Carlo Rovelli has recently put 3 papers on the arXiv, which have attracted some attention within the blogsphere (see here, here, here and here). The one that concerns us here at QQ is the paper about EPR in the relational approach to QM. I don't want to comment on the particular argument in that paper, which seems fine as far as it goes, but I do want to say a couple of things about Rovelli's approach in general, since it seems to be a popular topic at the moment. The main ideas of the approach can be found in Rovelli's original paper.
Here is an (admittedly cartoonish) summary:
1. We should shift attention from things like the measurement problem and instead try to derive QM from the idea that it is a theory of the information about one system that is available relative to other systems.
2. Quantum states are not absolute concepts and the state of a system is only defined relative to some other reference systems. Different reference systems do not have to agree on this state. If they do come to agreement it is only after the reference systems themselves interact with each other according to some Hamiltonian.
3. The question of whether a system has some particular property has no absolute meaning. However, some property of a system can be well-defined relative to some other system, provided the systems happen to have interacted in such a way that the second system records the appropriate information about the first system.
4. All the relational states just represent the subjective point of view that one system has about another. There is no absolute meaning to such states and no meaningful "wave-vector of the universe" can be constructed because there is no external system for it to enter into relations with.
5. This is all just a twist on the usual kind of relationalism that we have in other physical theories, e.g. special and general relativity.
In my opinion, there is a good deal wrong with relational QM as formulated by Rovelli, although I am not particularly opposed to relationalism in general. In this post, I'll make some comments about 4 and 5. A forthcoming "Rovellifest 2" post will point out a problem with 3, which I believe is more serious.
To address 5, it is worth noting a striking disanalogy between relational QM and other sorts of relational theories in physics. For example, in Newtonian mechanics we are very used to the idea that that there is no absolute meaning of the position of a particle A, but you can define its distance to a reference system B. This is generally different from the distance of A relative to another reference system C. Similarly, there is no absolute notion of when two events are simultaneous in special relativity, but this is well defined relative to any inertial reference frame.
However, in these cases it is always possible to find some transformation that relates the descriptions relative to different reference frames, provided you know the relations between the frames themselves, e.g. the Lorentz transformations in special relativity.
Now consider a quantum system composed of a subsystem A and two observers B and C. Suppose both B and C separately interact with A, possibly measuring different observables on A. Relative to B, A is supposed to have some definite property after this interaction and similarly for C. However, you generally can't convert between B and C's description of the situation if you only know the state of B relative to C. You can if they happened to measure the same observable, but that's a very special case.
In fact, the only way to relaibly convert between different observers relative states of the same system is to know the entire "wave-vector of the universe", something that is meaningless for Rovelli due to 4.
So, it seems we are left with two options:
1. Add in a "state of the universe" so that one can reliably transform between different descriptions of the same subsystem.
2. Abandon the classical notion that one can reliably transform between different descriptions of the same system.
Adopting 1 would essentially entail accepting an Everettian/many-worlds type scenario, something that Rovelli is keen to distance himself from. Therefore, I conclude that he must accept 2.
Abandoning reliable transformations is not a completely absurd thing to do, but it is important to note that this is a departure from what we usually mean by the term "relational". I am still not entirely convinced that it is consistent, although I haven't managed to think up a scenario where it would cause a problem yet. My suspicion is that it might be attacked by a "Wigner's Enemy" type of argument of the sort that was levelled against Chris Fuchs' Bayesian approach by Amit Hagar, which seems much more relevant to the relational approach than to its original target.
N.B. "Wigner's Enemy" is a new name I just thought up for the argument. I figure he must be an enemy rather than a friend because friends don't usually try to erase your memory.