Statistical mechanics of multi-dimensional Cantor sets, Gödel theorem and quantum spacetime
✍ Scribed by M.S. El Naschie
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 883 KB
- Volume
- 330
- Category
- Article
- ISSN
- 0016-0032
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✦ Synopsis
Two d$ferent descriptions of an abstract n-dimensional dynamical system are discussed: a Sierpinski space setting and a statistical cellular space setting. The results suggest that in four dimensions the phase space dynamics is peano-like and resembles an Anosoc dtfleomorphism of a compact manifold which is dense and quasi-ergodic. The Hausdorfl capacity dimension in this case is d,--c4) -3 981 g 4 and we conjecture that the simplest fully developed turbulence is related to dl_I' zz 6.3. The corresponding Shannon information entropy of the second analysis are 9,s -(4) -3 68 and Yi?' = 6.12. The implications of the results .for quantum spacetime are outlined and ,found to be consistent with Heisenberg uncertainty relationship and Bekenstein-Hawking entropy. Finally, the connection between stranqe nonchaotic behaciour and Code1 theorem is discussed.