Skip to main content
SpringerLink
Log in

Around the Physical Church-Turing Thesis: Cellular Automata, Formal Languages, and the Principles of Quantum Theory

  • Conference paper
Language and Automata Theory and Applications (LATA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7183))

Abstract

The physical Church-Turing thesis explains the Galileo thesis, but also suggests an evolution of the language used to describe nature. It can be proved from more basic principle of physics, but it also questions these principles, putting the emphasis on the principle of a bounded density of information. This principle itself questions our formulation of quantum theory, in particular the choice of a field for the scalars and the origin of the infinite dimension of the vector spaces used as state spaces.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Google Scholar 

  2. Arrighi, P., Dowek, G.: Operational semantics for formal tensorial calculus. In: Proceedings of QPL, vol. 33, pp. 21–38. Turku Centre for Computer Science General Publication (2004); arXiv pre-print quant-ph/0501150

    Google Scholar 

  3. Arrighi, P., Dowek, G.: On the Completeness of Quantum Computation Models. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.) CiE 2010. LNCS, vol. 6158, pp. 21–30. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Arrighi, P., Nesme, V., Werner, R.: Unitarity plus causality implies localizability. In: QIP 2010, ArXiv preprint: arXiv:0711.3975 (2007)

    Google Scholar 

  5. Arrighi, P., Nesme, V., Werner, R.: Unitarity plus causality implies localizability (Full version). Journal of Computer and System Sciences (2010)

    Google Scholar 

  6. Arrighi, P., Nesme, V., Werner, R.F.: Quantum Cellular Automata Over Finite, Unbounded Configurations. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 64–75. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Beckman, D., Gottesman, D., Nielsen, M.A., Preskill, J.: Causal and localizable quantum operations. Phys. Rev. A 64(052309) (2001)

    Google Scholar 

  8. 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 

  9. Bell, J.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)

    Google Scholar 

  10. Benioff, P.: New gauge fields from extension of space time parallel transport of vector spaces to the underlying number systems. Arxiv preprint arXiv:1008.3134 (2010)

    Google Scholar 

  11. Boker, U., Dershowitz, N.: The Church-Turing Thesis Over Arbitrary Domains. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 199–229. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. Bournez, O., Campagnolo, M.: A survey on continuous time computations. New computational paradigms. Changing Conceptions of What is Computable, 383–423 (2008)

    Google Scholar 

  13. Boykin, P.O., Mor, T., Pulver, M., Roychowdhury, V., Vatan, F.: On universal and fault-tolerant quantum computing: A novel basis and a new constructive proof of universality for Shor’s basis. In: FOCS 1999: Proceedings of the 40th Annual Symposium on Foundations of Computer Science, p. 486. IEEE Computer Society, Washington, DC (1999)

    Google Scholar 

  14. Buchholz, D.: Current trends in axiomatic quantum field theory. Lect. Notes Phys, vol. 558, p. 4364 (2000)

    Google Scholar 

  15. Collins, P., Graça, D.S.: Effective computability of solutions of ordinary differential equations — The thousand monkeys approach. In: Brattka, V., Dillhage, R., Grubba, T., Klutsch, A. (eds.) 5th International Conference on Computability and Complexity in Analysis. Electronic Notes Theorerical Computer Science, vol. 221, pp. 103–114 (2008)

    Google Scholar 

  16. Collins, P., Graça, D.S.: Effective computability of solutions of differential inclusions — The ten thousand monkeys approach. Journal of Universal Computer Science 15(6), 1162–1185 (2009)

    MathSciNet  MATH  Google Scholar 

  17. Connes, A.: The Witt construction in characteristic one and quantization. Arxiv preprint arXiv:1009.1769 (2010)

    Google Scholar 

  18. Copeland, B., Shagrir, O.: Physical Computation: How General are Gandys Principles for Mechanisms? Minds and Machines 17(2), 217–231 (2007)

    Article  Google Scholar 

  19. Dershowitz, N., Gurevich, Y.: A natural axiomatization of the computability and proof of Church’s thesis. The Bulletin of Symbolic Logic 14(3) (2008)

    Google Scholar 

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

    Google Scholar 

  21. Dowek, G.: Non determinisitic computation over the real numbers (submited to publication)

    Google Scholar 

  22. Dowek, G.: The physical Church thesis as an explanation of the Galileo thesis (submited to publication)

    Google Scholar 

  23. Eggeling, T., Schlingemann, D., Werner, R.: Semicausal operations are semilocalizable. EPL (Europhysics Letters) 57, 782 (2002)

    Article  Google Scholar 

  24. Einstein, A.: Physics and Reality. Journal of the Franklin Institute 221(3), 349–382 (1936)

    Article  Google Scholar 

  25. Galilei, G.: Il Saggiatore (1623)

    Google Scholar 

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

    Google Scholar 

  27. Holevo, A.: Information-theoretical aspects of quantum measurement. Problemy Peredachi Informatsii 9(2), 31–42 (1973)

    MathSciNet  MATH  Google Scholar 

  28. Montague, R.: Towards a general theory of computability. Synthese 12(4), 429–438 (1960)

    Article  MathSciNet  Google Scholar 

  29. Pour-El, M., Richards, J.: Computability in Analysis and Physics. Springer, Heidelberg (1989)

    Book  MATH  Google Scholar 

  30. Rabin, M.: Computable algebra, general theory and theory of computable fields. Transactions of the American Mathematical Society 95(2), 341–360 (1960)

    MathSciNet  MATH  Google Scholar 

  31. Schumacher, B., Werner, R.: Reversible quantum cellular automata. ArXiv pre-print quant-ph/0405174 (2004)

    Google Scholar 

  32. Schumacher, B., Westmoreland, M.D.: Locality and information transfer in quantum operations. Quantum Information Processing 4(1), 13–34 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  34. Wigner, E.: The unreasonable effectiveness of mathematics in the natural sciences. Communications in Pure and Applied Mathematics 13(1) (1960)

    Google Scholar 

  35. Wolfram, S.: A new Kind of Science. Wolfram Media (2002)

    Google Scholar 

  36. Ziegler, M.: Physically-relativized Church-Turing hypotheses: Physical foundations of computing and complexity theory of computational physics. Applied Mathematics and Computation 215(4), 1431–1447 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INRIA, 23 avenue d’Italie, CS 81321, 75214, Paris Cedex 13, France

    Gilles Dowek

Authors
  1. Gilles Dowek
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dowek, G. (2012). Around the Physical Church-Turing Thesis: Cellular Automata, Formal Languages, and the Principles of Quantum Theory. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28332-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28331-4

  • Online ISBN: 978-3-642-28332-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation