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. 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. This implies that quantum entanglement is the fundamental property that gives rise to spacetime. In 1995,
Theodore Jacobson showed that the
Einstein field equations 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, 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. ==See also==