Spacetime as a New Frontier Advanced Material with Applications in Physics, Engineering, Chemistry and Cosmology

Abstract

Keywords Mae-Wan Ho (1941. A great scientist and a great lady.

Mass Constituents of a Flat Lattice Multiverse: Conclusion from Similarity between Two Universal Numbers, the Rocksalt-Type 2<i>D</i> Madelung Constant and the Golden Mean

“…The infinite extension of this system with a still immeasurable number of objects justifies once more the profitable application of number theory respectively set theory. In this sense, the found φ −2 -dependence of the cosmological mass fractions supports the "set-theoretical" interpretation given by El Naschie [31].…”

“…The representation of integers enhances the probability of this assumption to be realistic. Once assumed such diversification 31.18034 = 5(2φ −2 + 1); +) corresponds exactly to half the formerly Ω m value (see Table 1). Journal of Modern Physics of dark matter, could it leave a fingerprint on the nature of the otherwise unseen particles of which it consists?…”

“…with the Urysohn-Menger [29] [30] topological dimension n, yielding for n = −1 the result Recently, El Naschie [31] quantified this approach further. He places the five-fold quasi-crystal symmetry in a Kaluza-Klein five-dimensional manifold and finds a five-dimensional zero set topological volume of φ 5 .…”

Elements of a New Set Theory Based Quantum Mechanics with Applications in High Energy Quantum Physics and Cosmology

“…In the present work we draw in a nutshell the outline of a new quantum mechanics based mainly on transfinite set theory and noncommutative geometry . It turns out that such an undertaking is much simpler and by far more intuitive than what one would have initially expected [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. In fact tying together Penrose fractal tiling universe [28,29,31,32] and Connes noncommutative geometry [15][16][17][18][19] using the deductive dimensional theory of Menger-Urysohn [1][2][3][4][5][6][7] and modern nonlinear dynamics and fractals, we are almost at our destination [26,36].…”

“…We stress once more that the sources and elements of the present synthesis is an amalgamation of the thinking and results of D. Shechtman's quasi crystals [29,31,52], its geometrical topological description by Penrose fractal tiling universe [31] and its algebraic analytical description by A. Connes' noncommutative geometry [15][16][17][18][19] which is based on von Neumann's pointless continuous geometry [24,32] and where the Menger-Urysohn dimensional theory also plays a pivotal role. We added to that the bijection formula [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] to replace and extend Connes' dimensional function and made extensive use of the Menger-Urysohn deductive theory of dimensions [9][10][11][12][13][14] [26,36] which resulted in a giant step forward in our understanding of the essential differences between zero, empty and nothing and by realizing that way that the empty set must be negative topological dimension starting at minus one [38][39][40][41][42]. We did not stop there but extended the notion of empty set using the concept of the degree of emptiness of an empty set introduced some time ago by the late B. Mandelbrot [39] and that way made a profoun...…”