III. Organic Universe: An Animate, Amniotic Cosmos

F. Fractal Spacetime

			Both the depths of elemental matter and the expanses of the celestial raiment are being found to display a discrete, self-similar organization. From quantum phenomena to interstellar clouds and galactic clusters, a fine grained, variegated yet analogous correspondence once again appears, this time uncovered by the composite efforts of scientists and mathematicians worldwide. This image is from the Fractales site at http://fractales.free.fr.

Aguirre, Jacobo, et al. Fractal Structures in Nonlinear Dynamics. Reviews of Modern Physics. 81/1, 2009. A technical tutorial which courses through various dissipative systems, with an emphasis on basins of attraction.

Since the relation between fractality and nonlinear dynamics was established, it has been observed that fractality in ubiquitous in nature. (334)

Ambjorn, J., et al. The Universe from Scratch. Contemporary Physics. 47/2, 2006. By way of a method to observe and quantify a fluctuating quantum geometry at Planck scales (10-33 centimeters) called Causal Dynamical Triangulations.

The paradigm of spacetime beginning to emerge from CDT is that of a scale-invariant, fractal and effectively lower-dimensional structure at the Planck scale, which only at a larger scale requires well-known features of geometry which accord with our classical intuition. (115)

Argyris, J., et al. Fractal Space Signatures in Quantum Physics and Cosmology. Chaos, Solitons and Fractals. 11/11, 2000. How the topology of nature (space, time, matter, and fields) is “intrinsically fractal.” A self-similarity is then evident from galactic clusters to the allometric scale of life.

…we observe that biological systems can indeed be considered as biological fractals. (1689)

Argyris, J., et al. Fractal Space, Cosmic Strings and Spontaneous Symmetry Breaking. Chaos, Solitons and Fractals. 12/1, 2001. A theoretical encounter with a finely grained, iterative universal genesis.

We show that, starting from the most fundamental of elementary particles and rising up to the largest scale structure of the Universe, the fractal nature of spacetime is imprinted onto matter and fields via the common concept for all scales emanating from the physical spacetime vacuum fluctuations….The key aspect of fractals in physics and of fractal geometry is to understand why nature gives rise to fractal structures. Our present answer is: because a fractal structure is a manifestation of the universality of self-organization processes. (1)

Aschwanden, Markus. Self-Organized Criticality in Solar Physics and Astrophysics. http://arxiv.org/abs/1003.0122. A paper presented at the 2010 Interdisciplinary Symposium on Chaos and Complex Systems, in Istanbul, Turkey, which shows how nonlinear SOC, as a “universal and ubiquitous law” throughout nature, can be likewise found to hold for an array of celestial phenomena. The author’s forthcoming book on the subject Self-Organized Criticality in Astrophysics will be out in January 2011 from Springer.

On a most general level, SOC is the statistics of coherent nonlinear processes, in contrast to the Poisson statistics of incoherent random processes. The SOC concept has been applied to laboratory experiments (of rice or sand piles), to human activities (population growth, language, economy, traffic jams, wars), to biophysics, geophysics (earthquakes, landslides, forest fires), magnetospheric physics, solar physics (flares), stellar physics (flares, cataclysmic variables, accretion disks, black holes, pulsar glitches, gamma ray bursts), and to galactic physics and cosmology. (Abstract)

Auffran, 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)

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.

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)

Chown, Marcus. All the World’s a Hologram. New Scientist. January 17, 2009. Each week this magazine has a cover story with spectacular claims, always intriguing, often true. In this case spurious results from the GEO600 satellite gravitational wave search seem to affirm Fermilab physicist Craig Hogan quantum theories that predict a breakdown or shift at Planck scale lengths or edges from a continuum into a pixilated state that might imply a fundamental holographic reality.

If space-time is a grainy hologram, then you can think of the universe as a sphere whose outer surface is papered in Planck length-sized squares, each containing one bit of information. The holographic principle says that the amount of information papering the outside must match the number of bits contained inside the volume of the universe. (26)

De la Fuente Marcos, R. and C. Multifractal Evolution in Interacting Galaxies. Monthly Notices of the Royal Astronomical Society. 372/279, 2006. Suffolk University, Madrid campus, astronomers quantify the self-similar geometries that result via celestial confluences from supergiant clouds to stellar superclusters.

Multifractality can be understood as superposition of different fractal patterns. (280)

De Vega, H., et al. Fractal Structures and Scaling Laws in the Universe. Chaos, Solitons & Fractals. 10/2-3, 1999. More mathematical insights into nature’s iterative geometry.

Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10-4pc till 100pc. Secondly, the galaxy distribution has been observed to be fractal in scales up to hundreds of Mpc.” (329) (pc = parsecs = 3.26 light years).

1 | 2 | 3 | 4  Next