From Wikipedia, the free encyclopedia
Induced gravity (or emergent gravity ) is an idea in
quantum gravity that
spacetime 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.
Overview
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 in which the lattice spacing is of the order of a
Planck length .
[1] 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 spacetime arises as an emergent phenomenon of the quantum degrees of freedom that are entangled and live in the boundary of the spacetime. 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 showed that the
Einstein field equations can be derived from the first law of thermodynamics applied at local
Rindler horizons .
[3]
Thanu Padmanabhan and
Erik Verlinde explore links between gravity and
entropy , Verlinde being known for an
entropic gravity proposal.
[4]
[5] The Einstein equation for gravity can emerge from the entanglement first law.
[6]
[7]
[8] In the "quantum graphity" proposal of Konopka,
Markopoulu-Kalamara ,
Severini and
Smolin , the fundamental degrees of freedom exist on a dynamical graph that is initially
complete , and an effective spatial lattice structure emerges in the low-temperature limit.
[9]
[10]
See also
References
^
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 .
S2CID
13223728 .
^ 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 .
S2CID
209835245 .
^ 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 .
S2CID
3597565 .
^ 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 .
S2CID
118494859 .
^ 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.
arXiv :
1709.05752 .
Bibcode :
2018PhRvD..98b6020O .
doi :
10.1103/PhysRevD.98.026020 .
S2CID
119084958 .
^ Konopka, Tomasz;
Markopoulou, Fotini ;
Smolin, Lee (2006-11-17). "Quantum Graphity".
arXiv :
hep-th/0611197 .
^ Konopka, Tomasz;
Markopoulou, Fotini ;
Severini, Simone (2008-05-27). "Quantum graphity: A model of emergent locality".
Physical Review D . 77 (10): 104029.
arXiv :
0801.0861 .
Bibcode :
2008PhRvD..77j4029K .
doi :
10.1103/PhysRevD.77.104029 .
ISSN
1550-7998 .
S2CID
6959359 .
External links
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 .
Standard
Alternatives to general relativity
Paradigms Classical Quantum-mechanical Unified-field-theoric Unified-field-theoric and quantum-mechanical Generalisations / extensions of GR
Pre-Newtonian theories and
toy models Related topics