Toward a Formal Foundation for Time Travel in Stories and Games

  • Michiel Helvensteijn
  • Farhad Arbab
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9660)


Time-travel is a popular topic not only in science fiction, but in physics as well, especially when it concerns the notion of “changing the past”. It turns out that if time-travel exists, it will follow certain logical rules. In this paper we apply the tools of discrete mathematics to two such sets of rules from theoretical physics: the Novikov Self Consistency Principle and the Many Worlds Interpretation of quantum mechanics. Using temporal logic, we can encode the dynamics of a time-travel story or game, and model-check them for adherence to the rules. We also present the first ever game-engine following these rules, allowing the development of technically accurate time-travel games.


Time Travel Temporal Logic Causality Chain Kripke Structure Causality Diagram 
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.


  1. 1.
    Chellas, B.F.: Modal Logic: An Introduction, vol. 316. Cambridge University Press, Cambridge (1980)CrossRefzbMATHGoogle Scholar
  2. 2.
    Friedman, J., Morris, M.S., Novikov, I.D., Echeverria, F., Klinkhammer, G., Thorne, K.S., Yurtsever, U.: Cauchy problem in spacetimes with closed timelike curves. Phys. Rev. D 42(6), 1915–1930 (1990)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Fujibayashi, H.: The Legend of Zelda: Oracle of Ages (2001).
  4. 4.
    Gabbay, D., Pnueli, A., Shelah, S., Stavi, J.: On the temporal analysis of fairness. In: Proceedings of the 7th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 163–173. ACM (1980)Google Scholar
  5. 5.
    Heinlein, R.A.: By His Bootstraps, October 1941Google Scholar
  6. 6.
    Laroussinie, F., Schnoebelen, P.: Specification in CTL+ past for verification in CTL. Inf. Comput. 1(156), 236–263 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Lichtenstein, O., Pnueli, A., Zuck, L.: The glory of the past. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 196–218. Springer, Heidelberg (1982)Google Scholar
  8. 8.
    Markey, N.: Temporal logic with past is exponentially more succinct. EATCS Bull. 79, 122–128 (2003)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Nahin, P.: Time Travel: A Writer’s Guide to the Real Science of Plausible Time Travel. Johns Hopkins University Press, Baltimore (2011)Google Scholar
  10. 10.
    Nahin, P.: Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction, 2nd edn. Springer, New York (2014). Softcover reprint of the original, 2nd edn. 1999th ednzbMATHGoogle Scholar
  11. 11.
    Schrödinger, E.: Die gegenwärtige situation in der quantenmechanik. Naturwissenschaften 23(49), 823–828 (1935)CrossRefzbMATHGoogle Scholar
  12. 12.
    Stephenson, M.: NetHack (1987).
  13. 13.
    Zemeckis, R.: Back to the Future, iMDB ID: tt0088763, July 1985Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Universiteit LeidenLeidenThe Netherlands
  2. 2.University College LondonLondonUK
  3. 3.Centrum voor Wiskunde En InformaticaAmsterdamThe Netherlands

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