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
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of ...
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
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, that arise from electromagnetic forces between atoms and electrons. More gen ...
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
A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell para ...
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
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 act ...
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
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 ...
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 (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
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 Princeton ...
) 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
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 topologi ...
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
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.
See also
*
Black hole thermodynamics
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. As the study of the statistical mechanics of black-body radiation led to the deve ...
*
Entropic force
In physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale.
Mathematical formula ...
*
Entropic gravity
*
List of quantum gravity researchers
*
Superfluid vacuum theory
Superfluid vacuum theory (SVT), sometimes known as the BEC vacuum theory, is an approach in theoretical physics and quantum mechanics where the fundamental physical vacuum (non-removable background) is considered as a superfluid or as a Bose–E ...
*
Einstein–Cartan theory
In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation, one of several alternatives to general relativity. The theory was first proposed by Élie C ...
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