Wormhole and entanglement (non-)detection in the ER=EPR correspondence


The recently proposed ER=EPR correspondence postulates the existence of wormholes (Einstein-Rosen bridges) between entangled states (such as EPR pairs). Entanglement is famously known to be unobservable in quantum mechanics, in that there exists no observable (or, equivalently, projector) that can accurately pick out whether a generic state is entangled. Many features of the geometry of spacetime, however, are observables, so one might worry that the presence or absence of a wormhole could identify an entangled state in ER=EPR, violating quantum mechanics, specifically, the property of state-independence of observables. In this note, we establish that this cannot occur: there is no measurement in general relativity that unambiguously detects the presence of a generic wormhole geometry. This statement is the ER=EPR dual of the undetectability of entanglement.

A preprint version of the article is available at ArXiv.


  1. [1]

    J.M. Bardeen, B. Carter and S.W. Hawking, The Four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].

    MATH  MathSciNet  Article  ADS  Google Scholar 

  2. [2]

    J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. [3]

    S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  4. [4]

    L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  5. [5]

    G. ’t Hooft, On the Quantum Structure of a Black Hole, Nucl. Phys. B 256 (1985) 727 [INSPIRE].

  6. [6]

    G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B 335 (1990) 138 [INSPIRE].

  7. [7]

    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  8. [8]

    K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].

    Article  ADS  Google Scholar 

  9. [9]

    K. Papadodimas and S. Raju, Black Hole Interior in the Holographic Correspondence and the Information Paradox, Phys. Rev. Lett. 112 (2014) 051301 [arXiv:1310.6334] [INSPIRE].

    Article  ADS  Google Scholar 

  10. [10]

    K. Papadodimas and S. Raju, State-Dependent Bulk-Boundary Maps and Black Hole Complementarity, Phys. Rev. D 89 (2014) 086010 [arXiv:1310.6335] [INSPIRE].

    ADS  Google Scholar 

  11. [11]

    K. Papadodimas and S. Raju, Local Operators in the Eternal Black Hole, arXiv:1502.06692 [INSPIRE].

  12. [12]

    K. Papadodimas and S. Raju, Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior, arXiv:1503.08825 [INSPIRE].

  13. [13]

    R. Bousso, Firewalls from double purity, Phys. Rev. D 88 (2013) 084035 [arXiv:1308.2665] [INSPIRE].

    ADS  Google Scholar 

  14. [14]

    D. Marolf and J. Polchinski, Violations of the Born rule in cool state-dependent horizons, arXiv:1506.01337 [INSPIRE].

  15. [15]

    J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  16. [16]

    A. Einstein and N. Rosen, The Particle Problem in the General Theory of Relativity, Phys. Rev. 48 (1935) 73 [INSPIRE].

    Article  ADS  Google Scholar 

  17. [17]

    M.D. Kruskal, Maximal extension of Schwarzschild metric, Phys. Rev. 119 (1960) 1743 [INSPIRE].

    MATH  MathSciNet  Article  ADS  Google Scholar 

  18. [18]

    R.W. Fuller and J.A. Wheeler, Causality and Multiply Connected Space-Time, Phys. Rev. 128 (1962) 919 [INSPIRE].

    MATH  MathSciNet  Article  ADS  Google Scholar 

  19. [19]

    K. Jensen and A. Karch, Holographic Dual of an Einstein-Podolsky-Rosen Pair has a Wormhole, Phys. Rev. Lett. 111 (2013) 211602 [arXiv:1307.1132] [INSPIRE].

    Article  ADS  Google Scholar 

  20. [20]

    J. Sonner, Holographic Schwinger Effect and the Geometry of Entanglement, Phys. Rev. Lett. 111 (2013) 211603 [arXiv:1307.6850] [INSPIRE].

    Article  ADS  Google Scholar 

  21. [21]

    J.C. Baez and J. Vicary, Wormholes and Entanglement, Class. Quant. Grav. 31 (2014) 214007 [arXiv:1401.3416] [INSPIRE].

    Article  ADS  Google Scholar 

  22. [22]

    H. Gharibyan and R.F. Penna, Are entangled particles connected by wormholes? Evidence for the ER=EPR conjecture from entropy inequalities, Phys. Rev. D 89 (2014) 066001 [arXiv:1308.0289] [INSPIRE].

    ADS  Google Scholar 

  23. [23]

    G. Mandal, R. Sinha and N. Sorokhaibam, The inside outs of AdS 3 /CFT 2 : exact AdS wormholes with entangled CFT duals, JHEP 01 (2015) 036 [arXiv:1405.6695] [INSPIRE].

    Article  ADS  Google Scholar 

  24. [24]

    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].

    MATH  MathSciNet  Article  Google Scholar 

  25. [25]

    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MATH  MathSciNet  ADS  Google Scholar 

  26. [26]

    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  27. [27]

    N. Bao, J. Pollack and G.N. Remmen, Splitting Spacetime and Cloning Qubits: Linking No-Go Theorems across the ER=EPR Duality, Fortsch. Phys. 63 (2015) 705 [arXiv:1506.08203] [INSPIRE].

    Article  Google Scholar 

  28. [28]

    R. Geroch, Singularities in the Spacetime of General Relativity: Their Definition, Existence, and Local Characterization, Ph.D. Thesis, Princeton University, Princeton, (1967).

  29. [29]

    F.J. Tipler, Singularities and Causality Violation, Annals Phys. 108 (1977) 1 [INSPIRE].

    MATH  MathSciNet  Article  ADS  Google Scholar 

  30. [30]

    M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, (2010).

  31. [31]

    J. Griffiths and J. Podolský, Exact Space-Times in Einsteins General Relativity, Cambridge University Press, (2009).

  32. [32]

    K. Lake and R.C. Roeder, Effects of a Nonvanishing Cosmological Constant on the Spherically Symmetric Vacuum Manifold, Phys. Rev. D 15 (1977) 3513 [INSPIRE].

    ADS  Google Scholar 

  33. [33]

    S. Hemming and E. Keski-Vakkuri, Hawking radiation from AdS black holes, Phys. Rev. D 64 (2001) 044006 [gr-qc/0005115] [INSPIRE].

  34. [34]

    G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  35. [35]

    L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The Black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  36. [36]

    J.L. Friedman, K. Schleich and D.M. Witt, Topological censorship, Phys. Rev. Lett. 71 (1993) 1486 [Erratum ibid. 75 (1995) 1872] [gr-qc/9305017] [INSPIRE].

Download references

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.

Author information



Corresponding author

Correspondence to Grant N. Remmen.

Additional information

ArXiv ePrint: 1509.05426

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bao, N., Pollack, J. & Remmen, G.N. Wormhole and entanglement (non-)detection in the ER=EPR correspondence. J. High Energ. Phys. 2015, 126 (2015). https://doi.org/10.1007/JHEP11(2015)126

Download citation


  • Black Holes
  • Gauge-gravity correspondence
  • AdS-CFT Correspondence