Moshe Rozali opened his and David Berenstein's blog to a discussion of background independence (BI) and emergent character of gravity, especially in the context of the anti de Sitter (AdS) space. As explained in that thread, the following facts are important:
- states in a theory of quantum gravity with different asymptotic conditions than the AdS space are physically disconnected; they're in different superselection sectors
- states within the same superselection sectors allow any physical configurations "in the bulk", i.e. inside the space defined by the boundary, to evolve; all physically conceivable configurations in the "bulk" are included in the gauge theory; the latter is therefore at least as background independent as general relativity
- Riemannian geometry, strings, string fields, and/or branes are just approximate, emergent degrees of freedom in this context; they're no longer fundamental, universally valid, or leading to a known exact description of physics
- gauge theory is the fundamental description of all physical phenomena in the superselection sector and it is defined beyond any perturbative expansion and beyond other limits
- while this gauge theory can be found as a limit of another string theory, it can also be formulated completely independently of string theory, which is the philosophy relevant for the AdS/CFT correspondence
- there is additional, virtually unquestionable evidence that string theory is more background-independent: it inevitably makes topology transitions legal, and leads to the exact equivalences of physical phenomena at geometrically vastly and qualitatively different backgrounds (dualities)
In a theory of gravity, extending general relativity, the spacetime may have many different shapes. The space may get curved or less curved, approximate event horizons may be created for a while, the shape (and topology) of internal dimensions of space may change.
However, there are certain changes that can't really happen because they would take an infinite amount of effort or energy. If your spacetime is infinite, you can't change the spacetime in such a way that the asymptotic character of the spacetime at infinity qualitatively changes.
More concretely, in the flat or AdS space, the metric tensor at infinity approaches the metric tensor of the empty space plus small corrections, encoding the mass (and other moments of the energy distribution). If you imagine that such a space evolves into another space that has completely different asymptotics, it is similar to adding new objects into your spacetime whose energy is infinite. That can't be done in the real world where the energy always stays finite.
We say that the states in the Hilbert space are divided into many superselection sectors: the full Hilbert space is a direct sum. You have a chance to evolve from one state to another state in the superselection sector but you can be absolutely certain that the probability to evolve into a state in another superselection sector is exactly zero because these other states are "infinitely different". That's true both in classical physics as well as quantum physics. And it would be arguably true even in a new non-classical non-quantum framework that you may speculatively propose to replace quantum mechanics.