# Induced gravity

**Induced gravity** (or **emergent gravity**) is an idea in quantum gravity that space-time curvature and its dynamics emerge as a mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics approximation of Bose–Einstein condensates. The concept was originally proposed by Andrei Sakharov in 1967.

## Contents

## Overview[edit]

Sakharov observed that many condensed matter systems give rise to emergent phenomena that are analogous to general relativity. For example, crystal defects can look like curvature and torsion in an Einstein–Cartan spacetime. This allows one to create a theory of gravity with torsion from a world crystal model of spacetime^{[1]} in which the lattice spacing is of the order of a Planck length.
Sakharov's idea was to start with an arbitrary background pseudo-Riemannian manifold (in modern treatments, possibly with torsion) and introduce quantum fields (matter) on it but not introduce any gravitational dynamics explicitly. This gives rise to an effective action which to one-loop order contains the Einstein–Hilbert action with a cosmological constant. In other words, general relativity arises as an emergent property of matter fields and is not put in by hand. On the other hand, such models typically predict huge cosmological constants.

Some argue that the particular models proposed by Sakharov and others have been proven impossible by the Weinberg–Witten theorem. However, models with emergent gravity are possible as long as other things, such as spacetime dimensions, emerge together with gravity. Developments in AdS/CFT correspondence after 1997 suggest that the microphysical degrees of freedom in induced gravity might be radically different. The bulk space-time arises as an emergent phenomenon of the quantum degrees of freedom that are entangled and live in the boundary of the space-time. According to some prominent researchers in emergent gravity (such as Mark Van Raamsdonk) spacetime is built up of quantum entanglement.^{[2]} This implies that quantum entanglement is the fundamental property that gives rise to spacetime. In 1995, Jacobson ^{[3]} showed that the Einstein field equations can be derived from the first law of thermodynamics applied at local Rindler horizons. Thanu Padmanabhan ^{[4]} and Erik Verlinde^{[5]} explore links between gravity and entropy. The Einstein equation for gravity can emerge from the entanglement first law.^{[6]}^{[7]}^{[8]}

## See also[edit]

- AdS/CFT correspondence
- Mark Van Raamsdonk
- Abraham–Lorentz force
- Beyond black holes
- Entropic force
- List of quantum gravity researchers
- Gravitation
- Entropic gravity

## References[edit]

**^**H. Kleinert (1987). "Gravity as Theory of Defects in a Crystal with Only Second-Gradient Elasticity".*Annalen der Physik*.**44**(2): 117. Bibcode:1987AnP...499..117K. doi:10.1002/andp.19874990206.**^**Van Raamsdonk, Mark (19 June 2010). "Building up spacetime with quantum entanglement".*General Relativity and Gravitation*.**42**(10): 2323–2329. arXiv:1005.3035. Bibcode:2010GReGr..42.2323V. doi:10.1007/s10714-010-1034-0.**^**Jacobson, Ted (1995-08-14). "Thermodynamics of Spacetime: The Einstein Equation of State".*Physical Review Letters*.**75**(7): 1260–1263. arXiv:gr-qc/9504004. Bibcode:1995PhRvL..75.1260J. doi:10.1103/PhysRevLett.75.1260. PMID 10060248.**^**Padmanabhan, T. (2010-04-01). "Thermodynamical Aspects of Gravity: New insights".*Reports on Progress in Physics*.**73**(4): 046901. arXiv:0911.5004. Bibcode:2010RPPh...73d6901P. doi:10.1088/0034-4885/73/4/046901. ISSN 0034-4885.**^**Verlinde, Erik (2011). "On the origin of gravity and the laws of Newton".*Journal of High Energy Physics*.**2011**(4): 29. arXiv:1001.0785. Bibcode:2011JHEP...04..029V. doi:10.1007/jhep04(2011)029. ISSN 1029-8479.**^**Lee, Jae-Weon; Kim, Hyeong-Chan; Lee, Jungjai (2013). "Gravity from quantum information".*Journal of the Korean Physical Society*.**63**(5): 1094–1098. arXiv:1001.5445. Bibcode:2013JKPS...63.1094L. doi:10.3938/jkps.63.1094. ISSN 0374-4884.**^**Swingle, Brian; Van Raamsdonk, Mark (2014). "Universality of Gravity from Entanglement". arXiv:1405.2933 [hep-th].**^**Oh, Eunseok; Park, I. Y.; Sin, Sang-Jin (2018-07-13). "Complete Einstein equations from the generalized First Law of Entanglement".*Physical Review D*.**98**(2): 026020. Bibcode:2018PhRvD..98b6020O. doi:10.1103/PhysRevD.98.026020.

## External links[edit]

- Carlos Barcelo, Stefano Liberati, Matt Visser,
*Living Rev.Rel.*8:12, 2005. - D. Berenstein,
*Emergent Gravity from CFT*, online lecture. - C. J. Hogan
*Quantum Indeterminacy of Emergent Spacetime*, preprint - A.D. Sakharov,
*Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation*, 1967. - Matt Visser,
*Sakharov's induced gravity: a modern perspective*, 2002. - H. Kleinert,
*Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation*, 2008. - M. Brouwer et al.,
*First test of Verlinde's theory of Emergent Gravity using Weak Gravitational Lensing measurements*, 2016.