Physics Monkey said:
Should we really think of LQG of a theory of emergent spacetime? I already argued that Verlinde has background dependence in much of his paper. LQG is considerably more background independent that Verlinde's proposal at this point, but even LQG is deeply rooted in the mathematics of manifolds (without a prior metric of course). I'm skeptical of calling a theory that starts from manifolds a theory of emergent spacetime. Perhaps we will understand later that manifolds weren't essential, that it the manifold will fall away as physically irrelevant, but I don't think anyone is in a position to claim that right now in LQG. Or am I wrong?
The theory
starts with a manifold but moves on to dispense with it. It does not assume the physical existence of a continuum.
Nor does it assume the physical existence of loops, spin networks, foams, 4-simplices or tetrahedra.
This is an interesting and fairly high-level question which Rovelli gave the definitive word on last summer in about twelve slides of a May 2009 seminar talk.
http://relativity.phys.lsu.edu/ilqgs/panel050509.pdf
This file begins with a dozen or so slides from Ashtekar, and then a series from Carlo, and finishes with some from Laurent Freidel. It was not prepared for wide distribution but is primarily a discussion among a small group of colleagues about issues of ontology and interpretation which arose two weeks earlier when John Barrett (Nottingham, UK) gave a talk to the same group.
My crude summary: LQG is not talking about what Nature is "made of" but about how Nature responds to measurements.
It uses various formalisms---the simplices of Group Field Theory (GFT), the networks and foams of the canonical and covariant versions of LQG---as alternative ways of imagining and calculating which the researchers have discovered are consistent.
So one is looking for deeper systems of description, a deeper layer of degrees of freedom
from which familiar spacetime emerges. But one does not re-ify these deeper d.o.f.
In LQG the geometry of spacetime is certainly emergent, but in LQG one does not, at least as yet, say
from what it is emergent.
The best is to read the dozen or so slides, because they say more than the one-slide summary at the end. But I will quote the summary slide:
==Rovelli 5 May 2009 seminar slide 12==
Summary
1. “Loopy, polymer, triangulated” spaces are helps for intuition, not descriptions of reality. No incompatibility between them.
2. In quantum gravity, flat space is neither many small Planck scale things not few big large-spin 4 simplices. It is a process with a transition amplitudes. We can represent it with different pictures, according to the measurements we are considering, the calculation scheme, and the approximation scheme.
3. We must compute diff-invariant amplitudes, including when dealing with excitations over a flat space. The only way of doing so that I know is to code the background into the boundary space. (Boundary formalism.)
4. We need an approximation scheme. For scattering amplitudes, we can truncate degrees of freedom to a finite number, very much like is done in computing in QED and QCD. (Vertex expansion.)
5. Regime of validity of the vertex expansion: processes whose size L is not much larger than the minimal relevant wavelength λ. Includes the large distance behavior of the scattering amplitudes in coordinate space.
6. At given ratio λ/L, the Large-spin Limit captures processes at scales larger than the Planck length. It gives the semiclassical limit.
→ This does not mean that flat space is “made out of large 4-simplices”!
→ It means that we describe measurements performed at scales larger that the
Planck scale, at low order.
==endquote==
Some of these points specifically address questions raised in the discussion of John Barrett's talk, two weeks earlier.
(sorry)