Induced gravity
Encyclopedia
Induced gravity is an idea in quantum gravity
that space-time background emerges as
a mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics
approximation of Bose–Einstein condensate
s. The concept was originally proposed by Andrei Sakharov
in 1967.
Sakharov observed that many condensed matter
systems give rise to emergent phenomena which are identical 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.
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 argue that the particular models proposed by Sakharov and others have been proven impossible by the Weinberg-Witten theorem. But, models with emergent gravity are always 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 space-time arises as an emergent phenomenon of the quantum degrees of freedom that live in the boundary of the space-time.
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
that space-time background emerges as
a mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
approximation of Bose–Einstein condensate
Bose–Einstein condensate
A Bose–Einstein condensate is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero . Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at...
s. The concept was originally proposed by Andrei Sakharov
Andrei Sakharov
Andrei Dmitrievich Sakharov was a Soviet nuclear physicist, dissident and human rights activist. He earned renown as the designer of the Soviet Union's Third Idea, a codename for Soviet development of thermonuclear weapons. Sakharov was an advocate of civil liberties and civil reforms in the...
in 1967.
Sakharov observed that many condensed matter
Condensed Matter
Condensed matter may refer to several things*Condensed matter physics, the study of the physical properties of condensed phases of matter*European Physical Journal B: Condensed Matter and Complex Systems, a scientific journal published by EDP sciences...
systems give rise to emergent phenomena which are identical to general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. For example, crystal defects
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...
can look like curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
and torsion
Torsion
The word torsion may refer to the following:*In geometry:** Torsion of a curve** Torsion tensor in differential geometry** The closely related concepts of Reidemeister torsion and analytic torsion ** Whitehead torsion*In algebra:** Torsion ** Tor functor* In medicine:** Ovarian...
in an Einstein-Cartan spacetime.
This allows one to create a theory of gravity with torsion
from a World Crystal
World Crystal
Theoretical models of the universe are valid only at large distances. The properties of spacetime at ultrashort distances of the order of the Planck length are completely unknown since they have not been explored by any experiment...
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
Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold is a generalization of a Riemannian manifold. It is one of many mathematical objects named after Bernhard Riemann. The key difference between a Riemannian manifold and a pseudo-Riemannian manifold is that on a pseudo-Riemannian manifold 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
Effective action
In quantum field theory, the effective action is a modified expression for the action, which takes into account quantum-mechanical corrections, in the following sense:...
which to one-loop order contains the Einstein-Hilbert action
Einstein-Hilbert action
The Einstein–Hilbert action in general relativity is the action that yields the Einstein's field equations through the principle of least action...
with a cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
. 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
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
s.
Some argue that the particular models proposed by Sakharov and others have been proven impossible by the Weinberg-Witten theorem. But, models with emergent gravity are always possible as long as other things, such as spacetime dimensions, emerge together with gravity. Developments in AdS/CFT correspondence
AdS/CFT correspondence
In physics, the AdS/CFT correspondence , sometimes called the Maldacena duality, is the conjectured equivalence between a string theory and gravity defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more...
after 1997 suggest that the microphysical degrees of freedom in induced gravity might be radically different. The bulk space-time arises as an emergent phenomenon of the quantum degrees of freedom that live in the boundary of the space-time.
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.