Emergent spacetime and gravity from quantum information

The first indication of the emergent nature of spacetime and gravity comes from the laws of black hole thermodynamics [1]. A central role herein is played by the Bekenstein-Hawking entropy [2, 3] and Hawking temperature [4, 5] given by

                 and            .                                    (1.1)

Here A denotes the area of the horizon and κ equals the surface acceleration. In the past decades the theoretical understanding of the Bekenstein-Hawking formula has advanced significantly, starting with the explanation of its microscopic origin in string theory [6] and the subsequent development of the AdS/CFT correspondence [7]. In the latter context it was realized that this same formula also determines the amount of quantum entanglement in the vacuum [8]. It was subsequently argued that quantum entanglement plays a central role in explaining the connectivity of the classical spacetime [9]. These important insights formed the starting point of the recent theoretical advances that have revealed a deep connection between key concepts of quantum information theory and the emergence of spacetime and gravity.

Currently the first steps are being taken towards a new theoretical framework in which spacetime geometry is viewed as representing the entanglement structure of the microscopic quantum state. Gravity emerges from this quantum information theoretic viewpoint as describing the change in entanglement caused by matter. These novel ideas are best understood in Anti-de Sitter space, where the description in terms of a dual conformal field theory allows one to compute the microscopic entanglement in a well defined setting. In this way it was proven [10, 11] that the entanglement entropy indeed obeys (1.1), when the vacuum state is divided into two parts separated by a Killing horizon. This fact was afterwards used to extend earlier work on the emergence of gravity [12, 13, 14] by deriving the (linearized) Einstein equations from general quantum information theoretic principles [15, 16, 17].

The fact that the entanglement entropy of the spacetime vacuum obeys an area law has motivated various proposals that represent spacetime as a network of entangled units of quantum information, called ‘tensors’. The first proposal of this kind is the MERA approach [18, 19] in which the boundary quantum state is (de-)constructed by a multi-scale entanglement renormalization procedure. More recently it was proposed that the bulk spacetime operates as a holographic error correcting code [20, 21]. In this approach the tensor network representing the emergent spacetime produces a unitary bulk to boundary map defined by entanglement. The language of quantum error correcting codes and tensor networks gives useful insights into the entanglement structure of spacetime. In particular, it suggests that the microscopic constituents from which spacetime emerges should be thought of as basic units of quantum information whose short range entanglement gives rise to the Bekenstein-Hawking area law and provides the microscopic ‘bonds’ or ‘glue’ responsible for the connectivity of spacetime.

References

  • M. Bardeen, B. Carter and S. W. Hawking, “The Four laws of black hole mechanics,” Commun. Math. Phys. 31, 161 (1973).
  • D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7, 2333 (1973).
  • S . W. Hawking , “Particle Creation By Black Holes,” Commun Math. 43, 199-220, (1975).
  • C. W. Davies, “Scalar particle production in Schwarzschild and Rindler metrics,” J. Phys. A 8, 609 (1975).
  • G. Unruh, “Notes on black hole evaporation,” Phys. Rev. D 14, 870 (1976).
  • Strominger and C. Vafa, “Microscopic origin of the Bekenstein-Hawking entropy,” Phys. Lett. B 379 (1996) 99, [hep-th/9601029].
  • M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2, 231 (1998) [arXiv:hep-th/9711200].
  • Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96, 181602 (2006) [arXiv:hep-th/0603001]; “Aspects of holographic entanglement entropy,” JHEP 0608, 045 (2006) [arXiv:hepth/0605073].

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