International Journal of Theoretical Physics

, Volume 25, Issue 6, pp 617–661

Cosmological limits on computation

  • Frank J. Tipler
Article

Abstract

A true universal Turing machine can be constructed only if it is possible to actually process and store an infinite number of bits between now and the end of the universe. Conditions on the universe are derived that must hold if such processing and storage is to be possible. In particular, it is shown that it is possible only if the universe is closed and only if its futurec-boundary consists of a single point.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barrow, J. D. and Matzner, R. A. (1977).Monthly Notices of the Royal Astronomical Society,180, 317.Google Scholar
  2. Barrow, J. D., and Tipler, F. J. (1978).Nature,276, 453.Google Scholar
  3. Barrow, J. D., and Tipler, F. J. (1985).Monthly Notices of the Royal Astronomical Society,216, 395.Google Scholar
  4. Barrow, J. D., and Tipler, F. J. (1986).The Anthropic Cosmological Principle, Oxford University Press, Oxford.Google Scholar
  5. Barrow, J. D., and Turner, M. S. (1970).Nature,292, 35.Google Scholar
  6. Bekenstein, J. D. (1981).Physical Review Letters,46, 623.Google Scholar
  7. Bekenstein, J. D. (1981a).Physical Review D,23, 287.Google Scholar
  8. Bekenstein, J. D. (1983).Physical Review D,27, 2262.Google Scholar
  9. Bennett, C. H. (1973).IBM Journal of Research and Development,17, 525.Google Scholar
  10. Bennett, C. H. (1982).International Journal of Theoretical Physics,21, 905.Google Scholar
  11. Bennett, C. H., and Landauer, R. (1985).Scientific American,253(July), 48.Google Scholar
  12. Bethe, H. A., and Salpeter, E. E. (1957).Quantum Mechanics of One and Two-Electron Atoms, Academic Press, New York, p. 115.Google Scholar
  13. Bremermann, (1982).International journal of Theoretical Physics,21, 203.Google Scholar
  14. Brill, D. R., and Glaherty, F. (1976).Communications in Mathematical Physics,50, 157.Google Scholar
  15. Brillouin, L. (1962).Science and Information Theory, Academic Press, New York.Google Scholar
  16. Bucic, R., and Sachs, R. K. (1976).General Relativity and Gravitation,7, 21.Google Scholar
  17. Caves, C. M., Thorne, K. S., Drever, R P., Sandberg, V. D., and Zimmermann, M. (1980).Reviews of Modern Physics,52, 341.Google Scholar
  18. Chandrasekhar, S. (1960).Principles of Stellar Dynamics, Dover, New York.Google Scholar
  19. Collins, C. B., and Hawking, S. W. (1973).Astrophysical Journal,180, 317.Google Scholar
  20. Dicus, D. A., Letaw, J. R., Teplitz, D. C., and Teplitz, V. L. (1982).Astrophysical Journal,252, 1.Google Scholar
  21. Dicus, D. A., Letaw, L. R., Teplitz, D. C., and Teplitz, V. L. (1983).Scientific American,248(3), 90.Google Scholar
  22. Dyson, F. J. (1979).Reviews of Modern Physics,51, 447.Google Scholar
  23. Dyson, F. J. (1981). Life in the Universe, unpublished Darwin Lecture, Darwin College, Cambridge, England, November 10, 1981.Google Scholar
  24. Ellis, G. R. R. (1973). InCargese Lectures in Physics, Volume 6, E. Schatzman, ed., Gordon and Breach, New York.Google Scholar
  25. Feinberg, G. (1981).Physical Review, D,23, 3075.Google Scholar
  26. Frautschi, S. (1982).Science,217, 593.Google Scholar
  27. Gerhardt, C. (1983).Communications in Mathematical Physics,89, 523.Google Scholar
  28. Geroch, R. P. (1970).Journal of Mathematical Physics,11, 437.Google Scholar
  29. Gibbons, G. W., Hawking, S. W., Horowitz, G. T., and Perry, M. J. (1983).Communications in Mathematical Physics,88, 295.Google Scholar
  30. Hawking, S. W. (1974).Nature,248, 30.Google Scholar
  31. Hawking, S. W. (1975).Communications in Mathematical Physics,43, 199.Google Scholar
  32. Hawking, S. W. (1984).Nuclear Physics B,239, 257.Google Scholar
  33. Hawking, S.W., and Ellis, G. F. R. (1973).The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge.Google Scholar
  34. Horowitz, G. T., and Perry, M. J. (1982).Physical Review Letters,48, 371.Google Scholar
  35. Islam, J. N. (1977).Quarterly Journal of the Royal Astronomical Society,18, 3.Google Scholar
  36. Islam, J. N. (1979).Sky & Telescope,57, 13.Google Scholar
  37. Jammer, M. (1974).The Philosophy of Quantum Mechanics, Wiley, New York.Google Scholar
  38. Landau, L., and Lifshitz, E. M. (1975).The Classical Theory of Fields, 4th ed., Pergamon, New York.Google Scholar
  39. Landauer, R. (1961).IBM Journal of Research and Development,3, 183.Google Scholar
  40. Landauer, R. and Woo, J. W. F. (1971).Journal of Applied Physics,42, 2301.Google Scholar
  41. Landauer, R. (1982).International Journal of Theoretical Physics,21, 283.Google Scholar
  42. Landauer, R. (1985).Annals of the New York Academy of Sciences,426, 161.Google Scholar
  43. Likharev, K. K. (1982).International Journal of Theoretical Physics,21, 311.Google Scholar
  44. Marsden, J. E., and Tipler, F. J. (1980).Phys Reports,66, 109.Google Scholar
  45. Matzner R. A. (1971).Annals of Physics,65, 482.Google Scholar
  46. Metzner, A. W. K. and Morrison, P. (1959).Monthly Notices of the Royal Society,119, 657.Google Scholar
  47. Misner, C. W. (1968).Astrophysical Journal,151, 431.Google Scholar
  48. Misner, C, W. (1969).Physical Review,186, 1328.Google Scholar
  49. Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation, Freeman, San Francisco.Google Scholar
  50. Mundici, D. (1981).Nuovo Cimento,61B, 297.Google Scholar
  51. Page, D. N. (1982).Physical Review D,26, 947.Google Scholar
  52. Page, D. N., and McKee M. R. (1981).Physical Review D,24, 1458.Google Scholar
  53. Page, D. N., and McKee, M. R. (1983).Mercury,12, 17.Google Scholar
  54. Porod, W., Grondin, R. O., Ferry, D. K., and Porod, G. (1984a).Physical Review Letters,52, 232.Google Scholar
  55. Porod, W., Grondin, R. O., Ferry, D. K., and Porod, G. (1984b).Physical Review Letters,53, 1202Google Scholar
  56. Rees, M. (1969).Observatory,89, 193.Google Scholar
  57. Ryan, M. P., and Shepley, L. C. (1975).Homogeneous Relativistic Cosmologies, Princeton University Press, Princeton, New Jersey.Google Scholar
  58. Sakurai, J. J. (1967).Advanced Quantum Mechanics, Addison-Wesley, Reading, Massachusetts, p. 44.Google Scholar
  59. Saslaw, W. C. (1973).Publications Astronomical Society of the Pacific,85, 5.Google Scholar
  60. Saslaw, W. C. (1974). InIAU Symposium No. 58, J. R. Shakesaft, ed., Reidel, Dordrecht.Google Scholar
  61. Schoen, R., and Yau, S.-T. (1978).Communications in Mathematical Physics,65, 45.Google Scholar
  62. Schoen, R. and Yau, S.-T. (1979).Physical Review Letters,42, 547.Google Scholar
  63. Seifert, H.-J. (1971).General Relativity and Gravitation,1. Google Scholar
  64. Shannon, C. E., and Weaver, W. (1949).The Mathematical Theory of Communication, University of Illinois Press, Urbana, Illinois.Google Scholar
  65. Spitzer, L., and Hära, R. (1958).Astrophysical Journal,127, 544.Google Scholar
  66. Thorne, K. S. (1967).Astrophysical Journal,148, 51.Google Scholar
  67. Tipler, F. J. (1977).Physical Review D,15, 942.Google Scholar
  68. Tipler, F. J. (1979a).Nature,280, 203.Google Scholar
  69. Tipler, F. J. (1979b).General Relativity and Gravitation,10, 1005.Google Scholar
  70. Tipler, F. J. (1980). InEssays in General Relativity, F. J. Tipler, ed., Academic Press, New York.Google Scholar
  71. Tipler, F. J. (1986).Journal of Mathematical Physics,27, 559.Google Scholar
  72. Toffoli, T., Bennett, C. H., Landauer, R., Feynman R. P.,et al. (1982).Proceedings of the Conference on Physics and Computation, International Journal of Theoretical Physics,21(3/4, 6/7, 12).Google Scholar
  73. Trimble, V. (1975).Review of Modern Physics,47, 877.Google Scholar
  74. Unruh, W. G. and Wald, R. M. (1983).Physical Review D,27, 2271.Google Scholar
  75. Weinberg, S. (1972).Gravitation and Cosmology, Wiley, New York.Google Scholar
  76. Witten, E. (1981).Communications in Mathematical Physics,80, 381.Google Scholar
  77. Zel'dovich, Ya. B., and Novikov, I. D. (1971).Relativistic Astrophysics, Volume I:Stars and Relativity, University of Chicago Press, Chicago, pp. 337–338.Google Scholar
  78. Zurek, W. H. (1984).Physical Review Letters,53, 391.Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Frank J. Tipler
    • 1
  1. 1.Departments of Mathematics and PhysicsTulane UniversityNew Orleans

Personalised recommendations