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Journal of Science / Vol 5 / Issue 2 / 2015 / 65-67 Paolo Di Sia . / Journal of Science / Vol 5 / Issue 2 / 2015 / 65-67. e ISSN 2277 - 3290 Print ISSN 2277 - 3282 Journal of Science Physics www.journalofscience.net SPACETIME UNIFIED CURRENT MODELS AND DETERMINISTIC COMPUTATION Paolo Di Sia Free University of Bolzano-Bozen, Viale Ratisbona 16, 39042 Bressanone-Brixen, Italy. University of Verona, Lungadige Porta Vittoria 17, 37129 Verona, Italy. ABSTRACT In this work considerations about the idea of “computational universe” with specific peculiarities of discreteness, determinism and computability are presented. Such characteristics divide scientists, even if the idea is admitted by important modern models on the deep structure of spacetime. Key words: Spacetime, Mathematical Modelling, Universe, Computation, Discreteness, Determinism, Theoretical Physics. INTRODUCTION The idea of “computational universe” assumes “working hypothesis” for exploring alternative theories of the existence of a strong link between the concept of physics, the foundations of which lie in the plane of the complexity of the physical world and the structures of relative simplicity. self-organization emerging within the computational Discrete implies that there is an ultra- environment. Currently researchers are working in the microscopic scale at which the spacetime texture is made direction of putting the powerful notion of “emergency of up of indivisible distinct elements; this approach is calculation” to the service of recent theories on adopted in currently very relevant theories and models, as unification of the fundamental forces of Nature, such as the “Loop Quantum Gravity” (LQG) by Carlo Rovelli and the quantum gravity [1], with particular attention to the co-workers [4], the “Spin Networks” by Roger Penrose “Causal Set Programme”. [5], the “Spin Foam” by John Archibald Wheeler [6]. Deterministic means that the reality obeys to METHODS AND DISCUSSION precise rules that do not involve the random factor. This The “Causal Set Programme” [2] is a research way has been and is currently being followed in searching program which assumes the causality among events as for a deterministic substrate under the probabilistic fundamental structure of spacetime, and the “Causal Sets” connotation of quantum mechanics, for example through as suitable ways for describing it. The ideas of causality works of physics Nobel Prize Gerard T’Hooft [7]. and discretization of spacetime are important in many Computational indicates that these rules can be approaches to quantum gravity; however, if the implemented and executed by computers, not meaning, discretization is accepted as initial assumption for these however, that it is possible to postulate the existence of a models, it appears also some undesired consequence, as digital “otherworldly divine computer”, which constantly the contrast with the Lorentz invariance. The causal set is runs the software of the universe. a discrete structure that avoids this problem and provides Richard Feynman was one of scientists attracted a possible method for constructing a theory of quantum by the idea of a discrete and computational universe, gravity through “integration on paths” (path integral) [3]. being perplexed about the need for an infinite number of Not all researchers agree in considering our physical logical operations for determining what happens in a universe as discrete, deterministic and computational, but small region of space, or in a time interval [8]. in recent years a number of them have assumed these Corresponding Author:- Paolo Di Sia Email:- [email protected] 65 Paolo Di Sia . / Journal of Science / Vol 5 / Issue 2 / 2015 / 65-67. He proposed that physics might not have a hardware structures. There is not one only way for “canonical” mathematical formulation, but that a different representing the computation of a given model and for mechanism could be revealed, discovering that the laws defining indicators of complexity, which characterize the are simple, even despite the manifested complexity. Since behaviour and the emergence of interesting phenomena, 1970 it became popular a two-dimensional cellular such as interacting particles or pseudo-randomness. automaton, called “Game of Life”. This robot has been Among them, especially attractive is the use of the so- developed by the British mathematician John Conway, in called “Causal Set”, or “Causet”, consisting of the set of order to show how similar-to-life behaviours can emerge calculation events and the relative causal relations. This from simple rules and many-body interactions [9]. This approach is particularly suitable for applications to principle has been accepted, it is currently at the basis of fundamental physics, since the causal sets are considered eco-biology [10] and it makes use of complexity theory as one of the most appropriate discrete models of physical too [11]. The game has been subsequently developed in spacetime [14-18]. various versions with different typologies, such as the extension to three-dimensionality, different biological CONCLUSION rules and different types of cells. The possibility to derive causal sets through In the original version, programming the cells of computation of simple models, such as Turing machines, a square grid so that they follow, synchronously, a simple mobile automata on networks, rewriting systems on rule, referred for examples to the color of one of them and graphs, is a not particularly complicated process, which to the eight of its neighbors, populations of unexpectedly brings to interesting results. In particular: complex moving structures were formed. The cells a) In relation to speculations about the survive or die according to the number of occupied computational universe, the “algorithmic causets” can positions close to each other. represent the informations of physical relevance; The fact, that simple deterministic rules of b) This approach is a deterministic alternative calculation allow to raise highly complex structures and with respect to the probabilistic techniques adopted in the dynamics, is currently an important research field for “Causal Set Programme” for creating discrete spacetime physicists and mathematicians, such as the British environments. It is clearly not so easy and trivial to place Stephen Wolfram. He showed how the so-called in a deterministic framework extremely articulated “elementary” calculation models, as cellular automata, theories as the loop quantum gravity, avoiding quantum can highlight emergent behaviours of considerable mechanics. complexity [12]. The history of research teaches however how A cellular automaton, or cellular automata, or simple deterministic rules can lead to very complex “CA”, is a mathematical model used for describing the behaviours, but this fact does not mean that the indicated evolution of complex discrete systems, studied in the way may involve, for example, an overcoming of theory of computation, in mathematics, physics, biology. quantum mechanics. If pseudo-particles and pseudo- Originally this idea was developed by Stanislaw Ulam randomness emerge from simple deterministic and John von Neumann around 1960 [13], growing then computation, it is possible and desirable to expect similar through the development of theories of computation and phenomena also in causets derived by them. REFERENCES 1. Rovelli C. Quantum Gravity, 1st ed., Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 2013. 2. Sverdlov RM. Quantum Field Theory and Gravity in Causal Sets, Proquest, Umi Dissertation Publishing, USA, 2011. 3. Grosche C. An Introduction into the Feynman Path Integral, arXiv:hep-th/9302097, 1993. 4. Gambini R, Pullin J. A First Course in Loop Quantum Gravity, Oxford University Press, Oxford, 2011. 5. Rovelli C, Smolin L. Spin Networks and Quantum Gravity, arxiv.org/pdf/gr-qc/9505006, 1995. 6. Baez JC. An Introduction to Spin Foam Models of Quantum Gravity and BF Theory, Lecture Notes in Physics, gr- qc/9905087, 543, 2000, 25-94. 7. Santos D. The Hidden Variables of the Atomic World: The New Quantum Field Theory, Dorrance Publishing Co. Inc., Pittsburgh, USA, 2006. 8. Feynman R. The Character of Physical Law, 24th printing, The MIT Press, USA, 2001. 9. Gardner M. Mathematical Games: the Fantastic Combinations of John Conway’s New Solitaire Game “Life”, Scientific American, 223, 1970, 120-123. 10. Doetsch RN. Introduction to Bacteria and Their Ecobiology, University Park Press, USA, 1973. 11. Girard J-Y. Proof theory and logical complexity, Bibliopolis, Italy, 2007. 12. Wolfram S. A New Kind of Science, Wolfram Media, Champaign, USA, 2002. 13. Von Neumann J. Theory of Self-Reproducing Automata, University of Illinois Press, Urbana and London, 1966. 66 Paolo Di Sia . / Journal of Science / Vol 5 / Issue 2 / 2015 / 65-67. 14. Henson J. The causal set approach to quantum gravity, arXiv:gr-qc/0601121, 2006. 15. Bombelli L, Lee J, Meyer D, and Sorkin RD. Space-time as a causal set. Physical Review Letters, 59, 1987, 521-524. 16. Bolognesi T. Building Discrete Spacetimes by Simple Deterministic Computations. ERCIM News, ERCIM EEIG, 83, 2010, 52-53. 17. Di Sia P. Extreme Physics and Informational/Computational Limits. Journal of Physics: Conference Series 306, 2011, 012067 (8 pp). 18. Di Sia P. Exciting Peculiarities of the Extreme Physics, Journal of Physics: Conference Series, 442(1), 2013, 012068, pp 6. 67 .
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