Skip to main content
SpringerLink
Log in

Quantum Information and Quantum Black Holes

  • Chapter
Advances in the Interplay Between Quantum and Gravity Physics

Part of the book series: NATO Science Series ((NAII,volume 60))

Abstract

A naive view of physics—classical or quantum—would have us believe that an infinite amount of information can be contained in a finite 3-D space. After all, matter can have an infinity of classical configurations there, and quantum fields have an infinity of modes in that region. ’ t Hooft and Susskind’s holographic principle [1, 2] has shattered this popular view: it holds that insofar as the information required to describe them is concerned, physical systems are inherently two-dimensional in space. In particular, the information or entropy (see Sec. 1.2 below for the relation) in an isolated system is expected to be bounded from above by one quarter the area of a circumscribing surface expressed in Planck units (holographic bound):

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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. ’t Hooft, G. (1993) in Aly, A., Ellis, J. and Randjbar-Daemi, S. (eds.), Salamfestschrifft, World Scientific, Singapore, gr-qc/9310026.

    Google Scholar 

  2. Susskind, L. (1995) J. Math. Phys., 36, 6377.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Bekenstein, J.D. (1974) Lett. Nuovo Cimento, 4, 737 and Phys. Rev. D, 9, 3292.

    Article  ADS  Google Scholar 

  4. Wald, R.M. (2001) Living Reviews in Relativity, 2001-2006.

    Google Scholar 

  5. Bekenstein, J.D. (2000) Phys. LettersB, 481, 339; (2001) in Ruffini, R. (ed.), Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, World Scientific, Singapore.

    MathSciNet  ADS  MATH  Google Scholar 

  6. Bousso, R. (1999) J. High Energy Phys., 9906, 028.

    Article  MathSciNet  ADS  Google Scholar 

  7. Peres, A. (1993) Quantum Theory: Concepts and Methods, Kluwer, Dordrecht.

    MATH  Google Scholar 

  8. Shannon, C. and Weaver, W. (1949) The Mathematical Theory of Communication, Univ. of Illinois Press, Urbana.

    MATH  Google Scholar 

  9. Katz, A. (1967) Principles of Statistical Mechanics, Freeman, San Francisco.

    Google Scholar 

  10. Bekenstein, J.D. (1981) Phys. Rev. D, 23, 287.

    Article  MathSciNet  ADS  Google Scholar 

  11. Bekenstein, J.D. (1973) Phys. Rev. D, 7, 2333.

    Article  MathSciNet  ADS  Google Scholar 

  12. Unruh, W.G. and Wald, R.M. (1982) Phys. Rev. D, 25, 942 and (1983) Phys. Rev. D, 27, 2271; Pelath, M.A. and Wald, R.M. (1999) Phys. Rev. D, 60, 104009.

    Article  ADS  Google Scholar 

  13. Bekenstein, J.D. (1982) Phys. Rev. D, 26, 950; (1983) Phys. Rev. D, 27, 2262.

    MathSciNet  ADS  Google Scholar 

  14. Bekenstein, J.D. (1994) Phys. Rev. D, 49, 1912; (1999) Phys. Rev. D, 60, 124010.

    MathSciNet  ADS  Google Scholar 

  15. Zaslavskii, O. (1991) Phys. Lett. A, 160, 339.

    Article  MathSciNet  Google Scholar 

  16. Hod, S. (1999) Phys. Rev. D, 60, 104031; (2000) Phys. Rev. D, 61, 024018 and 61, 024023.

    Article  MathSciNet  Google Scholar 

  17. Mayo, A.E. (1999) Phys. Rev. D, 60, 104044; Bekenstein, J.D. and Mayo, A.E. (2000) Phys. Rev. D, 61, 024022.

    Article  MathSciNet  Google Scholar 

  18. Bekenstein, J.D. (1996) in Jantzen, R.T. and Reiser, G.M. (eds.), Proceedings of the VII Marcel Grossmann Meeting on General Relativity, World Scientific, Singapore, gr-qc/9409015.

    Google Scholar 

  19. Bousso, R. (2001) J. High Energy Phys., 0104, 035.

    Google Scholar 

  20. Verlinde, E. (2000) preprint hep-th/0008140.

    Google Scholar 

  21. Cardy, J. L. (1986) Nucl. Phys. B, 270, 317.

    Article  MathSciNet  Google Scholar 

  22. Bekenstein, J.D. (1989) Int. J. Theor. Phys., 28, 967; Schiffer, M. (1991) Int. J. Theor. Phys., 30, 419; Fischler, W. and Susskind, L. (1998) preprint hep-th/9806039; Bousso, R. (1999) J. High Energy Phys., 9907, 004; Easther R. and Lowe, D. (1999) Phys. Rev. Letters, 82, 4967; Veneziano, G. (1999) Phys. Lett. B, 454, 22; Kaloper, N. and Linde, A. (1999) Phys. Rev. D, 60, 103509; Bak D. and Rey, S.-J. (2000) Class. Quant. Grav., L83, 17; Brustein, R. and Veneziano, G. (2000) Phys. Rev. Letters, 84, 5695.

    Google Scholar 

  23. Page, D.N. (1983) Phys. Rev. Letters, 50, 1013.

    Article  ADS  Google Scholar 

  24. Page, D.N. (1976) Phys. Rev. D, 13, 198.

    Article  ADS  Google Scholar 

  25. Bekenstein, J.D. and Schiffer, M. (1990) Int. J. Mod. Physics C, 1, 355.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Pendry, J.B. (1983) J. Phys. A, 16, 2161.

    Article  MathSciNet  ADS  Google Scholar 

  27. Landau, L.D. and Lifshitz, E.M. (1980) Statistical Physics, Part I, Third Edition, Pergamon, Oxford.

    Google Scholar 

  28. Volkov, A.M., Izmest’ev, A.A. and Skrotskii, G.V. (1971) Sov. Phys. JETP, 32, 686.

    MathSciNet  ADS  Google Scholar 

  29. Marko, H. (1965) Kybernetik, 2, 274.

    Article  Google Scholar 

  30. Bekenstein, J.D. and Mayo, A.E. (2001) preprint gr-qc/0105055, to appear in General Relativity and Gravitation.

    Google Scholar 

  31. Bekenstein, J.D. (1981) Phys. Rev. Letters, 46, 623.

    Article  MathSciNet  ADS  Google Scholar 

  32. Bekenstein, J.D. (1988) Phys. Rev. A, 37, 3434.

    Article  MathSciNet  Google Scholar 

  33. Bekenstein, J.D. (1974) Lett. Nuovo Cimento, 11, 467.

    Article  ADS  Google Scholar 

  34. Bekenstein, J.D. (1996) in da Silva, A. J. et. al (eds.), XVII Brazilian National Meeting on Particles and Fields, Brazilian Physical Society, São Paulo.

    Google Scholar 

  35. Bekenstein, J.D. (1998) in Proceedings of the VIII Marcel Grossmann Meeting on General Relativity, Piran, T. and Ruffini, R. eds, World Scientific, Singapore, grqc/9710076.

    Google Scholar 

  36. Bekenstein, J.D. (1999) in Novello, M. (ed.), IX Brazilian School of Cosmology and Gravitation, Atlantiscience, Paris, gr-qc/9808028.

    Google Scholar 

  37. Born, M. (1969) Atomic Physics, Eight Edition, Blackie, London.

    Google Scholar 

  38. Penrose, R. and Floyd, R.M. (1971) Nature, 229, 177.

    ADS  Google Scholar 

  39. Christodoulou, D. (1970) Phys. Rev. Letters, 25, 1596

    Article  ADS  Google Scholar 

  40. Hawking, S.W. (1971) Phys. Rev. Letters, 26, 1344.

    Article  ADS  Google Scholar 

  41. Christodoulou, D. and and Ruffini, R. (1971) Phys. Rev. D, 4, 3552.

    Article  ADS  Google Scholar 

  42. Bekenstein, J.D. (1998) in Iyer, B.R. and Bhawal, B. (eds.), Black Holes, Gravitational Radiation and the Universe, Kluwer, Dordrecht.

    Google Scholar 

  43. Mayo, A.E. (1998), Phys. Rev. D 58, 104007.

    Google Scholar 

  44. Duez, M.W. et. al (1999) Phys. Rev. D, 60, 104024.

    Google Scholar 

  45. Barvinsky, A, Das, S. and Kunstatter, G. (2000) preprint gr-qc/0012066 and (2001) preprint hep-th/0102061.

    Google Scholar 

  46. Gour, G. (2000) Phys. Rev. D, 61, 124007.

    Article  MathSciNet  ADS  Google Scholar 

  47. Merzbacher E., 1970, Quantum Mechanics., Second Edition, Wiley, New York.

    Google Scholar 

  48. Bekenstein, J.D. (2002) in Duff, M. and Liu, J. T. (eds.), 2001: A Spacetime Odyssey, World Scientific Publishing, Singapore, hep-th/0107045.

    Google Scholar 

  49. Schiffer, M. (1989) “Black hole spectroscopy”, preprint IFT/P-38/89, São Paulo; Peleg, Y. (1995) Phys. Lett. B, 356, 462; Kastrup, H. (1996) Phys. Lett. B, 385, 75; Louko, J. and Mäkelä, J. (1996) Phys. Rev. D, 54, 4982; Barvinsky, A. and Kunstatter, G. (1996) Phys. Lett. B, 329, 231; Berezin, V.A. (1997) Phys. Rev. D, 55, 2139; Vaz, C. and Witten, L. (1999) Phys. Rev. D, 60, 024009; Vaz, C. (2000) Phys. Rev. D, 61 064017.

    Google Scholar 

  50. Dolgov, A.D. and Khriplovich, I B. (1997) Phys. Lett. B, 400, 12; Berezin, V.A. (1997) Phys. Rev. D, 55, 2139; Berezin, V.A., Boyarsky, A.M. and Neronov, A.Yu. (1998) Phys. Rev. D, 57 1118.

    MathSciNet  Google Scholar 

  51. Mäkelä, J. and Repo, P. 1997 Phys. Rev. D, 57, 4899.

    Google Scholar 

  52. Mäkelä, J., Repo, P., Luomajoki, M. and Piilonen, J. (2000) Phys. Rev. D, 64, 024018 (2001)

    Google Scholar 

  53. Vaz, C. and Witten, L. (2001) Phys. Rev. D, 63, 024008.

    Google Scholar 

  54. Mukhanov, V.F. (1986) JETP Letters, 44, 63.

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Racah Institute of Physics, Hebrew University of Jerusalem Givat Ram, Jerusalem, 91904, Israel

    Jacob D. Bekenstein

Authors
  1. Jacob D. Bekenstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. New York University, USA

    Peter G. Bergmann

  2. University of Bologna, Italy

    Venzo de Sabbata

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Bekenstein, J.D. (2002). Quantum Information and Quantum Black Holes. In: Bergmann, P.G., de Sabbata, V. (eds) Advances in the Interplay Between Quantum and Gravity Physics. NATO Science Series, vol 60. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0347-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0347-6_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0593-0

  • Online ISBN: 978-94-010-0347-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation