Hi all, This is partially motivated by the thread on Ashtekar's new review and by old results on emergent spacetime in condensed matter models. Has any progress been made on the problem of emergent space (not emergent spacetime) in LQG or allied approaches? By this I mean problems that take as given a non-emergent time and are able to demonstrate two phases - one without a well defined spatial metric (non-geometric) and one with a spatial metric (geometric)?
There's some weird stuff like http://arxiv.org/abs/1009.3195 http://arxiv.org/abs/1102.0270 http://arxiv.org/abs/1201.3206 Within LQG, the most interesting analysis is probably Jonathan Engle's http://arxiv.org/abs/1107.0709 http://arxiv.org/abs/1111.2865 http://arxiv.org/abs/1201.2187 Hellmann has summarized the situation in 2+1D. http://arxiv.org/abs/1102.1688
Interesting. I would have thought this problem would be a lot easier if "quantizing" time or seeing time "emerge" was the critical stumbling block. I think this is part of the reason why AdS/CFT works so well while flat/? and dS/? are still in their infancy.