Induced gravity (or emergent gravity) is an idea in quantum gravity that

spacetime curvature General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. G ...

and its dynamics emerge as a mean field approximation of underlying microscopic degrees of freedom, similar to the

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...

approximation of

Bose–Einstein condensate In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.6 ...

s. The concept was originally proposed by

Andrei Sakharov Andrei Dmitrievich Sakharov ( rus, Андрей Дмитриевич Сахаров, p=ɐnˈdrʲej ˈdmʲitrʲɪjevʲɪtɕ ˈsaxərəf; 21 May 192114 December 1989) was a Soviet nuclear physicist, dissident, nobel laureate and activist for n ...

in 1967.

Overview

Sakharov observed that many

condensed matter Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the su ...

systems give rise to emergent phenomena that are analogous to

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

. For example,

crystal defects A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in Crystal, crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the Crysta ...

can look like curvature and

torsion Torsion may refer to: Science * Torsion (mechanics), the twisting of an object due to an applied torque * Torsion of spacetime, the field used in Einstein–Cartan theory and ** Alternatives to general relativity * Torsion angle, in chemistry Bi ...

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. Sakharov's idea was to start with an arbitrary background

pseudo-Riemannian manifold In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the ...

(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 In quantum field theory, the quantum effective action is a modified expression for the classical action taking into account quantum corrections while ensuring that the principle of least action applies, meaning that extremizing the effective ac ...

which to one-loop order contains the

Einstein–Hilbert action The Einstein–Hilbert action (also referred to as Hilbert action) in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the metric signature, the gravitational part of the ac ...

with a

cosmological constant In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...

. 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

s. Some argue that the particular models proposed by Sakharov and others have been proven impossible by the

Weinberg–Witten theorem In theoretical physics, the Weinberg–Witten (WW) theorem, proved by Steven Weinberg and Edward Witten, states that massless particles (either composite or elementary) with spin ''j'' > 1/2 cannot carry a Lorentz-covariant current, while massle ...

. 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 In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter s ...

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 Mark Van Raamsdonk is a professor at the Department of Physics and Astronomy at the University of British Columbia since 2002. Before that, he was a postdoc at Stanford University from 2000 until 2002 and studied as a graduate student at Princeto ...

) spacetime is built up of quantum entanglement. This implies that quantum entanglement is the fundamental property that gives rise to spacetime. In 1995, Jacobson showed that the

Einstein field equations In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...

can be derived from the first law of thermodynamics applied at local Rindler horizons.

Thanu Padmanabhan Thanu Padmanabhan (10 March 1957 – 17 September 2021) was an Indian theoretical physicist and cosmologist whose research spanned a wide variety of topics in gravitation, structure formation in the universe and quantum gravity. He published n ...

and

Erik Verlinde Erik Peter Verlinde (; born 21 January 1962) is a Dutch theoretical physicist and string theorist. He is the identical twin brother of physicist Herman Verlinde. The Verlinde formula, which is important in conformal field theory and topolog ...

explore links between gravity and

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

, Verlinde being known for an

entropic gravity Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes gravity as an ''entropic force''—a force with macro-scale homogeneity but which is subject to quantum-level disorder—and not a fundamental intera ...

proposal. The Einstein equation for gravity can emerge from the entanglement first law. 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 Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies t ...

, and an effective spatial lattice structure emerges in the low-temperature limit.

References

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'', preprintA.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
{{Theories of gravitation Theories of gravity Emergence

Overview

See also

References

External links