Skip to main content
SpringerLink
Log in

Quantum-First Gravity

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity and other phenomena. A key principle in this approach is that of correspondence: this structure should reproduce spacetime, general relativity, and quantum field theory in a limit of weak gravitational fields. A central question is that of “Einstein separability,” and asks how to define mutually independent subsystems, e.g. through localization. Familiar definitions involving tensor products or operator subalgebras do not clearly accomplish this in gravity, as is seen in the correspondence limit. Instead, gravitational behavior, particularly gauge invariance, suggests a network of Hilbert subspaces related via inclusion maps, contrasting with other approaches based on tensor-factorized Hilbert spaces. Any such localization structure is also expected to place strong constraints on evolution, which are also supplemented by the constraint of unitarity.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. For an earlier but somewhat different approach to describing quantum structure for gravity, see [7, 8].

  2. Ref. [14]; for translation of relevant passages see [15].

  3. For further discussion see [3, 21]. Concretely, examples of operators in the subalgebra are field operators smeared against test functions with support restricted to the neighborhood.

  4. As described below, this also connects with proposals for the importance of “soft quantum hair” on black holes [24, 25].

  5. See [26], and for review [27].

  6. For previous related work, see [28, 29].

  7. Note, however, that one regularization of a gravitational line is to smear it over a cone extending to infinity, and moreover that in classical GR one can show that even at higher-orders gravitational fields can be localized to conical regions as one approaches infinity [32]. This provides evidence that such gravitational dressings can be consistent at higher orders in \(\kappa \).

  8. See, e.g., [21], and references therin.

  9. Here we make contact with a generalization of the Corvino-Schoen gluing theorem [35, 36] to the case with sources [34]. This theorem states that given initial vacuum initial data, one may find new initial data that agrees with the original data in a compact region, but matches a boosted Kerr solution outside large enough radius.

  10. For gauge invariance, these operators should also be dressed; e.g. analogues to \(\Phi (x)\) may be used.

  11. For the ultra-boosted case, this condition must be appropriately modified.

  12. Note that, unlike entropic bounds, this bound involves energy localized in a region.

  13. A possibly related structure has been described in [39].

  14. Note also that the neighborhoods \(U_\epsilon \) labeling the Hilbert subspaces are not necessarily fundamental at the nonperturbative level, and may need to be replaced by labels not directly associated to neighborhoods.

  15. Of course there is an inherent problem in this approach for closed universes, as the Hamiltonian vanises.

  16. This is also connected to puzzles about Wilson line operators running between such regions [46], which also seem to indicate that factorization is problematic, or that such operators are state-dependent [47].

References

  1. Giddings, S.B.: Universal quantum mechanics. Phys. Rev. D 78, 084004 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  2. Giddings, S.B.: Black holes, quantum information, and unitary evolution. Phys. Rev. D 85, 124063 (2012)

    Article  ADS  Google Scholar 

  3. Giddings, S.B.: Hilbert space structure in quantum gravity: an algebraic perspective. JHEP 1512, 099 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  4. Cao, C., Carroll, S.M., Michalakis, S.: Space from Hilbert space: recovering geometry from bulk entanglement. Phys. Rev. D 95(2), 024031 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  5. Cao, C., Carroll, S.M.: Bulk entanglement gravity without a boundary: towards finding Einstein’s equation in Hilbert space. Phys. Rev. D 97(8), 086003 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  6. Carroll, S.M., Singh, A.: Mad-Dog everettianism: quantum mechanics at its most minimal. arXiv:1801.08132 [quant-ph]

  7. Banks, T., Fischler, W.: M theory observables for cosmological space-times. arXiv:hep-th/0102077

  8. Banks, T.: Lectures on holographic space time. arXiv:1311.0755 [hep-th]

  9. Hartle, J.B.: The quantum mechanics of cosmology. In: Coleman, S., Hartle, J., Piran, T., Weinberg, S. (eds.) Quantum Cosmology and Baby Universes: Proceedings, 7th Jerusalem Winter School for Theoretical Physics, Jerusalem, Israel, December 1989. World Scientific (1991)

  10. Hartle, J.B.: Space-time coarse grainings in nonrelativistic quantum mechanics. Phys. Rev. D 44, 3173 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  11. Hartle, J.B.: Space-time quantum mechanics and the quantum mechanics of space-time. arXiv:gr-qc/9304006

  12. Hartle, J.B.: Quantum mechanics at the planck scale. arXiv:gr-qc/9508023

  13. Giddings, S.B.: (Non)perturbative gravity, nonlocality, and nice slices. Phys. Rev. D 74, 106009 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  14. Einstein, A.: Quanten-Mechanik und Wirklichkeit. Dialectica 2, 320 (1948)

    Article  MATH  Google Scholar 

  15. Howard, D.: Einstein on locality and separability. Stud. Hist. Philos. Sci. A 16(3), 171 (1985)

    Article  MathSciNet  Google Scholar 

  16. Van Raamsdonk, M.: Building up spacetime with quantum entanglement. Gen. Relativ. Grav. 42, 2323 (2010) [Int. J. Mod. Phys. D 19, 2429 (2010)]

  17. Maldacena, J., Susskind, L.: Cool horizons for entangled black holes. Fortsch. Phys. 61, 781 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Giddings, S.B., Rota, M.: Quantum information/entanglement transfer rates between subsystems. arXiv:1710.00005 [quant-ph]

  19. Brown, A.R., Roberts, D.A., Susskind, L., Swingle, B., Zhao, Y.: Complexity, action, and black holes. Phys. Rev. D 93(8), 086006 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  20. Zurek, W.H.: Quantum darwinism, classical reality, and the randomness of quantum jumps. Phys. Today 67, 44 (2014)

    Article  Google Scholar 

  21. Haag, R.: Local Quantum Physics, Fields, Particles. Algebras. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  22. Donnelly, W., Giddings, S.B.: Diffeomorphism-invariant observables and their nonlocal algebra. Phys. Rev. D 93(2), 024030 (2016), Erratum: [Phys. Rev. D 94, no. 2, 029903 (2016)]

  23. Donnelly, W., Giddings, S.B.: Observables, gravitational dressing, and obstructions to locality and subsystems. Phys. Rev. D 94(10), 104038 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  24. Hawking, S.W., Perry, M.J., Strominger, A.: Soft hair on black holes. Phys. Rev. Lett. 116(23), 231301 (2016)

    Article  ADS  Google Scholar 

  25. Hawking, S.W., Perry, M.J., Strominger, A.: Superrotation charge and supertranslation hair on black holes. JHEP 1705, 161 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Buchholz, D., Verch, R.: Scaling algebras and renormalization group in algebraic quantum field theory. Rev. Math. Phys. 7, 1195 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yngvason, J.: The role of type III factors in quantum field theory. Rep. Math. Phys. 55, 135 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Heemskerk, I.: Construction of bulk fields with gauge redundancy. JHEP 1209, 106 (2012)

    Article  ADS  Google Scholar 

  29. Kabat, D., Lifschytz, G.: Decoding the hologram: scalar fields interacting with gravity. Phys. Rev. D 89(6), 066010 (2014)

    Article  ADS  Google Scholar 

  30. Giddings, S.B., Lippert, M.: Precursors, black holes, and a locality bound. Phys. Rev. D 65, 024006 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  31. Giddings, S.B., Lippert, M.: The Information paradox and the locality bound. Phys. Rev. D 69, 124019 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  32. Chruściel, P.T.: Anti-gravity à la Carlotto-Schoen. arXiv:1611.01808 [math.DG]

  33. Bao, N., Carroll, S.M., Singh, A.: The Hilbert space of quantum gravity is locally finite-dimensional. Int. J. Mod. Phys. D 26(12), 1743013 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  34. Donnelly, W., Giddings, S.B.: How is quantum information localized in gravity? Phys. Rev. D 96(8), 086013 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  35. Corvino, J., Schoen, R.M.: On the asymptotics for the vacuum Einstein constraint equations. J. Diff. Geom. 73(2), 185 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. Chrusciel, P.T., Delay, E.: On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications. Mem. Soc. Math. France 94, 1 (2003)

    MATH  Google Scholar 

  37. Donnelly, W., Giddings, S.B.: Gravitational splitting at first order: quantum information localization in gravity. Phys. Rev. D 98, 086006 (2018)

    Article  ADS  Google Scholar 

  38. Giddings, S.B.: Locality in quantum gravity and string theory. Phys. Rev. D 74, 106006 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  39. Bzowski, A., Gnecchi, A., Hertog, T.: Interactions resolve state-dependence in a toy-model of AdS black holes. arXiv:1802.02580 [hep-th]

  40. Giddings, S.B., Kinsella, A.: Gauge-invariant observables, gravitational dressings, and holography in AdS. arXiv:1802.01602 [hep-th]

  41. Zanardi, P., Lidar, D.A., Lloyd, S.: Quantum tensor product structures are observable induced. Phys. Rev. Lett. 92, 060402 (2004)

    Article  ADS  Google Scholar 

  42. Cotler, J.S., Penington, G.R., Ranard, D.H.: Locality from the spectrum. arXiv:1702.06142 [quant-ph]

  43. Maldacena, J.M.: Eternal black holes in anti-de Sitter. JHEP 0304, 021 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  44. Harlow, D.: Wormholes, emergent gauge fields, and the weak gravity conjecture. JHEP 1601, 122 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Donnelly, W., Freidel, L.: Local subsystems in gauge theory and gravity. JHEP 1609, 102 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. Guica, M., Jafferis, D.L.: On the construction of charged operators inside an eternal black hole. SciPost Phys. 3(2), 016 (2017)

    Article  ADS  Google Scholar 

  47. Papadodimas, K., Raju, S.: Local operators in the eternal Black hole. Phys. Rev. Lett. 115(21), 211601 (2015)

    Article  ADS  Google Scholar 

  48. Susskind, L.: Why do things fall? arXiv:1802.01198 [hep-th]

  49. Giddings, S.B.: Models for unitary black hole disintegration. Phys. Rev. D 85, 044038 (2012)

    Article  ADS  Google Scholar 

  50. Giddings, S.B.: Nonviolent nonlocality. Phys. Rev. D 88, 064023 (2013)

    Article  ADS  Google Scholar 

  51. Giddings, S.B.: Modulated Hawking radiation and a nonviolent channel for information release. arXiv:1401.5804 [hep-th]

  52. Giddings, S.B.: Nonviolent unitarization: basic postulates to soft quantum structure of black holes. JHEP 1712, 047 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This material is based upon work supported in part by the U.S. Department of Energy, Office of Science, under Award Number DE-SC0011702. I thank J. Hartle for useful conversations and comments on a draft of this paper.

Author information

Authors and Affiliations

  1. Department of Physics, University of California, Santa Barbara, CA, 93106, USA

    Steven B. Giddings

Authors
  1. Steven B. Giddings
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steven B. Giddings.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Giddings, S.B. Quantum-First Gravity. Found Phys 49, 177–190 (2019). https://doi.org/10.1007/s10701-019-00239-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-019-00239-1

Keywords

Search

Navigation