Induced gravity (or emergent gravity) is an idea in

quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v ...

that spacetime curvature and its dynamics emerge as a mean field approximation of underlying microscopic

degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...

, similar to the

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...

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 Density, densities is cooled to temperatures very close to absolute zero#Relation with Bose–Einste ...

s. The concept was originally proposed by

Andrei Sakharov Andrei Dmitrievich Sakharov (; 21 May 192114 December 1989) was a Soviet Physics, physicist and a List of Nobel Peace Prize laureates, Nobel Peace Prize laureate, which he was awarded in 1975 for emphasizing human rights around the world. Alt ...

in 1967.

Overview

Sakharov observed that many condensed matter systems give rise to emergent phenomena that are analogous to

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

. For example, crystal defects can look like

curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...

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 In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: '' c'', '' G'', '' ħ'', and ''k''B (described further below). Expressing one of ...

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

pseudo-Riemannian manifold In mathematical physics, 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 which to one-loop order contains the

Einstein–Hilbert action The Einstein–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 action is given as :S = \int R \sqrt ...

with a

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

. 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. 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 (frequently abbreviated as AdS/CFT) is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) that are used ...

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. This implies that quantum entanglement is the fundamental property that gives rise to spacetime. In 1995, Theodore Jacobson showed that the

Einstein field equations In the General relativity, 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#In general relativity and cosmology, matter within it. ...

can be derived from the first law of thermodynamics applied at local Rindler horizons. Thanu Padmanabhan and Erik Verlinde explore links between gravity and

entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...

, Verlinde being known for an entropic gravity 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, 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