The Emergence of Temporal Structures in Dynamical Systems
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Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time.
KeywordsDynamical system Complexity Symmetry breaking Emergence Operator time Parameter time
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- 1.Audretsch, K., Mainzer, J. (eds.): Philosophie und Physik der Raum-Zeit, 2nd edn. Grundlagen der exakten Naturwissenschaften, vol. 7. B.I. Wissenschaftsverlag, Mannheim (1994). Ed. P. Mittelstaedt Google Scholar
- 2.Haken, A., Mikhailov, H. (eds.): Interdisciplinary Approaches to Nonlinear Complex Systems. Springer, Berlin (1993) Google Scholar
- 3.Hawking, S.W.: A Brief History of Time: From the Big Bang to the Black Holes, 10th anniversary edn. Bantam, New York (1998) Google Scholar
- 7.Mainzer, K.: The Little Book of Time. Copernicus Books, New York (2002) Google Scholar
- 8.Mainzer, K.: Zeit in dynamischen Systemen. Von der Urzeit zur Computerzeit. In: Simon, D. (ed.) Zeithorizonte in der Wissenschaft, vol. 7. Symposium der deutschen Akademien der Wissenschaften, Berlin-Brandenburgische Akademie der Wissenschaften, Berlin, 31 October–1 November 2002, pp. 75–100. de Gruyter, Berlin (2002) Google Scholar
- 9.Mittelstaedt, P.: Der Zeitbegriff in der Physik, 2nd edn. B.I.-Wissenschaftsverlag, Mannheim (1980) Google Scholar
- 10.Moltmann, J.: Das Kommen Gottes. Christliche Eschatologie. Gütersloher Verlagshaus, Gütersloh (2005) Google Scholar
- 11.Nietzsche, F.: Werke in drei Bänden, vol. III, ed. K. Schlechta, München (1956), p. 834 Google Scholar
- 12.Prigogine, I.: From Being to Becoming: Time and Complexity in Physical Sciences. W.H. Freeman, New York (1981) Google Scholar