III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet Lifescape
F. Systems Cosmology: Fractal SpaceTimeMatter
2020: When this section was first posted in the early 2000s, only rare, spurious inklings of intrinsic celestial self-similarities and self-organizing topological dynamics could be found. Two decades later, a pervasive structuration and activity has been well quantified across galactic cluster, interstellar medium, stellar coronae and more onto elemental atomic and material phases. The once formless, sterile, forbidding void can presently evince still another robust instance of the one, same vivifying code basis as everywhere else.
Nobel Prize in Physics 2016. www.nobelprize.org/nobel_prizes/physics/laureates/2016/press. This is the Royal Swedish Academy of Sciences press release about this award to David Thouless, Duncan Haldane, and Michael Kosterlitz for for theoretical discoveries of topological phase transitions and topological phases of matter. We chose it from many (Google title) to post a summary notice of this joint, multi-faceted achievement, which has broadly sanctioned a topological turn in theoretical physics (see Wolchover herein). For technical reviews, see Highlights of the Physics Nobel Prize 2016 at arXiv:1612.060132, and their Nobel Lecture on Topological Quantum Matter in Review of Modern Physics (89/4, 2017).
The three Laureates' use of topological concepts in physics was decisive for their discoveries. Topology is a branch of mathematics that describes properties that only change step-wise. Using topology as a tool, they were able to astound the experts. In the early 1970s, Michael Kosterlitz and David Thouless demonstrated that superconductivity could occur at low temperatures and also explained the mechanism, phase transition, that makes superconductivity disappear at higher temperatures. At around the same time, Duncan Haldane discovered how topological concepts can be used to understand the properties of chains of small magnets found in some materials. We now know of many topological phases, not only in thin layers and threads, but also in ordinary three-dimensional materials. Over the last decade, this area has boosted frontline research in condensed matter physics, not least because of the hope that topological materials could be used in new generations of electronics and superconductors, or in future quantum computers. (Edited excerpts)
Aerts, Diederik, et al. Crystallization of Space: Space-Time Fractals from Fractal Arithmetics. arXiv:1506.00487. Vrije Universiteit Brussel mathematicians post a 2015 update on a pervasive self-similar, scale invariant topology across every domain of cosmic phenomena. See also Relativity of Arithmetic as a Fundamental symmetry of Physics by coauthor Marek Czachor at arXiv:1412.8583.
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)
Alexander, Stephon, et al. Fermi-Bounce Cosmology and Scale Invariant Power-Spectrum. arXiv:1402.5880. Theoretical physicists Alexander, Dartmouth College, along with Cosimo Bambi, Antonio Marciano, and Leonardo Modesto, Fudan University, China, contribute to the latest universe-multiverse scheme with usual technical vernacular. We also note as a mid 2010s exemplar of international collaborations as a worldwise learning and knowledge unto discovery proceeds on its own. SA is an African-American physicist, CB, AM, and LM have doctorates in physics from Italian universities, but are now researchers Fudan, where the working language is English. One might then muse, what mathematical or textual dialect is Nature actually written in, where does “scale-invariance” come from, is it an independent propensity?
We develop a novel non-singular bouncing cosmology, due to the non-trivial coupling of general relativity to fermionic fields. The resolution of the singularity arises from the negative energy density provided by fermions. Our theory is ghost-free because the fermionic operator that generates the bounce is equivalent to torsion, which has no kinetic terms. The physical system is minimal in that it consists of standard general relativity plus a topological sector for gravity, a U(1) gauge field reducing to radiation at late times and fermionic matter described by Dirac fields with a non-minimal coupling. We show that a scale invariant power-spectrum generated in the contracting phase can be recovered for a suitable choice of the fermion number density and the bare mass, hence providing a possible alternative to the inflationary scenario. (Abstract)
Anitas, Eugen Mircea and Azat Slyamov. Emergence of Surface Fractals in Cellular Automata. Annalen der Physik. Online October, 2018. In this German journal since 1799, Joint Institute for Nuclear Research, Dubna, Russia physicists, with other postings in Almaty, Kazakhstan and Bucharest, Romania describe a clever method for visualizing this topological presence. Our interest extends beyond the global research facility only now possible to a mindfulness that we phenomenal learners are witnessing an intrinsic geometry and mathematics, as Galileo and others foresaw, that does exist on its prior own. Such nascent realizations then one to wonder “whomever “put it all there in the first place.
Self‐similar (fractal) structures are present at every scale ranging from galaxies down to aggregates of atoms to elementary particles. For surface fractals, the self‐similarity is inherited from the superposition of non‐overlapping mass fractals. Despite long‐standing theoretical investigations, no generic framework exists yet to describe the nature and generation of surface fractal systems. Here, cellular automata (CA) are identified as a generic mathematical system and, by exploring the associated small‐angle scattering (neutrons, X‐rays, light) intensity curves, the emergence of surface fractals is reported. The finding on the emergence of surface fractals in CA will enrich the understanding of their structural properties while the approximation of independent objects can provide a route toward testing randomness generated by CA. (Abstract excerpt)
Ardizzone, Vincenzo, et al. Formation and Control of Turing Patterns in a Coherent Quantum Fluid. Nature Scientific Reports. 3/3016, 2013. An international 16 member team from Ecole Normale Superieure, Paris, Universitat Paderborn, Germany, Chinese University of Hong Kong, University of Arizona, and CNRS Laboratoire de Photonique et de Nanostructures, France, achieves an iconic portal unto the “systems nature” revolution. At once, as abstracts or first paragraphs can now state, a ubiquity of the same self-organizing, complex adaptive network patterns and dynamics have been found at each and every realm and instance. In this paper, they are similarly noted in these quantum reaches. By the breadth and depth of these findings, it becomes strongly evident that an independent, universal source must be at work. But is it an algorithm software, or might it actually be broached as a natural genetic code?
Nonequilibrium patterns in open systems are ubiquitous in nature, with examples as diverse as desert sand dunes, animal coat patterns such as zebra stripes, or geographic patterns in parasitic insect populations. A theoretical foundation that explains the basic features of a large class of patterns was given by Turing in the context of chemical reactions and the biological process of morphogenesis. Analogs of Turing patterns have also been studied in optical systems where diffusion of matter is replaced by diffraction of light. The unique features of polaritons in semiconductor microcavities allow us to go one step further and to study Turing patterns in an interacting coherent quantum fluid. We demonstrate formation and control of these patterns. We also demonstrate the promise of these quantum Turing patterns for applications, such as low-intensity ultra-fast all-optical switches. (Abstract)
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. A Macroscopic Description of a Generalized Self-Organized Criticality System: Astrophysical Applications. Astrophysical Journal. 782/1, 2014. A technical tutorial upon this constant propensity of natural systems everywhere to become optimally poised between order and chaos. A physical definition of SOC is broached as “a critical state of a nonlinear energy dissipation system that is slowly and continuously driven towards a critical value of a system-wide instability threshold, producing scale-free, fractal-diffusive, with powerlaw-like size distributions.” In some translation, what kind of developmental universe does this describe, who are we earthlings as its way of achieving its own self-cognizance?
We suggest a generalized definition of self-organized criticality (SOC) systems: SOC is a critical state of a nonlinear energy dissipation system that is slowly and continuously driven toward a critical value of a system-wide instability threshold, producing scale-free, fractal-diffusive, and intermittent avalanches with power law-like size distributions. We develop here a macroscopic description of SOC systems that provides an equivalent description of the complex microscopic fine structure, in terms of fractal-diffusive transport (FD-SOC). Quantitative values for the size distributions of SOC parameters (length scales L, time scales T, waiting times Δt, fluxes F, and fluences or energies E) are derived from first principles, using the scale-free probability conjecture, N(L)dL L –d , for Euclidean space dimension d. We apply this model to astrophysical SOC systems, such as lunar craters, the asteroid belt, Saturn ring particles, magnetospheric substorms, radiation belt electrons, solar flares, stellar flares, pulsar glitches, soft gamma-ray repeaters, black-hole objects, blazars, and cosmic rays. The FD-SOC model predicts correctly the size distributions of 8 out of these 12 astrophysical phenomena, and indicates non-standard scaling laws and measurement biases for the others. (Abstract)
Aschwanden, Markus. Self-Organized Criticality in Astrophysics: The Statistics of Nonlinear Processes in the Universe. Berlin: Springer, 2011. Since the 1990s, the author has been at the forefront of the study of celestial phenomena such as solar flares in terms of complex dynamical systems. The endeavor has spread across cosmic reaches with robust mathematical veracity to an extent that a book length treatment is now merited. An appropriate Introduction scopes out the science of SOC as broadly arrayed across Stellar Physics, Planetary Realms, Geophysics, Biophysics and onto Human Activities. On the Springer site can be found the table of contents, chapter abstracts, and text samples.
The concept of ‘self-organized criticality’ (SOC) has been applied to a variety of problems, ranging from population growth and traffic jams to earthquakes, landslides and forest fires. The technique is now being applied to a wide range of phenomena in astrophysics, such as planetary magnetospheres, solar flares, cataclysmic variable stars, accretion disks, black holes and gamma-ray bursts, and also to phenomena in galactic physics and cosmology. Self-organized Criticality in Astrophysics introduces the concept of SOC and shows that, due to its universality and ubiquity, it is a law of nature. The theoretical framework and specific physical models are described, together with a range of applications in various aspects of astrophysics. The mathematical techniques, including the statistics of random processes, time series analysis, time scale and waiting time distributions, are presented and the results are applied to specific observations of astrophysical phenomena. (Publisher)
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)
Aschwanden, Markus and Manuel Guedel.. Self-Organized Criticality in Stellar Flares. arXiv:2106.06490. Solar and Stellar Astrophysics Laboratory, Palo Alto and University of Vienna (search MA) researchers report an even more robust propensity for all manner of natural phenomena such as active sunny stars to hold to scale-invariant self-similarities. Of especial note is a persistent arrival at this middle way balance. See also The Universality of Power Law Slopes in the Solar Photosphere by MA and Nived Nhalil at 2211.08323 for later work.
What does it mean when we say that stellar flares exhibit self-organized criticality? If stellar flares would occur by pure random processes, their size distribution would fit a Poissonian or Gaussian function. In contrast, the fact that stellar flares are consistent with power law functions strongly supports the evolution of nonlinear (exponential-growing) energy dissipation processes, triggered by local fluctuations that exceed a system-wide threshold. The statistics of physical parameters in such nonlinear energy dissipation processes can be expressed with volumetric scaling laws, characterized by the scale-free probability, the (spatial) fractal dimension, classical diffusion, and the flux-volume scaling. (11)