Abstract
In a one-dimension Mauldin-Williams Random Cantor Set Universe, the Sigalotti topological speed of light is where . It follows then that the corresponding topological acceleration must be a golden mean downscaling of c namely . Since the maximal height in the one-dimensional universe must be where is the unit interval length and note that the topological mass (m) and topological dimension (D) where m = D = 5 are that of the largest unit sphere volume, we can conclude that the potential energy of classical mechanics translates to . Remembering that the kinetic energy is , then by the same logic we see that when m = 5 is replaced by for reasons which are explained in the main body of the present work. Adding both expressions together, we find Einstein’s maximal energy . As a general conclusion, we note that within high energy cosmology, the sharp distinction between potential energy and kinetic energy of classical mechanics is blurred on the cosmic scale. Apart of being an original contribution, the article presents an almost complete bibliography on the Cantorian-fractal spacetime theory.
Highlights
Space, time, matter and energy are concepts far from being trivial or obvious even within Newtonian classical mechanics [1]-[6]
Starting more or less from there it became the Author’s lifelong work and even magical fascination to incorporate the basic structure of quantum mechanics into the very topology and geometry of space and time [7]-[428]
The author followed a path inspired by the work of Richard Feynman and its development by the Canadian Physicist G
Summary
Time, matter and energy are concepts far from being trivial or obvious even within Newtonian classical mechanics [1]-[6]. ( ) where=φ 5 −1 2 is just a compact version of Von-Neumann-Connes’ dimensional function of a Penrose tiling universe [7] [14] [165] In addition this dimensional function is generic and can be used to understand some of the most complex and difficult problems in Physics and Astrophysics [9]-[429]. It is shown using the above that the quantum particle may be described by the zero set as given by the bi-dimension [7] [27]. The empty set quantum wave is fixed by the bi-dimension minus one for the topological dimension and φ 2 for the Hausdorff dimension [7] [9] [73]. By contrast in the present work, we will take another route to arrive at the same result by stressing an optional separation between kinetic energy and potential energy in fractal spacetime
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