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The Principle of a Finite Density of Information

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Part of the book series: Emergence, Complexity and Computation ((ECC,volume 2))

Abstract

The possibility to describe the laws of the Universe in a computational way seems to be correlated to a principle that the density of information is bounded. This principle, that is dual to that of a finite velocity of information, has already been investigated in Physics, and is correlated to the old idea that there is no way to know a magnitude with an infinite precision. It takes different forms in classical Physics and in quantum Physics.

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References

  1. Arrighi, P., Dowek, G.: The physical Church-Turing thesis and the principles of quantum theory. Int. J. Found. of Computer Science (2011) (to appear)

    Google Scholar 

  2. Arrighi, P., Dowek, G.: Causal graph dynamics. Pre-print arXiv:1202.1098 (2012)

    Google Scholar 

  3. Arrighi, P., Fargetton, R., Nesme, V., Thierry, E.: Applying Causality Principles to the Axiomatization of Probabilistic Cellular Automata. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds.) CiE 2011. LNCS, vol. 6735, pp. 1–10. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Arrighi, P., Nesme, V., Werner, R.: Unitarity plus causality implies localizability (full version). Journal of Computer and System Sciences 77(2), 372–378 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bekenstein, J.D.: Universal upper bound to entropy-to-energy ratio for bounded systems. Phys. Rev. D 23, 287–298 (1981)

    Article  MathSciNet  Google Scholar 

  6. Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990) 400(1818), 97–117 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gandy, R.: Church’s thesis and principles for mechanisms. In: The Kleene Symposium. North-Holland Publishing Company, Amsterdam (1980)

    Google Scholar 

  8. Nielsen, M.A.: Computable functions, quantum measurements, and quantum dynamics. Phys. Rev. Lett. 79(15), 2915–2918 (1997)

    Article  Google Scholar 

  9. Weihrauch, K.: Computable analysis: an introduction. Springer (2000)

    Google Scholar 

  10. Wolfram, S.: A new kind of science. Wolfram Media Inc. (2002)

    Google Scholar 

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Arrighi, P., Dowek, G. (2013). The Principle of a Finite Density of Information. In: Zenil, H. (eds) Irreducibility and Computational Equivalence. Emergence, Complexity and Computation, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35482-3_11

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  • DOI: https://doi.org/10.1007/978-3-642-35482-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35481-6

  • Online ISBN: 978-3-642-35482-3

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