# Quantum Gravity and Calculations of Mercury's Perihelion

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.

-
This is a GREAT question ! –  user346 Dec 25 '10 at 17:30
I am not sure this is such a good question at all. Even if LQG was a complete theory containing not only gravitation but also matter (which it is not) and even if it reduced to GR in continuum limit (which I am not sure it does) it would still be stupid (really, really stupid) to calculate this effect in it. We don't use particle physics + complete Standard Model to compute free fall of a ball (say). Not because it's technically infeasible. But because Newtonian picture is good enough. Using lower level theory just adds complexity and precision at unimportant place far after decimal point. –  Marek Dec 25 '10 at 19:01
@Marek - the point @inflector is making is an important one. True it might have its weaknesses. But coming from a student/lqg-beginner that is to be expected. The points he makes are worthy of discussion - such as the question of the dynamics of objects in an lqg framework, the reduction of lqg to gr in a suitable limit, the inclusion of matter in lqg. And I have not seen a single lqg question on this site yet. Mercury's perihelion might not be best line of attack. I think lqg effects at a big-bounce/big-bang might be a more relevant topic. –  user346 Dec 25 '10 at 21:36
Also for lqg the equivalent of mercury's precession might be the question of orbits of objects around the black hole at the center of the galaxy - which have only recently become accessible to observation - or some similar strong-field situation. –  user346 Dec 25 '10 at 21:37
@space_cadet: I don't know much about LQG, but supposedly it is a theory of quantum gravity and therefore operates at Planck scale, i.e. some 40 to 50 orders of magnitude below the scale relevant for Mercury's precession. It's quite obvious that this problem can't be attacked directly. And if LQG reduces to GR in continuum limit (which it has to, if it wants to have any chances as a correct theory), then it would give the same results as GR and negligible corrections. That's why I think this question is pointless. I would welcome other questions about LQG though, if they make some sense. –  Marek Dec 25 '10 at 21:48

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.