Editing Loop quantum gravity (section)

== Background independence ==
LQG is formally [[background independence|background independent]], meaning the equations of LQG are not embedded in, or dependent on, space and time (except for its invariant topology). Instead, they are expected to give rise to space and time at distances which are 10 times the [[Planck length]]. The issue of background independence in LQG still has some unresolved subtleties. For example, some derivations require a fixed choice of the [[topology]], while any consistent quantum theory of gravity should include topology change as a dynamical process.{{Citation needed|date=July 2021}}

Spacetime as a "container" over which physics takes place has no objective physical meaning and instead the gravitational interaction is represented as just one of the fields forming the world. This is known as the relationalist interpretation of spacetime. In LQG this aspect of [[general relativity]] is taken seriously and this symmetry is preserved by requiring that the physical states remain invariant under the generators of [[diffeomorphism]]s. The interpretation of this condition is well understood for purely spatial [[diffeomorphism]]s. However, the understanding of diffeomorphisms involving time (the [[Hamiltonian constraint]]) is more subtle because it is related to [[Relativistic dynamics|dynamics]] and the so-called "[[problem of time]]" in general relativity.{{sfn|Kauffman|Smolin|1997}} A generally accepted calculational framework to account for this constraint has yet to be found.{{sfn|Smolin|2006|pp=196''ff''}}{{sfn|Rovelli|2004|pp=13ff}} A plausible candidate for the quantum Hamiltonian constraint is the operator introduced by Thiemann.{{sfn|Thiemann|1996|pp=257–264}}