marcus
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Finbar said:or do they...?
Nearly all theories of quantum gravity seem to imply that spacetime emerges from an effectively two dimension theory either by starting from two dimensional degrees of freedom, in string theory or LQG, or by predicting that spacetime is two dimensional on small scales e.g. CDT, asymptotic safety or Horava gravity. So two dimensions seems to be an input or an output in all the top theories of quantum gravity. The reason for this is very simple; two dimensions is the dimension in which Newton's constant is dimensionless. The problem for strings and LQG is to get from the two dimensional degrees of freedom to the standard model. In strings one has to compactify the extra dimensions in a clever way whereas LQG faces the problem of recovering classical GR from its highly non-perturbative and non-standard stating point.
CDT and AS are much more conservative and have both already shown that they have classical spacetime as an appropriate limit. The challenge for these theories is to understand the underlying microscopic degrees of freedom that they seem to be uncovering.
This is intriguing and even inspiring---it may contain an important insight. However it seems to me that LQG could be more in the situation of CDT and AS. That is, according to Modesto's work, 2D emerges at small scales. Steve Carlip's review of QG spontaneous dimensional reduction echoed and cited Modesto on this.
http://arxiv.org/abs/0911.0437
Fractal Space-Time from Spin-Foams
Elena Magliaro, Claudio Perini, Leonardo Modesto
(Submitted on 2 Nov 2009)
"In this paper we perform the calculation of the spectral dimension of spacetime in 4d quantum gravity using the Barrett-Crane (BC) spinfoam model. We realize this considering a very simple decomposition of the 4d spacetime already used in the graviton propagator calculation and we introduce a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the spacetime runs from approximately 2 to 4..."
So they found the dimensionality (measured by a diffusion process) to be around 2 at very small scale and 4 at macro scale. This is similar to what Loll et al found for CDT, using the same measure of dimensionality.
Also quite a lot of evidence has accumulated that Loop gets ordinary gravity at large scale, but no rigorous proof---the eyes and tees still need to be dotted and crossed on that. Rovelli's February review discusses the current situation:
http://arxiv.org/abs/1102.3660
E.g. starting on page 18 with section D3: "Large distance expansion", and continuing into sections E1 and E2: "n-point functions" and "cosmology".Opinions can of course differ but offhand I would say the situation with Loop is more comparable with CDT on that score (than you suggest) and less comparable with String.
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