论文信息 - Statistical mechanics of multi-dimensional Cantor sets, Gödel theorem and quantum spacetime

Statistical mechanics of multi-dimensional Cantor sets, Gödel theorem and quantum spacetime

Abstract Two different 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 Anosov diffeomorphism of a compact manifold which is dense and quasi-ergodic. The Hausdorff capacity dimension in this case is d(4)C= 3.981 ≅ 4 and we conjecture that the simplest fully developed turbulence is related to d(5)C≅ 6.3. The corresponding Shannon information entropy of the second analysis are l (4)S = 3.68 and l (5)S = 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 strange nonchaotic behaviour and Godel theorem is discussed.

M. S. El Naschie | M. Naschie

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