Editing Background independence (section)

==Theories of quantum gravity==
Because of the speculative nature of quantum-gravity research, there is much debate as to the correct implementation of background independence. Ultimately, the answer is to be decided by experiment, but until experiments can probe quantum-gravity phenomena, physicists have to settle for debate. Below is a brief summary of the two largest quantum-gravity approaches.

Physicists have studied models of 3D quantum gravity, which is a much simpler problem than 4D quantum gravity (this is because in 3D, quantum gravity has no local degrees of freedom). In these models, there are non-zero transition amplitudes between two different topologies,<ref>{{Cite journal |first1=Hiroshi |last1=Ooguri |year=1992 |title=Partition Functions and Topology-Changing Amplitudes in the 3D Lattice Gravity of Ponzano and Regge |journal=Nuclear Physics B |volume=382 |issue=2 |publication-date=September 1992 |pages=276–304 |doi=10.1016/0550-3213(92)90188-H |arxiv=hep-th/9112072 |s2cid=12824742 }}</ref> or in other words, the topology changes. This and other similar results lead physicists to believe that any consistent quantum theory of gravity should include topology change as a dynamical process.

===String theory===
[[String theory]] is usually formulated with [[perturbation theory]] around a fixed background.  While it is possible that the theory defined this way is locally background-invariant, if so, it is not manifest, and it is not clear what the exact meaning is.  One attempt to formulate string theory in a manifestly background-independent fashion is [[string field theory]], but little progress has been made in understanding it.

Another approach is the conjectured, but yet unproven [[AdS/CFT correspondence|AdS/CFT duality]], which is believed to provide a full, non-perturbative definition of string theory in spacetimes with [[anti-de Sitter space|anti-de Sitter]] asymptotics. If so, this could describe a kind of [[superselection|superselection sector]] of the putative background-independent theory. But it would still be restricted to anti-de Sitter space asymptotics, which disagrees with the current observations of our Universe.  A full non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking.

Topology change is an established process in [[string theory]].

===Loop quantum gravity===
A very different approach to quantum gravity called [[loop quantum gravity]] is fully non-perturbative and manifestly background-independent: geometric quantities, such as area, are predicted without reference to a background metric or asymptotics (e.g. no need for a background metric or [[anti-de Sitter space|anti-de Sitter]] asymptotics), only a given [[topology]].