Editing Quantum gravity (section)

=== Spacetime background dependence ===
{{Main|Background independence}}
A fundamental lesson of general relativity is that there is no fixed spacetime background, as found in [[Newtonian mechanics]] and [[special relativity]]; the spacetime geometry is dynamic. While simple to grasp in principle, this is a complex idea to understand about general relativity, and its consequences are profound and not fully explored, even at the classical level. To a certain extent, general relativity can be seen to be a [[relational theory]],<ref>{{cite book
|last = Smolin
|first = Lee
|author-link= Lee Smolin
|title = Three Roads to Quantum Gravity
|publisher = [[Basic Books]]
|date = 2001
|pages = [https://archive.org/details/threeroadstoquan00smol_0/page/20 20–25]
|isbn = 978-0-465-07835-6|title-link = Three Roads to Quantum Gravity
}} Pages 220–226 are annotated references and guide for further reading.</ref> in which the only physically relevant information is the relationship between different events in spacetime.

On the other hand, quantum mechanics has depended since its inception on a fixed background (non-dynamic) structure. In the case of quantum mechanics, it is time that is given and not dynamic, just as in Newtonian classical mechanics. In relativistic quantum field theory, just as in classical field theory, [[Minkowski spacetime]] is the fixed background of the theory.

==== String theory ====
[[File:Point&string.png|right|thumb|class=skin-invert-image|Interaction in the subatomic world: [[world line]]s of point-like [[Subatomic particle|particles]] in the [[Standard Model]] or a [[world sheet]] swept up by closed [[string (physics)|strings]] in string theory]]
[[String theory]] can be seen as a generalization of quantum field theory where instead of point particles, string-like objects propagate in a fixed spacetime background, although the interactions among closed strings give rise to [[space-time]] in a dynamic way.
Although string theory had its origins in the study of [[quark confinement]] and not of quantum gravity, it was soon discovered that the string spectrum contains the [[graviton]], and that "condensation" of certain vibration modes of strings is equivalent to a modification of the original background. In this sense, string perturbation theory exhibits exactly the features one would expect of a perturbation theory that may exhibit a strong dependence on asymptotics (as seen, for example, in the [[AdS/CFT]] correspondence) which is a weak form of [[Background independence|background dependence]].

==== Background independent theories ====
[[Loop quantum gravity]] is the fruit of an effort to formulate a [[background-independent]] quantum theory.

[[Topological quantum field theory]] provided an example of background-independent quantum theory, but with no local degrees of freedom, and only finitely many degrees of freedom globally. This is inadequate to describe gravity in 3+1 dimensions, which has local degrees of freedom according to general relativity. In 2+1 dimensions, however, gravity is a topological field theory, and it has been successfully quantized in several different ways, including [[spin network]]s.{{Citation needed|date=September 2020}}