Can General Relativistic Computers Break the Turing Barrier?

  • István Németi
  • Hajnal Andréka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)


- Can general relativistic computers break the Turing barrier? – Are there final limits to human knowledge? – Limitative results versus human creativity (paradigm shifts). – Gödel’s logical results in comparison/combination with Gödel’s relativistic results. – Can Hilbert’s programme be carried through after all?


Black Hole Event Horizon Turing Machine Relativistic Computer Newtonian Case 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Andréka, H., Madarász, J.X., Németi, I.: Logic of Spacetime. In: Aiello, M., van Benthem, J., Hartman-Pratt, I. (eds.) Logic of Space. Kluwer Academic Publishers, Dordrecht (in preparation)Google Scholar
  2. 2.
    Andréka, H., Madarász, J.X., Németi, I.: Logical axiomatizations of spacetime. In: Prékopa, A., Molnár, E. (eds.) Non-Euclidean Geometries, János Bolyai Memorial. Mathematics and its Applications, vol. 581, pp. 155–185. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Andréka, H., Madarász, J.X., Németi, I., Andai, A., Sain, I., Sági, G., Tőke, C., Vályi, S.: On the logical structure of relativity theories. Internet book, Budapest (2000),
  4. 4.
    Andréka, H., Németi, I., Wüthrich.: A twist in the geometry of rotating black holes: seeking the cause of acausality, 15 pages (manuscript, 2005)Google Scholar
  5. 5.
    Cooper, S.B.: How Can Nature Help Us Compute? In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 1–13. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Earman, J.: Bangs, crunches, whimpers, and shrieks. Singularities and acausalities in relativistic spacetimes. Oxford university Press, Oxford (1995)Google Scholar
  7. 7.
    Etesi, G., Németi, I.: Turing computability and Malament-Hogarth spacetimes. International Journal of Theoretical Physics 41(2), 342–370 (2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    Gödel, K.: Lecture on rotating universes. In: Feferman, S., Dawson, J.S., Goldfarb, W., Parson, C., Solovay, R.N. (eds.) Kurt Gödel Collected Works, vol. III, pp. 261–289. Oxford University Press, Oxford (1995)Google Scholar
  9. 9.
    Hogarth, M.L.: Predictability, computability, and spacetime. Ph.D Dissertation, University of Cambridge, UK (2000),
  10. 10.
    Hogarth, M.L.: Deciding arithmetic using SAD computers. Brit. J. Phil. Sci. 55, 681–691 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Madarász, J.X., Németi, I., Székely, G.: Twin Paradox and the logical foundation of space-time. Foundation of Physics (to appear) arXiv:gr-qc/0504118Google Scholar
  12. 12.
    Madarász, J.X., Németi, I., Székely, G.: First-order logic foundation of relativity theories. In: Mathematical problems from applied logic II. International Mathematical Series. Springer, Heidelberg (to appear)Google Scholar
  13. 13.
    Madarász, J.X., Székely, G.: The effects of gravitation on clocks, proved in axiomatic relativity. In: Abstracts for the conference Logic in Hungary (2005),
  14. 14.
    Németi, I.: On logic, relativity, and the limitations of human knowledge. Iowa State University, Department of Mathematics, Ph. D. course during the academic year (1987/1988)Google Scholar
  15. 15.
    Németi, I., Dávid, G.: Relativistic computers and the Turing barrier. Journal of Applied Mathematics and Computation (to appear)Google Scholar
  16. 16.
    Ori, A.: On the traversability of the Cauchy horizon: Herman and Hiscock’s argument revisited. In: Ori, A., Ori, L.M. (eds.) Internal Structures of Black Holes and Spacetime Singularitites. Ann. Isra. Phys. Soc, vol. 13, IOP (1997)Google Scholar
  17. 17.
    Reynolds, C.C., Brenneman, L.W., Garofalo, D.: Black hole spin in AGN and GBHCs. October 5 (2004) arXiv:astro-ph/0410116 (Evidence for rotating black holes)Google Scholar
  18. 18.
    Strohmayer, T.E.: Discovery of a 450 HZ quasi-periodic oscillation from the microquasar GRO J1655-40 wtih the Rossi X-Ray timing explorer. The Astrophysical Journal 553(1), L49–L53 (2001) (Evidence for rotating black holes.) arXiv:astro-ph/0104487CrossRefGoogle Scholar
  19. 19.
    Taylor, E.F., Wheeler, J.A.: Black Holes. Addison, Wesley, Longman, San Francisco (2000)Google Scholar
  20. 20.
    Tegmark, M.: Parallel Universes. Scientific American, 41–51 (May 2003)Google Scholar
  21. 21.
    Wiedermann, J., van Leeuwen, J.: Relativistic computers and non-uniform complexity theory. In: Calude, C.S., Dinneen, M.J., Peper, F. (eds.) UMC 2002. LNCS, vol. 2509, pp. 287–299. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • István Németi
    • 1
  • Hajnal Andréka
    • 1
  1. 1.Rényi Institute of MathematicsBudapestHungary

Personalised recommendations