The Aether of Spacetime Physics Is the Empty Set of Pure Mathematics

Abstract

The present note is basically an announcement of a theoretical and experimental resolution of one of the most basic fundamental problems of physics, namely the very existence and reality of the Aether [1][2][3][4][5][6][7][8][9][10][11]. This is not only basic philosophy of science or insightful results in theoretical physics and cosmology [1-24] but more than that because it may lead to actually realizing the futuristic dream of free energy [25][26][27][28].Our mathematical and indirect experimental verdict is that the Aether exists and it can be equated to the empty set of pure mathematics [3,[12][13][14][15][16]. More precisely the Aether may be understood for all mathematical and physical purposes as being identical to the empty set [8][9][10][11][12][13][14] underlying the Penrose fractal tessellation universe [17] which obeys the A. Connes' corresponding dimensional function of his noncommutative geometry [18][19][20][21].It is then a relatively short distance to conclude from the above that cosmic dark energy is simply the energy stored in the Aether empty set [22][23][24] so that the agreement between the theoretical calculation and the numerous accurate cosmological measurements may be taken as an indirect experimental confirmation of this spectacular model for the [22][23][24]. In fact the mere fact that Penrose fractal tessellation is a well known and valid model for quasi crystals, i.e. a real material with five fold symmetry as well as for the cosmos at large [10,17], is a sufficient fact to reinvigorate an old analogy between photons and phonon [7][8][9][10][11].Seen in this larger imaginative new reality [7], we can go on confidently repeating what we have claimed for many years, that spacetime is physically real and may be regarded as a highly advanced material which can be harnessed to yield practically infinite clean, free energy via what we called a dark energy-Casimir nanotech reactor [15]. Such a reactor was thought of by many visionaries before but was never given anything like a firm mathematical and experimental justification as we did within the E-infinity theory proposal [21][22][23][24][25][26][27][28].We leave it to the historians of science to relate our findings to that of the Tesla-Einstein discussion about the Aether [5]. However it is interesting to note that while Einstein started by thinking that his theory of relativity is a proof that the Aether could not exist or at a minimum is a totally unnecessary assumption, in his later years Einstein modified his stance and came much nearer to the thinking of N. Tesla who was a firm believer in the reality of the Aether [2,[5][6][7].We think that although within the limited space of the present announcement we could not possibly give any detailed mathematical derivation, we should at least state some of the most important equations Open Access

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

“…the 95.5 percent mentioned earlier on [43,44,46]. Furthermore we can easily reason that this quantum wave dark energy is actually more or less identical to the energy stored in spacetime ergo the Aether [39] which is in turn nothing else but a five dimensional empty set with the topological volume φ is the Hausdorff dimension of the empty set and 5 may be regarded as the Kaluza-Klein topological dimension of spacetime [46] or the topological mass of the dark energy section [41,43,44]. Unlike conventional quantum mechanics [11] our present theory endows a pre-quantum particle with a path, albeit a fractal like path with a Hausdorff dimension equal 1 + φ rather than the classical topological path dimension of a zero point, namely unity [8,12,46].…”

“…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...…”

“…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 profound conclusion preventing us from confusing zero with empty and empty with nothingness so that in this respect, we can claim to have the highest rigour possible not only in physics but also in pure mathematics [39]. Finally we must acknowledge that without L. Hardy's incredible result about the probability of quantum entanglement being equal 5…”

From Nikolay Umov <i>E=kmc<sup>2</sup></i> via Albert Einstein’s <i>E=γmc<sup>2</sup></i> to the Dark Energy Density of the Cosmos <i>E=(21/22)mc<sup>2</sup></i>

“…the state vector reduction of orthodox quantum mechanics[26] [30][31]. Following this line of re-search, it turns out that the pre-quantum particle could be modelled via the zero set[30] [31][32] and the pre-quantum wave can be modelled by the empty set[32] both in a Kaluza-Klein five dimensional space[30] [31][32] [33][34]. In addition it became obvious that the preceding model is confirmed by the exact…”