The hydrodynamics of quantum spacetime - The minimal essentials of a new quantum theory

This is a somewhat long and extended abstract of a paper that presents a relatively short and concise review of a new quantum mechanics. This new theory is anchored in the hydrodynamical paradigm first introduced by L. Prandtl in his famous boundary layer theory.  In addition the original ideas of L. Prandtl are expanded to encompass and combine with ideas from von Neumann-Connes’ pointless noncommutative geometry, Penrose-like fractal tiling cosmology, E-infinity Cantorian theory and the platonic golden mean number system based transfinite set theory.  Proceeding in this way it is reasoned that while the pre-quantum particle and the pre-quantum wave may be best described as a multi dimensional zero set and empty set respectively in stringent mathematical terms, in physical terms however the new picture of a bluff body modelling the quantum particle and a surrounding Prandtl boundary layer modelling the quantum wave is virtually a quantum jump in our understanding of quantum physics in general and quantum wave collapse in particular.  In that respect the work has some resemblance to that pilot wave theory of de Broglie and Bohm but is by no means more than that.  The work is naturally connected to very specialized hydrodynamics related fields apart of Batchelor’s law and the important earthquake engineering subject of liquefaction which is of paramount importance for designing buildings with high resistance to earthquakes among other things.  The concerted use of all these mathematical, experimental and number theoretical tools combine in the present paper to give a new synthesis for a deeper understanding of what we label the classical and quantum world predominantly for simplicity rather than logical, mandatory reasons

From fractal - Cantorian classical music to the symphony of the standard model of high energy particles physics

We report in this short letter on what we think is a major finding which could remove forever the schism that exists between Science and Art in an unprecedented way. In particular we believe that we were able to uncover an entire spectrum of scale invariant fractal Cantorian space-time manifolds starting from Einstein's D = 4 space-time and continuing via Kaluza-Klein D = 5, Superstring D = 10, Witten's M-theory D = 11 and Vafa's F-theory D = 12 to reach some tantalizing connections to the standard model of high energy particle physics as well as Arnold Schoenberg's twelve tone music. Our quantitative mathematical analysis depends in a crucial way on the golden mean number system of E-Infinity theory which implies not only a real  possibility of a theory of everything unifying all fundamental forces, but goes also far beyond that, suggesting a unification of facts and values i.e. Science and Art, encompassing music, poetry and philosophy

Topological vacuum fluctuation and Dvoretzky‘s theorem – Mathematical proofs in the context of the dark energy density of the universe

Starting from the initial triality of physics, namely mathematical philosophy, transfinite set theory and number theory we drive the inevitability of a topological quantum vacuum fluctuation of spacetime resulting in the fundamental reality of pair creation and annihilation. Subsequently we give a simple but strong mathematical proof of Dvoretzky‘s marvellous theorem on measure concentration, thus making dark energy and accelerated cosmic expansion not only an astrophysical measurement and observational reality, but also a plausible topological-geometrical fact of a pointless Cantorian actual universe akin to the Penrose fractal tiling space. This space is described accurately via the von Neumann-Conne noncommutative geometry using their golden mean dimensional function and the corresponding bijection of E-infinity theory. The said theory was developed by the authors of the present paper and their group and is based on and starts from the pioneering efforts of the Canadian physicist G. Ord and the French astrophysicist L. Nottale

A Grand Unification of the Sciences, Arts & Consciousness: Rediscovering the Pythagorean Plato’s Golden Mean Number System

In this condensed paper, by combining the insights from E-Infinity theory, along with Plato‘s initiatory insights into the golden section imbedded in his Principles of the One and Indefinite Dyad, David Bohm‘s ontological framework of the superimplicate, implicate and explicate orders, and the pervasive presence throughout physics, chemistry, biology and cosmology of the golden ratio (often veiled in Fibonacci and Lucas numbers), a profound golden mean number system emerges underlying the cosmos, nature and consciousness. This ubiquitous presence is evident in quantum mechanics, including quark masses, the chaos border, fine structure constant and entanglement, entropy and thermodynamic equilibrium, the periodic table of elements, nanotechnology, crystallography, computing, digital information, cryptography, genetics, nucleotide arrangement, Homo sapiens and Neanderthal genomes, DNA structure, cardiac anatomy and physiology, biometric measurements of the human and mammalian skulls, weather turbulence, plantphyllotaxis, planetary orbits and sizes, black holes, dark energy, dark matter, and even cosmogenesis – the very origin and structure of the universe. This has been pragmatically extended through the most ingenious biomimicry, from robotics, artificial intelligence, engineering and urban design, to extensions throughout history in architecture, music and the arts. We propose herein a grand unification of the sciences, arts and consciousness, rooted in an ontological superstructure known to the ancients as the One and IndefiniteDyad, that gives rise to a golden mean number system which is the substructure of all existence

Super Unification of Physics and Mathematics

This short letter proposes to convert physics and mathematics not to classical mathematical physics but to a far more radically different entity. We call this new logical product "wild topology" which is also known  as a general kind of topology ramifying into a Cantor set. Thus the work goes far more beyond our older P-Adicunification of physics and mathematics. In the course of this process, we enhance both understanding as well as computation of not only classical physics but more importantly also quantum physics and cosmology. In particular, we free quantum mechanics from several of the paradoxes and counter intuitive features which has historically plagued it since its very inception

The standing wave model of the mesons and baryons

Only photons are needed to explain the masses of the pi(0), eta, Lambda, Sigma(0), Xi(0), Omega(-), Lambda(c,+), Sigma(c,0), Xi(c,0), and Omega(c,0) mesons and baryons. Only neutrinos are needed to explain the mass of the pi(+-) mesons. Neutrinos and photons are needed to explain the masses of the K-mesons, the neutron and D-mesons. Surprisingly the mass of the mu-meson can also be explained by the oscillation energies and rest masses of a neutrino lattice. From the difference of the masses of the pi(+-) mesons and mu(+-) mesons follows that the rest mass of the muon-neutrino is 47.5 milli-eV. From the difference of the masses of the neutron and proton follows that the rest mass of the electron-neutrino is 0.55 milli-eV. The potential of the weak force that holds the lattices of the particles together can be determined with Born's lattice theory. From the weak force follows automatically the existence of a strong force between the sides of two lattices. The strong nuclear force is the sum of the unsaturated weak forces at the sides of each lattice and is therefore 10^6 times stronger than the weak force.Comment: 41 pages, 6 figure

Gauss map and Lyapunov exponents of interacting particles in a billiard

We show that the Lyapunov exponent (LE) of periodic orbits with Lebesgue measure zero from the Gauss map can be used to determine the main qualitative behavior of the LE of a Hamiltonian system. The Hamiltonian system is a one-dimensional box with two particles interacting via a Yukawa potential and does not possess Kolmogorov-Arnold-Moser (KAM) curves. In our case the Gauss map is applied to the mass ratio $\gamma = m_2/m_1$ between particles. Besides the main qualitative behavior, some unexpected peaks in the $\gamma$ dependence of the mean LE and the appearance of 'stickness' in phase space can also be understand via LE from the Gauss map. This shows a nice example of the relation between the "instability" of the continued fraction representation of a number with the stability of non-periodic curves (no KAM curves) from the physical model. Our results also confirm the intuition that pseudo-integrable systems with more complicated invariant surfaces of the flow (higher genus) should be more unstable under perturbation.Comment: 13 pages, 2 figure

Leech-Conwayeva sferna napolnitev v S-neskončno prostoru

Ocenimo dimenzijo glavne sfere v neskončno dimenzionalnem prostoru, pri čemer bomo uporabili Leech-Conwayevo mrežo. Numerični rezultati so izpopolnili El Naschiejeve izračune (Chaos, Solitons and Fractals 9 (8) 19981445-1471) in so potrdili štiridimenzionalnost pričakovane sfere.We estimate the dimensionality of the mean sphere in infinite dimensional space using the so-called Leech-Conway lattices. The numerical results improve previous calculation by El Naschie [Chaos, Solitons & Fractals 9(1998)8, 1445-1471] and confirms the essential four dimensionality of the expectation sphere

Povezava med redom enostavnih grup in maksimalnim številom elementarnih delcev

Namen tega članka je predstaviti sferične, evklidske in hiperbolične poliedre in najti nekaj povezav reda njihovih grup zrcaljenj in grup, kot so na primer PGL(2,7), PGL(2,8), PGL(2,7)▫$times C_2$▫, PSL(2,31)▫$times C_2$▫, s številom elementarnih delcev. V tem delu pokažemo, da je večje število 72 ali 84 elementarnih delcev konsistentno s teorijo super strun, ▫$M$▫-teorijo in teorijo heterotičnih strun. Filozofija dela temelji na El Naschiejevi ▫$E$▫-neskončni interpretaciji izreka Emmy Nötherjeve.The aim of this article is to present spherical, Euclidean and hyperbolic polyhedra and find some connections of the order of their reflection groups and groups such as PGL(2, 7), PGL(2, 8), PGL(2, 7)▫$times C_2$▫, PSL(2, 31)▫$times C_2$▫ to the number of elementary particles. In the present work we show that a larger number of 72 or 84 elementary particles is consistent with super string theory, ▫$M$▫-theory and heterotic string theory. The philosophy of the work is based on El Naschie\u27s ▫$E$▫-infinity interpretation of Emmy Nöther\u27s theorem