Quantum gravity: a quantum-first approach
Abstract
A “quantum-first” approach to gravity is described, where rather than quantizing gen- eral relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are the need for appropri- ate mathematical structure on Hilbert space, and correspondence with general relativity and quantum field theory in weak-gravity situations. A basic physical question is that of “Einstein separability:” how to define mutually independent subsystems, e.g. through localization. Standard answers via tensor products or operator algebras conflict with prop- erties of gravity, as is seen in the correspondence limit; this connects with discussions of “soft hair.” Instead, gravitational behavior suggests a networked Hilbert space structure. This structure plus unitarity provide important clues towards a quantum formulation of gravity.
References
[2] S. W. Hawking, “Black hole explosions,” Nature 248, 30 (1974); “Particle Creation by Black Holes,” Commun. Math. Phys. 43, 199 (1975), Erratum: [Commun. Math. Phys. 46, 206 (1976)].
[3] S. W. Hawking, “Breakdown of Predictability in Gravitational Collapse,” Phys. Rev. D 14, 2460 (1976).
[4] J. B. Hartle, “The Quantum mechanics of cosmology,” in Quantum cosmology and baby universes : proceedings, 7th Jerusalem Winter School for Theoretical Physics, Jerusalem, Israel, December 1989, ed. S. Coleman, J. Hartle, T. Piran, and S. Weinberg (World Scientific, 1991).
[5] J. B. Hartle, “Space-time coarse grainings in nonrelativistic quantum mechanics,” Phys. Rev. D 44, 3173 (1991).
[6] J. B. Hartle, “Space-Time Quantum Mechanics And The Quantum Mechanics Of Space-Time,” arXiv:gr qc/9304006.
[7] J. B. Hartle, “Quantum Mechanics At The Planck Scale,” arXiv:gr-qc/9508023.
[8] S. B. Giddings, “Universal quantum mechanics,” Phys. Rev. D 78, 084004 (2008). [arXiv:0711.0757 [quant-ph]].
[9] A. Einstein, “Quanten-Mechanik und Wirklichkeit,” Dialectica 2 (1948) 320.
[10] For translation, see D. Howard, “Einstein on locality and separability,” Studies in History and Philosophy of Science Part A 16 no. 3, (1985) 171.
[11] R. Haag, Local quantum physics, fields, particles, algebras, Springer (Berlin, 1996).
[12] E. Witten, “Notes on Some Entanglement Properties of Quantum Field Theory,” [arXiv:1803.04993 [hep-th]].
[13] I. Heemskerk, “Construction of Bulk Fields with Gauge Redundancy,” JHEP 1209, 106 (2012). [arXiv:1201.3666 [hep-th]].
[14] D. Kabat and G. Lifschytz, “Decoding the hologram: Scalar fields interacting with gravity,” Phys. Rev. D 89, no. 6, 066010 (2014). [arXiv:1311.3020 [hep-th]].
[15] W. Donnelly and S. B. Giddings, “Diffeomorphism-invariant observables and their nonlocal algebra,” Phys. Rev. D 93, no. 2, 024030 (2016), Erratum: [Phys. Rev. D 94, no. 2, 029903 (2016)]. [arXiv:1507.07921 [hep-th]].
[16] S. B. Giddings, “Hilbert space structure in quantum gravity: an algebraic perspective,” JHEP 1512, 099 (2015). [arXiv:1503.08207 [hep-th]].
[17] C. G. Torre, “Gravitational observables and local symmetries,” Phys. Rev. D 48, R2373 (1993). [gr-qc/9306030].
[18] W. Donnelly and S. B. Giddings, “Observables, gravitational dressing, and obstructions to locality and subsystems,” Phys. Rev. D 94, no. 10, 104038 (2016). [arXiv:1607.01025 [hep-th]].
[19] W. Donnelly and S. B. Giddings, “How is quantum information localized in gravity?,” Phys. Rev. D 96, no. 8, 086013 (2017). [arXiv:1706.03104 [hep-th]].
[20] W. Donnelly and S. B. Giddings, unpublished.
[21] A Carlotto and R Schoen, “Localizing solutions of the Einstein constraint equations,” Invent. Math. 205, 559 (2016).
[22] Piotr T. Chru ́sciel, “Anti-gravity `a la Carlotto-Schoen,” arXiv:1611.01808 [math.DG].
[23] J. Corvino and R. M. Schoen, “On the asymptotics for the vacuum Einstein constraint equations,” J. Diff. Geom. 73, no. 2, 185 (2006). [gr-qc/0301071].
[24] P. T. Chru ́sciel and E. Delay, “On mapping properties of the general relativistic con- straints operator in weighted function spaces, with applications,” Mem. Soc. Math. France 94, 1 (2003). [gr-qc/0301073].
[25] S. B. Giddings and M. Lippert, “Precursors, black holes, and a locality bound,” Phys. Rev. D 65, 024006 (2002). [hep-th/0103231].
[26] S. B. Giddings and M. Lippert, “The Information paradox and the locality bound,” Phys. Rev. D 69, 124019 (2004). [hep-th/0402073].
[27] S. B. Giddings, “Locality in quantum gravity and string theory,” Phys. Rev. D 74, 106006 (2006). [hep-th/0604072].
[28] T. Banks and W. Fischler, “M theory observables for cosmological space-times,” [hep-th/0102077].
[29] T. Banks, “Lectures on Holographic Space Time,” [arXiv:1311.0755 [hep-th]].
[30] S. B. Giddings, “Black holes, quantum information, and unitary evolution,” Phys. Rev. D 85, 124063 (2012). [arXiv:1201.1037 [hep-th]].
[31] C. Cao, S. M. Carroll and S. Michalakis, “Space from Hilbert Space: Recovering Geometry from Bulk Entanglement,” Phys. Rev. D 95, no. 2, 024031 (2017). [arXiv:1606.08444 [hep-th]].
[32] C. Cao and S. M. Carroll, “Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein’s Equation in Hilbert Space,” [arXiv:1712.02803 [hep-th]].
[33] S. M. Carroll and A. Singh, “Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal,” [arXiv:1801.08132 [quant-ph]].
[34] M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42, 2323 (2010), [Int. J. Mod. Phys. D 19, 2429 (2010)]. [arXiv:1005.3035 [hep-th]].
[35] J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortsch. Phys. 61, 781 (2013). [arXiv:1306.0533 [hep-th]].
[36] S. W. Hawking, M. J. Perry and A. Strominger, “Soft Hair on Black Holes,” Phys. Rev. Lett. 116, no. 23, 231301 (2016). [arXiv:1601.00921 [hep-th]]; “Superrotation Charge and Supertranslation Hair on Black Holes,” JHEP 1705, 161 (2017). [arXiv:1611.09175 [hep-th]].
[37] S. B. Giddings, “Models for unitary black hole disintegration,” Phys. Rev. D 85, 044038 (2012) [arXiv:1108.2015 [hep-th]].
[38] S. B. Giddings, “Nonviolent nonlocality,” Phys. Rev. D 88, 064023 (2013). [arXiv:1211.7070 [hep-th]].
[39] S. B. Giddings, “Nonviolent unitarization: basic postulates to soft quantum structure of black holes,” JHEP 1712, 047 (2017). [arXiv:1701.08765 [hep-th]].
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