Quantum Gravity and Calculations of Mercury's Perihelion

Question

In an astronomy forum that I frequent, I have been having a discussion where the state of quantum gravity research came up. I claimed that Loop Quantum Gravity theories couldn't prove GR in the continuum limit, nor could they compute Mercury's perihelion because they didn't have any matter, at this point. Another poster claimed that one of the first things that any gravity scientist checks for the theory is the theory's prediction for the precession of Mercury's perihelion.

Now for cosmological extensions to GR like, MOND, TeVeS or STVG, I can see where this might make sense. But I can't see how this poster's claim holds for quantum-gravity theories that haven't been able to establish that they reproduce GR in the continuum limit and that don't have matter at all.

So I feel like I'm either missing something important about quantum gravity theories, in general, or the poster's comment only applies to cosmological-scale gravity modifications designed as an alternative to dark matter and not quantum gravity theories. Or perhaps a little of each.

How, for instance, would one compute the precession of Mercury's perihelion using CDT, or Rovelli et al.'s spin-foam version of LQG? It may be that the dynamics of any object are implied in the spacetime microstructure, I don't understand the math well enough yet to follow the implications to know if this is true. But how can you compute the orbit of a planet when you require mass and fermions in order to even have the Sun and a planet like Mercury?

I note the very very recent paper of this week, Dec. 21, http://arxiv.org/abs/1012.4719, where the Marseille LQG group run by Carlo Rovelli claims they can now incorporate Fermions, so my question applies to research prior to this event, not that going forward.

I'm not even close to an expert, so I'm looking for enough information that I'll be able to respond intelligently to the other poster. I'll point them to the answer I received here so perhaps this will help the marketing for this excellent resource.

Answer 1

First of all, I think you're correct that Mercury's precession is only useful as a check on classical, large-scale theories of gravity, like MOND, which would actually govern astronomical interactions.

As pointed out in the comments, quantum gravity mainly concerns itself with an entirely different domain, namely Planck-scale distances, times, and densities, since those are the scenarios in which classical GR seems to break down. Accordingly, the typical checks on theories of quantum gravity are things like black hole entropy, and predicting some sort of non-singular behavior for the universe at the Big Bang. Using LQG to calculate a property of a complex real-world system like the solar system is at worst impossible and at best absurdly complicated, if it in fact reduces to classical GR (which I have also heard is yet to be proven).

On the other hand, a theory of quantum gravity could perhaps handle the "interesting" part of the calculation of planetary precession without incorporating mass directly. All it really needs is a connection, which in LQG is provided by the SU(2) gauge field $A^i_a$ defined on the edges of a graph. Given a graph and a connection, one might be able to compute something akin to a geodesic through the graph, which in the continuum limit would correspond to the orbit - though my knowledge of LQG falls short here, I'm not sure whether that's how you would actually get from quantum geometry to an orbit. And anyway, as far as I know, in order to get the connection for a given mass distribution (i.e. the Sun) in the first place, you would have to use classical GR to find the Christoffel symbols.