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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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III. An Organic, Conducive, Habitable MultiUniVerse

F. Systems Cosmology: Fractal SpaceTimeMatter

Aschwanden, Markus, et al. Order Out of Randomness: Self-Organization Processes Astrophysics. arXiv:1708.03394. On this popular preprint site, this is a 97 page posting by a premier 18 member team including Virginia Trimble, Juergen Kurths, Alexei Kritsuk, and William Bethune. Circa January 2018, the entry could be seen, after years of wide-ranging research, as a major fulfillment, synthesis and statement of an innately nonlinear, animate, self-developing, scalar cosmic complexity. With many examples from planetary spacings, solar magnetic fields to galactic physics, it can well represent a worldwide discovery of an evolutionary universe that forms and arranges itself by an independent, generative agency at each and every place and time. An appended table lists some 50 more instances from chemical to biological, neural, cooperative, cultural, and artificial realms as they exemplify the same phenomena. While it is alluded that something does seem to be going on by itself, the next step to allow a realization of a greater genesis of which our humankinder presence and conscious quantification is a centrally intended phenomenon is not yet taken.

Self-organization is a property of dissipative nonlinear processes that are governed by an internal driver and a positive feedback mechanism, which creates regular geometric and/or temporal patterns and decreases the entropy, in contrast to random processes. Here we investigate for the first time a comprehensive number of 17 self-organization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Self-organizing systems create spontaneous order out of randomness during the evolution from an initially disordered system to an ordered stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical resonances, or gyromagnetic resonances. (Abstract excerpt)

Self-organization is the spontaneous often seemingly purposeful formation of spatial, temporal, spatio-temporal structures or functions in systems composed of few or many components. In physics, chemistry, and biology, self-organization occurs in open systems driven away from thermal equilibrium. The process of self-organization can be found in many other fields also, such as economy, sociology, medicine, technology (Haken 2008). Self-organization creates “order out of randomness” that is opposite to random processes with increasing entropy. Self-organization is a spontaneous process that does not need any control by an external force. (1)

Star Formation Critical Assessment: The evidence for self-organization in the star formation process is the morphological change from an initial randomized molecular cloud to concentrations in a number of small localized zones in galaxies, which represent spatially ordered structures, in contrast to the initially uniform randomness of the interstellar gas. A size distribution of ordered structures, however, has not been quantified yet. The corresponding ordered time structures are produced by repetitive violent bursts of star formation. The physical process of self-organization in star formation is modeled in terms of highly compressible magnetized turbulence, which can trigger instabilities ending with high-density collapses. (23)

Galactic Physics Critical Assessment: According to the Hubble galaxy classification, galaxies can be formed in different morphologies, from ellipticals to normal spirals and barred spirals, which all represent a spatial pattern observed in our present time-slice. The evolution from an initial random-like state to a well-ordered spatial structure with a spiral pattern reveals the action of a self-organization process. (29)

Asorey, Manuel. Space, Matter and Topology. Nature Physics. 12/7, 2016. In a Focus on Topological Matter section, a Zaragoza University, Spain, theorist describes “hidden” geometric propensities, akin to multiplex networks (search Kleineberg), that suffuse an atomic to cosmic materiality. The key insight is that constructive propensities possess their own reality along with the elements they connect. Some other papers are Topological States in Photonic Systems, and Quasiperiodicity and Topology Transcend Dimensions. This review is timely because in September the 2016 Nobel Prize in Physics was awarded for topological phase transitions and material geometries, noted in the November issue editorial. In late 2016, as these network and structural properties gain wide recognition an intrinsic, common dynamic system becomes evident.

Auffray, Charles and Laurent Nottale. Scale Relativity Theory and Integrative Systems Biology. Progress in Biophysics and Molecular Biology. 97/1, 2008. A biologist and physicist respectively, each a research director at CNRS, the French National Center for Scientific Research, provide a two part explanation for a true evolutionary emergence: 1. Founding Principles and Scale Laws Macroscopic Quantum-Type Mechanics, and 2. Macroscopic Quantum –Type Mechanics. Nottale is the lead author for the second paper, see also above. But their work ought to be seen as more than another theory, rather a different kind of recapitulative universe is revealed which poses a “grand challenge” to discern its “multi-scale integration” across life’s ascendant array from arable quanta to our sentient witness.

In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. The first paper of this series was devoted, in this new framework, to the construction from first principles of scale laws of increasing complexity, and to the discussion of some tentative applications of these laws to biological systems. In this second review and perspective paper, we describe the effects induced by the internal fractal structures of trajectories on motion in standard space. Their main consequence is the transformation of classical dynamics into a generalized, quantum-like self-organized dynamics. (115)

Banda-Barragan, Wladimir, et al. On the Dynamics and Survival of Fractal Clouds in Galactic Winds. arXiv:1901.06924. Astrophysicists posted in Germany, Ecuador, Australia, and Japan, surely a global galaxy, quantify how all manner of celestial, interstellar gaseous phenomena seem to draw upon and exhibit a common self-similar geometry.

Recent observations suggest that dense gas clouds can survive even in hot galactic winds. Here we show that the inclusion of turbulent densities with different statistical properties has significant effects on the evolution of wind-swept clouds. We compare uniform, fractal solenoidal, and fractal compressive cloud models in both 3D and 2D hydrodynamical simulations. By comparing the cloud properties at the destruction time, we find that dense gas entrainment is more effective in uniform clouds than in either of the fractal clouds, and it is more effective in solenoidal than in compressive models. (Abstract excerpt)

Barrie, Neil, et al. Natural Inflation with Hidden Scale Invariance. Physics Letters B. Online March, 2016. University of Sydney physicists draw on recent findings to advance an intrinsic, recurrent in kind, genesis universe whence a collaborative sentience on a favorable bioworld, some 13.8 billion years on, can begin to achieve this cosmic self-discovery.

We propose a new class of natural inflation models based on a hidden scale invariance. In a very generic Wilsonian effective field theory with an arbitrary number of scalar fields, which exhibits scale invariance via the dilaton, the potential necessarily contains a flat direction in the classical limit. This flat direction is lifted by small quantum corrections and inflation is realised without need for an unnatural fine-tuning. (Abstract)

Bartelmann, Matthias. Structure Formation in the Universe. Meyer-Ortmanns, Hildegard and Stefan Thurner, eds. Principles of Evolution: From the Planck Epoch to Complex Multicellular Life. Berlin: Springer, 2011. A University of Heidelberg astronomer, as much the whole volume, waxes over a nonlinear, nonequilibrium cosmos whose intrinsic dynamical propensities seem to impel as if genetically, a progressive complexification from proto-planets to fractal galaxies.

Baryshev, Yurji and Pekka Teerikorpi. Discovery of Cosmic Fractals. Singapore: World Scientific, 2002. Astronomers from Russia and Finland provide the first full-length book on the subject of how the evolving galactic universe is arranged in a hierarchical, self-similar, fractal manner. The authors range widely from a historical survey of such a celestial model through technical and observational details to its increasing verification by a worldwide community.

Benedetti, Dario. Fractal Properties of Quantum Spacetime. Physics Review Letters. 102/111303, 2009. A Perimeter Institute wizard contends that via a mathematical “noncommutativity,” (for which it is difficult to get a good definition on the Web), quantum realms, in their group symmetries, are quite distinguished by fractal geometries. After some arcaneness such as k-deformed Klein-Gordon operators, what one might take home is an inkling of an implicate, dare we say genetic, material essence that repeats itself over and over in a wholly self-similar, living, developmental cosmos.

Bethune, William, et al. Self-Organization in Protoplanetary Disks. arXiv:1603.02475. As the Abstract conveys, University of Grenoble astronomers describe how globular, orbital objects come to exist by way of physical self-organizing dynamics.

Recent observations revealed organised structures in protoplanetary disks, such as axisymmetric rings or horseshoe concentrations evocative of large-scale vortices. These structures are often interpreted as the result of planet-disc interactions. However, these disks are also known to be unstable to the magneto-rotational instability (MRI) which is believed to be one of the dominant angular momentum transport mechanism in these objects. We confirm the transition from a turbulent to an organised state as the intensity of the Hall effect is increased. For intermediate Hall intensity, the flow self-organises into long-lived magnetised vortices. Neither the addition of a toroidal field nor ohmic or ambipolar diffusion drastically change this picture in the range of parameters we have explored. The ability of these structures to trap dust particles in this configuration is demonstrated. We conclude that Hall-MRI driven organisation is a plausible scenario which could explain some of the structures found in recent observations. (Abstract)

Bhattacharyya, Swarnapratim, et al. Multifractality in Charged Pion Production at a Gew GeV/n. Physica A. Online November, 2011. As the paper reports, Jadavpur University, Kolkata, physicists find even subatomic realms and reaches to be equally characterized by nature’s universal self-similar geometries.

The multifractal analysis of charged pion produced in 16O–AgBr interactions at 2.1 AGeV and 24Mg–AgBr interactions at 4.5 AGeV has been investigated using the Takagi moment method in pseudo-rapidity space. The generalized fractal dimensions Dq are determined for these two interactions for different orders of moment. Experimental data reflects multifractal geometry in the multipion production process. From the knowledge of the generalized fractal dimensions Dq, the multifractal specific heat has also been evaluated for these data. (Abstract)

The study of nucleus-nucleus interactions at high energies has been a subject of major interest for theoretical and experimental physicists. The nucleus-nucleus interactions can provide valuable information on the spatiotemporal development of multiparticle production processes, which is one of the prime interests in view of recent developments of quantum chromodynamics. (4144) The observation of the power law behavior of the factorial moments of the phase space interval has become indicative of self-similar fluctuations in multiparticle production in heavy-ion interactions. Analogous to the well-known phenomenon of self-similarity in geometrical and statistical systems, it has been suggested that the multiparticle production data may also exhibit fractal behavior and that there is a relation between intermittency and fractality. (4144)

Binggeli, Bruno and Tatjana Hascher. Is There a Universal Mass Function? Publications of the Astronomical Society of the Pacific. 119/592, 2007. Astronomers at the University of Basel report a scale-invariant universality which holds across all realms of celestial objects as evidence for a common mechanism of star formation. See also Elmegreen in this section for similar findings.

In conclusion, the title question of this paper can certainly be answered “yes.” There is a universal mass function in the sense that it is possible to put together a continuous mass function “of the universe” from asteroids and planets, over stars and stellar remnants, star clusters and gas clouds, and galaxies, all the way up to the richest clusters of galaxies. (604)

Calcagni, Gianluca. Fractal Universe and Quantum Gravity. Physics Review Letters. 104/251301, 2010. A prominent paper from the Max Planck Institute for Gravitational Physics researcher about his interpretations of natural self-similar geometries from quanta to cosmos. More contributions can be viewed on arXiv, such as “Diffusion in Multifractal Spacetime,” published in Physical Review E (Online January 2013). An Abstract from another paper is posted below.

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed. (Abstract)

Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of these models of Nature. Thus motivated, we entertain the idea that spacetime is a multifractal with integer dimension 4 at large scales, while it is two-dimensional in the ultraviolet. Consequences for particle physics, gravity and cosmology are discussed. (Abstract, "Gravity on a Multifractal" Physics Letters B (697/251, 2011.

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