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

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

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

Dimension in a Radiative Stellar Atmosphere

Dimensional scales are examined in an extended 3+1 Vaidya atmosphere surrounding a Schwarzschild source. At one scale, the Vaidya null fluid vanishes and the spacetime contains only a single spherical 2-surface. Both of these behaviors can be addressed by including higher dimensions in the spacetime metric.Comment: to appear in Gen. Rel. Gra

Scale relativity and fractal space-time: theory and applications

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to system biology.Comment: 63 pages, 14 figures. In : First International Conference on the Evolution and Development of the Universe,8th - 9th October 2008, Paris, Franc

Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas

Recently, a new perspective of gravitational-thermodynamic duality as an entropic force arising from alterations in the information connected to the positions of material bodies is found. In this paper, we generalize some aspects of this model in the presence of noncommutative Schwarzschild black hole by applying the method of coordinate coherent states describing smeared structures. We implement two different distributions: (a) Gaussian and (b) Lorentzian. Both mass distributions prepare the similar quantitative aspects for the entropic force. Our study shows, the entropic force on the smallest fundamental unit of a holographic screen with radius $r_0$ vanishes. As a result, black hole remnants are unconditionally inert even gravitational interactions do not exist therein. So, a distinction between gravitational and inertial mass in the size of black hole remnant is observed, i.e. the failure of the principle of equivalence. In addition, if one considers the screen radius to be less than the radius of the smallest holographic surface at the Planckian regime, then one encounters some unusual dynamical features leading to gravitational repulsive force and negative energy. On the other hand, the significant distinction between the two distributions is conceived to occur around $r_0$, and that is worth of mentioning: at this regime either our analysis is not the proper one, or non-extensive statistics should be employed.Comment: 15 pages, 2 figures, new references added, minor revision, Title changed, to appear in EPJ Plu

Self-organization of developing embryo using scale-invariant approach

<p>Abstract</p> <p>Background</p> <p>Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.</p> <p>Methods</p> <p>In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing <it>C. elegans </it>during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.</p> <p>Results and conclusion</p> <p>The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.</p