Relativeness in quantum gravity: limitations and frame dependence of semiclassical descriptions

  • Yasunori Nomura
  • Fabio Sanches
  • Sean J. Weinberg
Open Access
Regular Article - Theoretical Physics

Abstract

Consistency between quantum mechanical and general relativistic views of the world is a longstanding problem, which becomes particularly prominent in black hole physics. We develop a coherent picture addressing this issue by studying the quantum mechanics of an evolving black hole. After interpreting the Bekenstein-Hawking entropy as the entropy representing the degrees of freedom that are coarse-grained to obtain a semiclassical description from the microscopic theory of quantum gravity, we discuss the properties these degrees of freedom exhibit when viewed from the semiclassical standpoint. We are led to the conclusion that they show features which we call extreme relativeness and spacetime-matter duality — a nontrivial reference frame dependence of their spacetime distribution and the dual roles they play as the “constituents” of spacetime and as thermal radiation. We describe black hole formation and evaporation processes in distant and infalling reference frames, showing that these two properties allow us to avoid the arguments for firewalls and to make the existence of the black hole interior consistent with unitary evolution in the sense of complementarity. Our analysis provides a concrete answer to how information can be preserved at the quantum level throughout the evolution of a black hole, and gives a basic picture of how general coordinate transformations may work at the level of full quantum gravity beyond the approximation of semiclassical theory.

Keywords

Black Holes in String Theory Models of Quantum Gravity Black Holes 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    J. Preskill, Do black holes destroy information?, in Blackholes, membranes, wormholes and superstrings, S. Kalara and D.V. Nanopoulos eds., World Scientific, Singapore (1993), hep-th/9209058 [INSPIRE].
  2. [2]
    G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B 335 (1990) 138 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    C.R. Stephens, G. ’t Hooft and B.F. Whiting, Black hole evaporation without information loss, Class. Quant. Grav. 11 (1994) 621 [gr-qc/9310006] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    W.K. Wootters and W.H. Zurek, A single quantum cannot be cloned, Nature 299 (1982) 802 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  5. [5]
    L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].ADSMathSciNetGoogle Scholar
  6. [6]
    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An apologia for firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    D. Marolf and J. Polchinski, Gauge/gravity duality and the black hole interior, Phys. Rev. Lett. 111 (2013) 171301 [arXiv:1307.4706] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    S.W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].ADSMathSciNetGoogle Scholar
  10. [10]
    J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  11. [11]
    S.W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
  12. [12]
    Y. Nomura and S.J. Weinberg, Black holes, entropies and semiclassical spacetime in quantum gravity, JHEP 10 (2014) 185 [arXiv:1406.1505] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    Y. Nomura, Quantum mechanics, spacetime locality and gravity, Found. Phys. 43 (2013) 978 [arXiv:1110.4630] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    Y. Nomura, F. Sanches and S.J. Weinberg, The black hole interior in quantum gravity, arXiv:1412.7539 [INSPIRE].
  17. [17]
    Y. Nomura, Physical theories, eternal inflation and quantum universe, JHEP 11 (2011) 063 [arXiv:1104.2324] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  18. [18]
    B.S. DeWitt, Quantum theory of gravity. 1. The canonical theory, Phys. Rev. 160 (1967) 1113 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  19. [19]
    Y. Nomura, The static quantum multiverse, Phys. Rev. D 86 (2012) 083505 [arXiv:1205.5550] [INSPIRE].ADSGoogle Scholar
  20. [20]
    Y. Nomura, J. Varela and S.J. Weinberg, Low energy description of quantum gravity and complementarity, Phys. Lett. B 733 (2014) 126 [arXiv:1304.0448] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    D.N. Page, Is black hole evaporation predictable?, Phys. Rev. Lett. 44 (1980) 301 [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    Y. Nomura, J. Varela and S.J. Weinberg, Black holes, information and Hilbert space for quantum gravity, Phys. Rev. D 87 (2013) 084050 [arXiv:1210.6348] [INSPIRE].ADSGoogle Scholar
  23. [23]
    G. ’t Hooft, Dimensional reduction in quantum gravity, in Salamfestschrift, A. Ali, J. Ellis and S. Randjbar-Daemi eds., World Scientific, Singapore (1994), gr-qc/9310026 [INSPIRE].
  24. [24]
    Y. Nomura and S.J. Weinberg, Entropy of a vacuum: what does the covariant entropy count?, Phys. Rev. D 90 (2014) 104003 [arXiv:1310.7564] [INSPIRE].ADSGoogle Scholar
  25. [25]
    D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    Y. Takahashi and H. Umezawa, Thermo field dynamics, Collective Phenomena 2 (1975) 55.MathSciNetMATHGoogle Scholar
  27. [27]
    J.B. Hartle and S.W. Hawking, Path integral derivation of black hole radiance, Phys. Rev. D 13 (1976) 2188 [INSPIRE].ADSGoogle Scholar
  28. [28]
    W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].ADSGoogle Scholar
  29. [29]
    J.M. Bardeen, Black holes do evaporate thermally, Phys. Rev. Lett. 46 (1981) 382 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    R. Balbinot, Hawking radiation and the back reactiona first approach, Class. Quant. Grav. 1 (1984) 573.ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    G. Dvali, Black holes and large-N species solution to the hierarchy problem, Fortsch. Phys. 58 (2010) 528 [arXiv:0706.2050] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    W.G. Unruh and R.M. Wald, Acceleration radiation and generalized second law of thermodynamics, Phys. Rev. D 25 (1982) 942 [INSPIRE].ADSGoogle Scholar
  33. [33]
    A.R. Brown, Tensile strength and the mining of black holes, Phys. Rev. Lett. 111 (2013) 211301 [arXiv:1207.3342] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    D.N. Page, Particle emission rates from a black hole: massless particles from an uncharged, nonrotating hole, Phys. Rev. D 13 (1976) 198 [INSPIRE].ADSGoogle Scholar
  36. [36]
    W.H. Zurek, Entropy evaporated by a black hole, Phys. Rev. Lett. 49 (1982) 1683 [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    D.N. Page, Comment onentropy evaporated by a black hole’, Phys. Rev. Lett. 50 (1983) 1013 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    L. Susskind, Strings, black holes and Lorentz contraction, Phys. Rev. D 49 (1994) 6606 [hep-th/9308139] [INSPIRE].ADSMathSciNetGoogle Scholar
  39. [39]
    W.G. Unruh and R.M. Wald, What happens when an accelerating observer detects a Rindler particle, Phys. Rev. D 29 (1984) 1047 [INSPIRE].ADSGoogle Scholar
  40. [40]
    L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  41. [41]
    R. Bousso, A covariant entropy conjecture, JHEP 07 (1999) 004 [hep-th/9905177] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  42. [42]
    S.L. Braunstein, S. Pirandola and K. Życzkowski, Better late than never: information retrieval from black holes, Phys. Rev. Lett. 110 (2013) 101301 [arXiv:0907.1190] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    S.B. Giddings, Nonlocality versus complementarity: a conservative approach to the information problem, Class. Quant. Grav. 28 (2011) 025002 [arXiv:0911.3395] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  45. [45]
    G.W. Gibbons and S.W. Hawking, Cosmological event horizons, thermodynamics and particle creation, Phys. Rev. D 15 (1977) 2738 [INSPIRE].ADSMathSciNetGoogle Scholar
  46. [46]
    L. Susskind and J. Lindesay, An introduction to black holes, information and the string theory revolution: the holographic universe, World Scientific, Singapore (2005).MATHGoogle Scholar
  47. [47]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Yasunori Nomura
    • 1
    • 2
  • Fabio Sanches
    • 1
    • 2
  • Sean J. Weinberg
    • 1
    • 2
  1. 1.Berkeley Center for Theoretical Physics, Department of PhysicsUniversity of CaliforniaBerkeleyUnited States
  2. 2.Theoretical Physics GroupLawrence Berkeley National LaboratoryBerkeleyUnited States

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