces withchaotic effects at different lower levels. The two other prospective parts of the paper will refer tothe subjects: Part 2. Chaoticity of Anisotropic Cosmologies. Part 3. Elementary Particles, DarkMatter and Information Aspects in Relativity.