Advertisement

The Principle of a Finite Density of Information

  • Pablo Arrighi
  • Gilles Dowek
Part of the Emergence, Complexity and Computation book series (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.

Keywords

State Space Entangle State Cellular Automaton Superposition Principle Dual Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 2.
    Arrighi, P., Dowek, G.: Causal graph dynamics. Pre-print arXiv:1202.1098 (2012)Google Scholar
  3. 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)CrossRefGoogle Scholar
  4. 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)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bekenstein, J.D.: Universal upper bound to entropy-to-energy ratio for bounded systems. Phys. Rev. D 23, 287–298 (1981)MathSciNetCrossRefGoogle Scholar
  6. 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)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Gandy, R.: Church’s thesis and principles for mechanisms. In: The Kleene Symposium. North-Holland Publishing Company, Amsterdam (1980)Google Scholar
  8. 8.
    Nielsen, M.A.: Computable functions, quantum measurements, and quantum dynamics. Phys. Rev. Lett. 79(15), 2915–2918 (1997)CrossRefGoogle Scholar
  9. 9.
    Weihrauch, K.: Computable analysis: an introduction. Springer (2000)Google Scholar
  10. 10.
    Wolfram, S.: A new kind of science. Wolfram Media Inc. (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pablo Arrighi
    • 1
    • 2
  • Gilles Dowek
    • 3
  1. 1.École normale supérieure de LyonLyonFrance
  2. 2.Université de GrenobleGrenobleFrance
  3. 3.Institut national de recherche en informatique et en automatique (INRIA)ParisFrance

Personalised recommendations