III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet Incubator Lifescape
E. Systems Cosmology: Fractal SpaceTimeMatter
Paczuski, Myra and David Hughes. A Heavenly Example of Scale-Free Networks and Self-Organized Criticality. Physica A. 342/1-2, 2004. The Imperial College, London, mathematical physicists find even the sun’s corona and its magnetic field network to exhibit these ubiquitous complex system properties.
Palmer, Tim. Bell’s Theorem, Non-Computability and Conformal Cyclic Cosmology. arXiv:2108.10902. In this paper for Roger Penrose’s 90th birthday, he Oxford University polyphysicist (search) adds further reasons and evidence why a celestial reality may be most of all distinguished by a self-similar fractality across every expanse. See also Quantum Physics from Number Theory by TP (2209.05549) and Parametric Invariance by Mario de Oliveira (2203.07262) for further views.
This paper draws on a number of Roger Penrose's ideas such as a Conformal Cyclic Cosmology, non-computability and gravitationally induced quantum state reduction so to propose an unconventional approach to quantum gravity: Invariant Set Theory (IST). In IST, the fundamental laws of physics describe the geometry of the phase portrait of the universe as a whole: "quantum" process are associated with fine-scale fractal geometry. With this, it can explain the experimental violation of Bell Inequalities. (Abstract excerpt)
Palmer, Tim. Quantum Theory and the Symbolic Dynamics of Invariant Sets. arXiv: 1210.3940. Online October 2012, this follows up a 2009 paper “The Invariant Set Hypothesis: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity,” Proceedings of the Royal Society A (465/3165). Both run some 50 pages on arXiv. The author has a doctorate in statistical physics from Oxford University. In 2009 he was at the European Centre for Medium-Range Weather Forecasts, Reading, UK, as group leader for the application of nonlinear complexity to climate studies, in 2012 at the Clarendon Laboratory, Oxford. The earlier work was extolled in the New Scientist (March 28, 2009) by Mark Buchanan as revealing a “Fractal Reality.” Palmer offers a revised fundamental basis of quantum physics via a “contextual,” self-similar, structure of space and time. The endeavor has been vetted by the Perimeter Institute in Canada, because a radical rethinking is seen as in order. See also Palmer’s note “Climate Extremes and the Role of Dynamics” in PNAS (110/5281, 2013). Such a robust mathematical articulation of a scale-invariant, repetitive cosmic emergence would add vital credibility to a natural genesis uniVerse, implying its own iterative genetic program. We include two quotes from each edition. For a 2017 edition, see A Gravitational Theory of the Quantum at arXiv:1709.00329.
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally causal dynamics. This symbolic representation is constructed from self-similar families of quaternionic operators. Using number-theoretic properties of the cosine function, the statistical properties of the symbolic representation of the invariant set are shown to be consistent with the contextual requirements of the Kochen-Specker theorem, are not constrained by Bell inequalities, and mirror the statistics of entangled qubits. These number-theoretic properties in turn reflect the sparseness of the invariant set in state space, and relate to the metaphysical notion of counterfactual incompleteness. As a result, it is proposed that the complex Hilbert Space should merely be considered a computational convenience in the light of the algorithmic intractability of the invariant set geometry, and consequently the superposed state should not be considered a fundamental aspect of physical theory. Here some elements of an alternative ‘gravitational theory of the quantum’ are proposed, based on a deterministic and locally causal theory of gravity which extends general relativity by being geometric in both space-time and state. (2012 Abstract excerpt)
Pietronero, Luciano, et al.
Complexity in Cosmology.
Phuan Ong, N. and Ravin Bhatt, eds.
More Is Different.
Princeton: Princeton University Press, 2001.
By theory and observation, a growing comprehension is being achieved of a scale-invariant, self-organizing universe, which is seen as a “radically new and original” view of cosmic emergence.
Powell, Devin. Physicists Net Fractal Butterfly. Science. 501/144, 2013. A report on the experimental verification of a phenomena proposed some 30 years ago by Douglas Hofstadter that even atomic electron trajectories in quantum realms will take upon such recursive fractal topologies.
Ramos, F. M., et al.
Multiscaling and Nonextensivity of Large-Scale Structures in the Universe.
Whereby the problem of the transition from multifractal galaxies and clusters to an overall homogeneous universe is resolved by a generalized thermostatistics method.
Rohringer, Wolfgang, et al. Non-equilibrium Scale Invariance and Shortcuts to Adiabaticity in a One-dimensional Bose Gas. Nature Scientific Reviews. 5/9820, 2015. This brief note by Vienna Center for Quantum Science and Technology researchers is another indication of an inherent, universal self-similarity across every possible domain. When and how might these many disparate findings become a worldwise discovery of a creative organic universe?
Roukema, B. F., et al. A Hint of Poincare Dodecahedral Topology in the WMAP First Year Sky Map. Astronomy & Astrophysics. 423/821, 2004. Appropriately from the Nicolas Copernicus University in Torun, Poland, a further analysis of temperature fluctuations in the cosmic microwave background CMB as measured by the Wilkinson Microwave Anisotropy Probe WMAP satellite is seen to support the hypothesis that the overall universe is shaped as a dodecahedron rather than an infinite flat plane.
Rusin, D., et al. Self-Similar Models for the Mass Profiles of Early-Type Lens Galaxies. The Astrophysical Journal. 595/29, 2003. An example of how cosmologists are finding that scale-free power law profiles can describe the structure of the galactic clusters.
Sanchez, Nestor and Emilio Alfaro. The Fractal Distribution of H II Regions in Disk Galaxies. Astrophysical Journal. 178/1, Supplement, 2008. “H II” means areas of interstellar hydrogen that is ionized, sans an electron. Instituto de Astrofísica de Andalucía astronomers here find these domains to likewise possess a constant fractal structure over galactic reaches.
Sanchez, Nestor, et al. Fractal Dimension of Interstellar Clouds. Astrophysical Journal. 656/222, 2007. This conclusion is reached by studies of the opacity and noise of these celestial reaches.
There exists observational evidence that the interstellar medium has a fractal structure in a wide range of spatial scales. (222)
Slobodrian, R. Fractal Cosmogony. Chaos, Solitons and Fractals. 23/3, 2005. The structure of the early universe is noticed to exhibit a fractional self-similarity akin to microbial aggregates.
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