Editing Induced gravity (section)

==Overview==
Sakharov observed that many [[condensed matter]] systems give rise to emergent phenomena that are analogous to [[general relativity]]. For example, [[Crystallographic defect|crystal defects]] can look like [[curvature]] and [[Torsion tensor|torsion]] in an [[Einstein–Cartan theory|Einstein–Cartan spacetime]]. This allows one to create a theory of gravity with torsion from a [[world crystal]] model of spacetime in which the lattice spacing is of the order of a [[Planck length]].<ref>{{cite journal|author=H. Kleinert|author-link=Hagen Kleinert|year=1987|title=Gravity as Theory of Defects in a Crystal with Only Second-Gradient Elasticity|journal=Annalen der Physik|volume=44|issue=2|page=117|bibcode=1987AnP...499..117K|doi=10.1002/andp.19874990206}}</ref> 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 constant]]s.

Some{{who|date=November 2024}} 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 spacetime arises as an emergent phenomenon of the quantum degrees of freedom that are entangled and live in the boundary of the spacetime.{{cn|date=November 2024}} 

According to some prominent researchers in emergent gravity (such as [[Mark Van Raamsdonk]]) spacetime is built up of quantum entanglement.<ref>{{Cite journal|last=Van Raamsdonk|first=Mark|date=19 June 2010|title=Building up spacetime with quantum entanglement.|journal=General Relativity and Gravitation|volume=42|issue=10|pages=2323–2329|doi=10.1007/s10714-010-1034-0|arxiv=1005.3035|bibcode=2010GReGr..42.2323V}}</ref> This implies that quantum entanglement is the fundamental property that gives rise to spacetime. In 1995, [[Theodore Jacobson]] showed that the [[Einstein field equations]] can be derived from the first law of thermodynamics applied at local [[Rindler_coordinates#The_Rindler_horizon|Rindler horizons]].<ref>{{Cite journal|last=Jacobson|first=Ted|date=1995-08-14|title=Thermodynamics of Spacetime: The Einstein Equation of State|journal=Physical Review Letters|volume=75|issue=7|pages=1260–1263|arxiv=gr-qc/9504004|bibcode=1995PhRvL..75.1260J|doi=10.1103/PhysRevLett.75.1260|pmid=10060248|s2cid=13223728}}</ref> [[Thanu Padmanabhan]] and [[Erik Verlinde]] explore links between gravity and [[entropy]], Verlinde being known for an [[entropic gravity]] proposal.<ref>{{Cite journal|last=Padmanabhan|first=T.|date=2010-04-01|title=Thermodynamical Aspects of Gravity: New insights|journal=Reports on Progress in Physics|volume=73|issue=4|pages=046901|arxiv=0911.5004|bibcode=2010RPPh...73d6901P|doi=10.1088/0034-4885/73/4/046901|s2cid=209835245 |issn=0034-4885}}</ref><ref>{{Cite journal|last=Verlinde|first=Erik|date=2011|title=On the origin of gravity and the laws of Newton|journal=Journal of High Energy Physics|language=en|volume=2011|issue=4|pages=29|arxiv=1001.0785|bibcode=2011JHEP...04..029V|doi=10.1007/jhep04(2011)029|s2cid=3597565|issn=1029-8479}}</ref> The Einstein equation for gravity can emerge from the entanglement first law.<ref>{{Cite journal|last1=Lee|first1=Jae-Weon|last2=Kim|first2=Hyeong-Chan|last3=Lee|first3=Jungjai|date=2013|title=Gravity from quantum information|journal=Journal of the Korean Physical Society|language=en|volume=63|issue=5|pages=1094–1098|doi=10.3938/jkps.63.1094|issn=0374-4884|bibcode=2013JKPS...63.1094L|arxiv=1001.5445|s2cid=118494859}}</ref><ref>{{cite arXiv|last1=Swingle|first1=Brian|last2=Van Raamsdonk|first2=Mark|title=Universality of Gravity from Entanglement|eprint=1405.2933|year=2014|class=hep-th}}</ref><ref>{{Cite journal|last1=Oh|first1=Eunseok|last2=Park|first2=I. Y.|last3=Sin|first3=Sang-Jin|date=2018-07-13|title=Complete Einstein equations from the generalized First Law of Entanglement|journal=Physical Review D|volume=98|issue=2|pages=026020|doi=10.1103/PhysRevD.98.026020|bibcode=2018PhRvD..98b6020O|arxiv=1709.05752|s2cid=119084958}}</ref> In the "quantum graphity" proposal of Konopka, [[Fotini Markopoulou-Kalamara|Markopoulu-Kalamara]], [[Simone Severini|Severini]] and [[Lee Smolin|Smolin]], the fundamental degrees of freedom exist on a dynamical graph that is initially [[complete graph|complete]], and an effective spatial lattice structure emerges in the low-temperature limit.<ref>{{cite arXiv|eprint=hep-th/0611197 |title=Quantum Graphity |first1=Tomasz |last1=Konopka |first2=Fotini |last2=Markopoulou |author-link2=Fotini Markopoulou-Kalamara |first3=Lee |last3=Smolin |author-link3=Lee Smolin |date=2006-11-17}}</ref><ref>{{Cite journal|last1=Konopka|first1=Tomasz|last2=Markopoulou|first2=Fotini|author-link2=Fotini Markopoulou-Kalamara|last3=Severini|first3=Simone|author-link3=Simone Severini|date=2008-05-27|title=Quantum graphity: A model of emergent locality|journal=[[Physical Review D]]|language=en|volume=77|issue=10|pages=104029|arxiv=0801.0861|bibcode=2008PhRvD..77j4029K|doi=10.1103/PhysRevD.77.104029|s2cid=6959359|issn=1550-7998}}</ref>