Skip to main content
SpringerLink
Log in
Book cover

Conference on Computability in Europe

CiE 2012: How the World Computes pp 528–538Cite as

Existence of Faster than Light Signals Implies Hypercomputation already in Special Relativity

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7318))

Abstract

Within an axiomatic framework, we investigate the possibility of hypercomputation in special relativity via faster than light signals. We formally show that hypercomputation is theoretically possible in special relativity if and only if there are faster than light signals.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andréka, H., Madarász, J.X., Németi, I., Székely, G.: A logic road from special relativity to general relativity. Synthese, 1–17 (2011) (online-first)

    Google Scholar 

  2. Andréka, H., Madarász, J.X., Németi, I., Székely, G.: What are the numbers in which spacetime? (2012), arXiv:1204.1350

    Google Scholar 

  3. Andréka, H., Németi, I., Németi, P.: General relativistic hypercomputing and foundation of mathematics. Nat. Comput. 8(3), 499–516 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dávid, G., Németi, I.: Relativistic computers and the Turing barrier. Appl. Math. Comput. 178(1), 118–142 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. d’Inverno, R.: Introducing Einstein’s relativity. Oxford University Press, New York (1992)

    MATH  Google Scholar 

  6. Earman, J., Norton, J.D.: Forever is a day: supertasks in Pitowsky and Malament–Hogarth spacetimes. Philos. Sci. 60(1), 22–42 (1993)

    Article  MathSciNet  Google Scholar 

  7. Etesi, G., Németi, I.: Non-Turing computations via Malament–Hogarth space-times. Internat. J. Theoret. Phys. 41(2), 341–370 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Friedman, M.: Foundations of Space-Time Theories. Relativistic Physics and Philosophy of Science. Princeton University Press, Princeton (1983)

    Google Scholar 

  9. Hogarth, M.L.: Does general relativity allow an observer to view an eternity in a finite time? Found. Phys. Lett. 5(2), 173–181 (1992)

    Article  MathSciNet  Google Scholar 

  10. Madarász, J.X.: Logic and Relativity (in the light of definability theory). Ph.D. thesis, Eötvös Loránd Univ., Budapest (2002), http://www.math-inst.hu/pub/algebraic-logic/Contents.html

  11. Madarász, J.X., Németi, I., Székely, G.: Twin paradox and the logical foundation of relativity theory. Found. Phys. 36(5), 681–714 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Manchak, J.B.: On the possibility of supertasks in general relativity. Found. Phys. 40(3), 276–288 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Matolcsi, T., Rodrigues Jr., W.A.: The geometry of space-time with superluminal phenomena. Algebras Groups Geom. 14(1), 1–16 (1997)

    MathSciNet  MATH  Google Scholar 

  14. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W. H. Freeman and Co., San Francisco (1973)

    Google Scholar 

  15. Mittelstaedt, P.: What if there are superluminal signals? The European Physical Journal B - Condensed Matter and Complex Systems 13, 353–355 (2000)

    Article  Google Scholar 

  16. Németi, P., Székely, G.: Special relativistic hypercomputation is possible if there are faster than light signals (2012) (preprint version); arXiv:1204.1773

    Google Scholar 

  17. OPERA collaboration: Measurement of the neutrino velocity with the OPERA detector in the CNGS beam (2011), arXiv:1109.4897

    Google Scholar 

  18. Petkov, V.: Relativity and the nature of spacetime, 2nd edn. Frontiers Collection. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  19. Recami, E.: Tachyon kinematics and causality: a systematic thorough analysis of the tachyon causal paradoxes. Found. Phys. 17(3), 239–296 (1987)

    Article  MathSciNet  Google Scholar 

  20. Recami, E.: Superluminal motions? A bird’s-eye view of the experimental situation. Found. Phys. 31, 1119–1135 (2001)

    Article  Google Scholar 

  21. Recami, E., Fontana, F., Garavaglia, R.: Special relativity and superluminal motions: a discussion of some recent experiments. Internat. J. Modern Phys. A 15(18), 2793–2812 (2000)

    MathSciNet  Google Scholar 

  22. Rindler, W.: Relativity. Special, general, and cosmological, 2nd edn. Oxford University Press, New York (2006)

    Google Scholar 

  23. Selleri, F.: Superluminal signals and the resolution of the causal paradox. Found. Phys. 36, 443–463 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. Stannett, M.: The case for hypercomputation. Appl. Math. Comput. 178(1), 8–24 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. Székely, G.: First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers. Ph.D. thesis, Eötvös Loránd Univ., Budapest (2009)

    Google Scholar 

  26. Székely, G.: The existence of superluminal particles is consistent with the kinematics of Einstein’s special theory of relativity (2012), arXiv:1202.5790

    Google Scholar 

  27. Taylor, E.F., Wheeler, J.A.: Spacetime Physics. W. H. Freeman and Company, New York (1997)

    Google Scholar 

  28. Tolman, R.C.: The Theory of the Relativity of Motion. University of California, Berkely (1917)

    MATH  Google Scholar 

  29. Weinstein, S.: Super luminal signaling and relativity. Synthese 148, 381–399 (2006)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, 1364, Budapest, Hungary

    Péter Németi & Gergely Székely

Authors
  1. Péter Németi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gergely Székely
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Computer Laboratory, University of Cambridge, Willialm Gates Building, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  3. Institute for Logic, Language and Computation, University of Amsterdam, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Németi, P., Székely, G. (2012). Existence of Faster than Light Signals Implies Hypercomputation already in Special Relativity. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_53

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30870-3_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30869-7

  • Online ISBN: 978-3-642-30870-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation